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Free Practice Aptitude Tests

Take 16 free practice aptitude tests . Each test comes with answers and fully explained solutions to each question.

What Is the Saville Wave Test?

The Saville Wave test is a personality questionnaire that comes in different versions to suit all sorts of job roles and levels of seniority.

Created by Saville Assessment, the Wave tests are designed to be the ‘best-in-class predictor of workplace performance and potential’.

They blend digital innovation and science to cover aspects of competency, potential, motivation, talent and preferred company culture in one short assessment.

The Wave tests are usually used in recruitment and selection, but they are also used for talent management and succession planning.

There are two main types of Wave tests used in recruitment:

• The Wave Focus Styles
• The Wave Professional Styles

It is becoming increasingly common for employers to ask potential new employees to complete a variety of assessments as part of their recruitment processes.

One example of this is the Thomas International PPA assessment , which is a personality test commonly used by employers who are looking for individuals with specific personality types or strengths in defined areas.

In this article, you’ll learn what the Thomas International PPA Test is, what you can expect if you are asked to take the assessment and how your test will be scored.

We have also included plenty of helpful tips and free Thomas International PPA sample test questions to help you prepare ahead of taking the Thomas PPA assessment.

The NWEA MAP Growth Test is used in thousands of schools across the US to assess children academically.

The test can be given three times in a school year and helps teachers to plan their lessons so that children can reach their potential and continue to grow throughout their time in education.

In this article, you will learn more about the different levels of the test and the way it is structured to suit different grades, what types of questions are on the tests and how best to prepare your child for success.

If your child is under the age of 12 and aims to get into a gifted school program, they will most likely be required to take the NNAT test to assess their skills.

If you know that your child is expected to take the exam, you can help them prepare for it by letting them know what to expect.

This article contains the most relevant information concerning the NNAT test, including its purpose, scoring system and levels.

You will also receive plenty of helpful tips on how to help your child prepare for the exam by completing a Naglieri Nonverbal Ability Test sample and working on their weaknesses in each question type.

The Hogan Business Reasoning Inventory (HBRI) is a scientifically-based aptitude test.

It is designed to assess cognitive ability and a candidate’s preferences for using qualitative and quantitative reasoning skills.

The HBRI is a popular tool for pre-employment screening, particularly in the management, sales and marketing sectors.

If you have been asked to take the HBRI, your test results will offer prospective employers insight into your decision-making skills, problem-solving abilities, approach to processing information and ability to learn from past experiences.

In this article, you can learn what to expect when taking the Hogan Business Reasoning Inventory HBRI test, see examples of the type of Hogan Business Reasoning Inventory questions you might be faced with and guidance on how to prepare for the assessment.

The MAP Kindergarten Test is a computer-adaptive test that measures your child’s progress throughout their academic career.

The grades K through 2 tests assess mathematics and reading abilities.

The results from these tests allow teachers to identify the gaps in your child’s knowledge and to better understand their ability to learn and retain information.

The MAP test is administered three times in the academic year to ensure your child’s progress is properly recorded.

The Ramsay Mechanical Aptitude Test is used as part of the pre-employment screening process for a number of roles in different industries.

It is an excellent indicator of how well you can learn on the job, as well as your ability to use basic physics principles and mechanical knowledge to solve problems.

In this article, you will learn more about which job roles require completion of the Ramsay MAT as part of the application process, and what different types of tests are available.

The format of the assessment, as well as the number of questions and the time limit, will also be discussed. You’ll also learn how the Ramsay MAT is scored and what happens next.

There will be example questions that are similar to those you are likely to find on the assessment, as well as some top tips for success.

The SHL OPQ32 test is the flagship personality test from SHL.

Used by major organizations all over the world, it is considered to be one of the best psychometric assessment tools currently available on the market.

It is a trait-based personality test that is designed to gauge a candidate’s personality attributes and behavioral preferences in the workplace.

A candidate’s test results are analyzed by recruiters, helping them to decide whether a candidate is a good match for the job role they have applied for.

OLSAT stands for Otis-Lennon School Ability Test.

Children take the test to help schools decide admissions into their gifted-and-talented programs.

Preparing your children for taking the OLSAT is a good idea as it could determine their eligibility and acceptance to extra academic programs that are offered by their schools.

If you are looking for a career working with the emergency services, then becoming a 911 call handler and dispatcher might be just the role for you.

If you can handle working under pressure, helping the public and are able to deal with difficult and uncomfortable situations with a calm head, then you might have what it takes to be the first port of call in an emergency.

Becoming a 911 call handler and dispatcher means you will need to have some very specific skills and abilities, and as part of the recruitment process, you will have the opportunity to demonstrate your suitability by taking the CritiCall 911 dispatch test .

Used throughout the US for recruiting people for 911 roles, the CritiCall test does not assess your previous experience or your knowledge of the role.

Instead, it is designed to assess candidates on the inherent aptitudes that are needed to be successful in the role.

This article will discuss what the CritiCall test is assessing, the types of questions that you are likely to face and what the recruiters will be looking for.

There will be some example questions, as well as details about what mark you will need to achieve to pass the test.

Finally, there are some CritiCall test prep tips to help you prepare for the assessment and what to think about on the day.

The McQuaig Word Survey is a type of personality assessment.

Survey responses are used to measure a candidate’s key personality traits and compare these with how they are currently behaving in the workplace.

The results from the survey indicate whether a candidate is behaving naturally in their current role, or whether they are making changes to their behaviour.

This article will help you pass the McQuaig Word Survey assessment test by giving you all the tools and practice questions you will need.

The Caliper test is an assessment used by employers to gain a better understanding of a candidate’s personality traits, cognitive abilities and motivations.

The Caliper test is used to help employers predict a candidate's suitability for a role.

In this article, we'll take a detailed look at what the Caliper test is and how it is scored.

We’ll also share some tips on how you can perform at your best when taking your Caliper assessment test.

More and more employers are choosing to use psychometric testing as a part of their recruitment processes as it helps to highlight those candidates who are most likely to be suited to the roles they are looking to fill.

Employers will often use this form of testing when recruiting for mid-to-high level managerial roles or positions that require a specific set of skills.

Using the results of assessments, recruiters and employers are able to see the strengths and skills of individuals as well as being able to predict future performance.

One of the most popular options for psychometric testing is the Criteria Cognitive Aptitude test – more commonly known as the CCAT.

The Bennett Mechanical Comprehension Test (BMCT) , also referred to as the Bennett Mechanical Aptitude Test, is considered the most popular mechanical aptitude test.

However, it is also believed to be the hardest one to pass.

The BMCT requires you to have a knowledge and understanding of physical principles and answer 55 questions about the application of these concepts within 25 minutes.

You typically need to score in the top 20% of candidates to progress to the next stage of recruitment.

If you have applied for a job, apprenticeship or college course in the UK or Australia, you may have been asked to complete a Basic and Key Skills Builder or BKSB assessment) .

The initial BKSB assessment determines suitable applicants for an apprenticeship or places a student in the correct class level on a college course. The assessment tests you on your maths and English skills to identify areas that need improvement.

This guide will explain the BKSB assessment in detail, provide example questions, and answer your queries about the test content and format.

There are a variety of tests and assessments that can be used by companies for candidates applying for jobs.

One of those is the Thomas GIA Test .

This article will define what the Thomas GIA Test is and who it is for, in addition to looking at what the test involves, how it is scored and tips for the next chance to pass the test.

You will also find Thomas GIA test examples and explanations for each answer.

The IE Global Admissions Test (ieGAT) is an entrance exam for the IE University (IEU) in Spain.

It covers numerical , logical and verbal reasoning .

Not every IE program requires an ieGAT score. However, as the programs that do are highly competitive, those who take the ieGAT Test must prepare themselves to achieve the best score possible.

This article will help you understand:

• What the ieGAT is
• The structure
• ieGAT scoring
• How to register for the ieGAT
• The best ways to prepare

More and more companies are introducing psychometric testing as a part of their recruitment processes.

This means that, if you are considering changing careers or applying for a new role within your existing industry, you may need to take an assessment.

One of the most popular tests for corporate employers is the test by Sova Assessment .

The United States Postal Service (USPS) provides extensive career opportunities and seemingly endless possibilities for professional development.

However, anyone looking to work at the USPS must pass a Virtual Entry Assessment designed to find suitable applicants for the role they are trying to fill.

This article covers the Postal Exam 474 , including its main parts, how to pass it and how to prepare for the Virtual Entry Assessment.

Let's start by looking at what exactly the 474 Virtual Entry Assessment is.

Developed by Drs Joyce and Robert Hogan in the 1980s, the Hogan assessment is a collection of tests designed to assess personality traits, leadership skills and cognitive abilities.

The Hogan assessment is generally used as a pre-employment test for management roles.

This article will guide you through the online Hogan tests , provide a range of sample questions, discuss how the Hogan Assessment results are calculated and recommend ways that you can prepare to take the Hogan assessment yourself.

If you’ve recently applied for a managerial or executive role, you may have been asked to take a Saville Analysis Aptitude Test , also known as the Swift Aptitude test.

The Swift Analysis Aptitude Test was created by Saville Assessment, which is a huge name in the test publishing market.

The CAT4 cognitive ability test is an examination designed to measure a student’s academic progress.

When the CAT4 test is scored, teachers and parents will be given a summary of the academic potential of the student.

Any student taking the test will be asked questions that will measure their non-verbal reasoning abilities, verbal reasoning skills, quantitative reasoning abilities and spatial awareness .

In this article, you’ll learn more about what types of questions are asked to examine these skills.

The Korn Ferry Leadership Potential Assessment (KFALP) is used to test candidates to see if they have the potential to become leaders and managers.

It uses seven different categories, known as Seven Signposts, to assess potential leaders:

• Learning Agility
• Leadership Traits
• Derailment Risks

This article will examine the theory behind the assessment, the different topics that are tested and how the assessment is scored.

There will also be example questions so that you know what to expect when you take the KFALP and some tips to help you score as highly as possible when you take the test.

Pymetrics tests identify specific behavioral characteristics and traits.

This article examines why pymetrics tests are used and what to expect in your assessment.

Tips are included to help you get the best results.

The McQuaig Mental Agility Test (MMAT) is a 15-minute timed test that is designed to assess your ability to think quickly.

In this short test, you will face questions that will allow you to demonstrate your speed of thought and general mental agility, which are useful aptitudes when it comes to many jobs in different industries.

In this article, find out more about the structure of the test, the different types of McQuaig Mental Agility test questions and what to expect on the day. You’ll also get some mental agility practice test questions and top tips to help you be successful in the MMAT.

The Federal Bureau of Investigation (FBI) is responsible for the enforcement of federal law and the protection of national security in the US.

Working for the FBI can be highly stressful. As a special agent for the FBI, the working week is likely to be 50 hours or more.

Special agents must be willing to be based anywhere in the world. They are expected to carry a firearm and work in potentially dangerous situations.

With this in mind, the FBI has a rigorous application and selection process for potential new recruits. It can take more than 20 months to complete the entire process and commence employment with the FBI.

This guide to the USPS postal exam 955 will take you through the different sections of the test, including example questions, provide tips on how you can prepare for the exam and answer several frequently asked questions.

The USPS postal exam 955 is used to screen applicants for mechanic and technician positions , such as electronic technicians or motor vehicle mechanics. It also sometimes referred to as the postal maintenance 955 exam, USPS maintenance mechanic 955 test or the 955 maintenance exam.

It tests applicants’ suitability by assessing personal characteristics, work experience, and electronic and technical knowledge and skills.

The USPS postal exam 955 replaced the previous 931, 932 and 933 exams .

The USPS postal exam 955 is free of charge , but you will need access to the internet and an email address.

If you are looking to work in the United States Postal Service, you will need to pass the USPS Postal Exam 476.

The USPS Postal Exam 476 is an online test that screens for the best candidates. The exam is used to find suitable candidates for a range of positions, including mail processing clerk, data conversion operator and clerk-related positions.

This article will outline what the USPS Postal Exam 476 includes, with particular attention to the separate sections of the examination.

In addition to this, how the exam is scored and how you can best prepare for it will be covered. There will also be a list of frequently asked questions for you to refer to if you have any doubts.

A List of Amazon Assessment Tests Available for Practice in 2024

• Amazon Work Simulation Assessment
• Amazon Maintenance Technician Test
• Amazon Coding Assessment
• Amazon Workstyle Assessment
• Amazon Area Manager Assessment
• Amazon Operations Manager Assessment
• Amazon Online MBA Assessment
• Amazon RME Apprenticeship Skills Battery Test
• Amazon Financial Analyst Assessment
• Amazon ATA Technical Assessment
• Amazon Control Systems Technician Test
• Amazon Warehouse Assessment Test

The Amazon assessment test is an essential way for the corporation to find the best-suited employees.

It is a series of challenges used to evaluate all its candidates during the recruitment process.

Amazon online assessments typically include both numerical and verbal reasoning tests.

These types of tests examine a potential candidate’s logical skills.

Candidates will also have to sit work-style assessments that simulate the working environment at Amazon.

Other Amazon exams include:

• The Amazon coding assessment (also known as the Amazon SDE online assessment)
• The work sample simulation
• An Amazon versant test

These last two, amongst others, will be discussed later in this article.

This Amazon reviewer job article will also discuss how to pass the Amazon assessment tests, some Amazon assessment answers you should know and what you need to do to best prepare yourself.

There is also a comprehensive list of frequently asked questions from those who are interested in taking these Amazon job tests to find employment with the company.

What Is the SHL Verbal Reasoning Test?

The SHL Verbal Reasoning Test is a graduate-level and above pre-employment aptitude test that is used in graduate and management recruitment for many roles across different industries.

The test is usually taken online, and it is designed to evaluate candidates on their ability to understand written information and make informed, reasoned and logical decisions based on that information.

SHL is a well-established test publisher, providing tests for more than 10,000 companies around the world. It offers a range of tests, including psychometric, behavioural and personality assessments that are based in occupational psychology and aptitude science. 

The tests have specific aims – and recruitment teams use SHL tests like the Verbal Reasoning Test to filter through similarly qualified candidates to find the applicants who have what it takes to be successful in a graduate or management level role.

When taking a verbal reasoing test, bear in mind that you might also be asked to take numerical reasoning tests, logical reasoning tests or personality tests along side.

IQ stands for intelligence quotient and is usually thought to represent the reasoning skills of individuals.

The idea of intelligence relates to how quickly people can solve problems or puzzles, use logic to answer questions, or quickly recall information and facts they’ve heard.

The first type of IQ test was created by a French psychologist named Alfred Binet.

The assessment that he made is still used and is known as the Stanford-Binet intelligence test.

Considering cheating on your GMAT (Graduate Management Admission Test) Exam?

Want to know how to do it, if you should do it and what the consequences will be?

Well you came to the right place!

Read on to find out more about cheating on the GMAT exam, but be warned...

... it's certainly not something I advise!

Do you have an upcoming online aptitude test ? 

Are you looking for the best aptitude test prep material to give you the very best chance of getting the highest possible grade? 

If so, this article will help you. 

Aptitude tests are a crucial part of your job search, and you usually only have one chance to showcase your skills. 

Psychometric aptitude tests can measure many different aptitudes and skill sets, in many different formats:

• Numerical reasoning
• Verbal reasoning
• Diagrammatic or inductive reasoning
• Mechanical reasoning
• Personality types
• Situational judgement and work environment tests
• Work style tests

Aptitude tests can be challenging and it is important to be fully prepared before you attend your job interview or assessment centre.

Several free and paid aptitude test preparation websites offer preparation packs to help you score the best you can.

Those dreaming of working for the TSA will most likely need to take a challenging exam called the TSA CBT Test during the hiring process. Here we’ll look at exactly what it involves and how you can make sure you pass it. Read on to find out more.

If you plan to work as an inspector, manager, marshal or security officer in any agency governed by the Transportation Security Administration, you must pass the TSA CBT test as part of your application process.

Read on to learn more about this assessment, including its purpose, what types of questions it has, how challenging it is and how to prepare for it.

You'll also be provided with a few example questions to help you get an idea of what this test looks like.

Let’s get started.

Aptitude tests are administered to understand your inherent abilities to reason and respond to specific tasks.

They are widely used in various forms to screen candidates or evaluate existing employees for a future job role.

The most generic and widely used aptitude tests are curated to measure different facets of your abilities, mainly on the following areas:

• Abstract Reasoning
• Numerical Reasoning
• Logical Reasoning
• Verbal Reasoning
• Attention to Detail

Apart from these base types, there are various other specialized aptitude tests which you may face in specific industries or based on your role in different career stages.

We have discussed each of the most common job related aptitude tests in detail.

Illustrative examples and helpful hints are provided throughout to aid your preparation.

Read on to find out more.

The Cognify test is a game-based cognitive assessment designed to measure an individual's cognitive aptitude to measure key job performance linked abilities and skills in a prospective candidate.

The Cognify test was once a product of Revelian, an Australian assessment company, but was later acquired by CriteriaCorp.

Moving away completely from the question-answer based template of traditional tests, Cognify uses an innovative approach where candidates don't face a series of questions on a screen.

Instead, the Cognify Assessment comprises 6-7 timed game-based mini-tests categorized into three cognitive abilities categories:

• Problem-Solving
• Verbal Knowledge

Well, before you start raising your eyebrows at the mention of ‘game-based’ and dismiss it as just another fad, pay attention!

Cognify assessment is credited as having brought a paradigm shift in the field of psychometric testing.

Many Tier-I graduate recruiters globally have started using this assessment in their candidate selection process.

The train driver test is used to establish whether a candidate is suitable for work as a train driver. This unique suite of tests includes psychometric assessment tools such as:

• The Group Bourdon Test (GBT)
• Test of Everyday Attention (TEA-OCC)
• Adaptive Tachistoscopic Traffic Perception Test (ATAVT)
• Situational judgement tests
• Vigilance tests
• Written communication tests

What Is the Train Driver Test?

In most countries, you will need to sit the train driver online test if you want to work as a train driver. If you have been asked to sit the assessments, there is no train driver psychometric test cost associated with the train driver exam.

Working as a train driver is a challenging and demanding role. As a train driver, you must be able to ensure the safety of passengers at all times.

The UK’s train driving tests are some of the most challenging. As well as testing aptitude for the job role, they are used to assess whether candidates have the mental abilities to cope with the stress and demands of the job role.

The train driver test is used to establish whether a candidate is suitable for work as a train driver. The train driver test is a unique group of psychometric tests for train drivers designed to assess the psychomotor and cognitive skills needed to work safely as a train driver.

The Predictive Index (PI) test is a popular type of pre-employment testing used to accurately measure an individual’s cognitive ability and behavioral profile during the hiring process in a wide range of industries and organizations. They are most commonly used during the early stages of the recruitment process. 

The PI cognitive test assesses verbal, numerical and analytical reasoning ability. 

The PI behavioral test creates a behavioral persona that describes character traits and tendencies.

A mechanical aptitude reasoning test is an important way to assess your knowledge on mechanical topics for potential roles in the army, emergency services and many other professions. Here, you will get all the information you need on what a mechanical comprehension test is and how to pass it.

Those applying for jobs related to the army, the emergency services engineering service, and similar occupations that require mechanical aptitude, are likely to be asked to take a mechanical reasoning test as part of the recruitment process.

Mechanical aptitude tests assess knowledge in electricity, optics, pressure and other fields of mechanics related to a specific industry.

From this article, you'll learn what mechanical reasoning tests look like, when to take them, what to expect from these assessment types, and how to practise and prepare for them.

Let’s get started!

If you would like to take a free practice Cognitive Ability Test before reading this article, click here .

If you would like to purchase an online Cognitive Ability Test prep pack, visit our partner website JobTestPrep .

The following tests are common cognitive ability tests:

• Spatial Reasoning
• Mechanical Reasoning
• Logical Ability Tests
• Space Visualization
• Information Processing
• Visual Pursuit
• Manual Speed and Accuracy

Have you been asked to take a Deductive Reasoning test as part of an upcoming interview process?

Continue reading to find out more about this type of test, including:

• Why employers use Deductive Reasoning Tests.
• How you can improve your performance at Deductive Tests.
• What types of questions you will be asked during the Test.

What Is A Deductive Reasoning Test?

Logical thinking or deductive reasoning tests are used by employers to measure an applicant’s ability to make logical arguments and form sound conclusions.

During this type of test, you will be presented with a variety of scenarios, statements and arguments for which you will need to apply a given set of rules to determine the validity of the corresponding conclusion.

Spacial Reasoning Definition

A spatial awareness test is a type of assessment that tests your ability to think in three dimensions and use your imagination to see movement through space.

Someone with good spatial awareness will be able to see in their mind how different shapes interact and be able to manipulate them to make a reasoned and logical decision.

The test is based on pictures, diagrams and shapes. You will need to mentally manipulate the presented image by disassembling or reassembling, rotating, seeing it in a mirror image or from different angles, or otherwise visualizing it differently to find the right answer to the question from the multiple-choice options provided.

Spatial awareness is something that we use to a greater or lesser degree every day, from understanding our position relative to other things around us to imagining the route we will take to get from one place to another.

Spatial reasoning tests are distinct from other similar assessments such as diagrammatic reasoning tests and abstract reasoning tests. It is important to understand how they differ as they are often included in aptitude tests and cognitive assessments alongside spatial reasoning tests.

Psychometric tests are often used by organizations as part of the recruitment process. Different types of psychometric tests are designed to measure various aspects of cognitive ability, reasoning capabilities and personality traits. Potential employers use the results to assess a candidate’s suitability for a role. A psychometric test is generally administered online; this helps hiring managers filter applicants quickly and easily. 

As Capp Assessment Tests become more common perhaps you have encountered one for the first time.

This can be a bit daunting and, since they look and feel a bit different to more traditional psychometric reasoning tests, it isn’t necessarily obvious what you need to do to be successful…

Don’t worry.

With the insight and tips we share with you below, you’ll be smashing your tests in no time.

FREE BONUS: Get free unlimited access to Capp test practice (for 30 minutes) on our partner website JobTestPrep.

What are Capp Assessment Tests?

Capp are a consultancy and psychometric test publisher who specialise in Strengths Based Assessments.

They also offer a number of different psychometric tests that are widely used many major organisations including Google, Atkins, Amazon and RBS.

Their Assessment Tests include critical reasoning, numerical reasoning, verbal reasoning .

Psychometric reasoning tests like these are very common.

This is because they are a cheap and efficient way for organisations to identify candidates who aren’t likely to be able to succeed in a particular job.

Because they are often used to filter candidates out of application processes, they are sometimes called screening tests or gateway tests.

Candidates like you have to achieve a particular level of performance in order to progress in the selection process.

With practice you can dramatically improve your performance. Practice is the best way to improve your test scores.

In the rest of this article we’ll show you how the tests work, suggest how you can prepare, and then direct you towards some practice tests so that when the big day comes you are ready.

Before you do anything else, take a look at the Capp website , where you can take free practice tests.

How do Psychometric Reasoning Tests Work?

In general, psychometric reasoning tests challenge users to answer a series of questions and compare their performance on a test with the average performance level of a reference or ‘norm’ group.

This is typically made up of individual with similar characteristics, such as education level, nationality or workplace seniority.

If you do better than most of the norm group you will receive a high score, whereas a low score suggests that your performance was weaker than most of the norm group.

Usually, a minimum standard of performance necessary for success in a role is identified at the start of an assessment process, and all candidates that don’t meet this level will be unable to progress through the process.

What makes Capp Assessment Tests Different?

Capp Assessments are ‘Next Generation’ psychometric aptitude tests ; this means they might look and feel a bit different to other psychometric tests you have completed in the past.

The main difference between the Capp tests and more traditional psychometric ability tests is that the Capp tests are responsive.

This means that the actual questions presented to a candidate will depend upon their performance on the previous questions.

Capp say that the responsiveness of their tests and the size of their question bank mean that the chances of two candidates taking exactly the same test is currently less than one in a billion .

In practice, this means that if you’ve been able to quickly and accurately solve the previous questions, you can expect to be presented with incrementally more challenging questions.

By contrast, if you have made a number of errors, the test will present questions at a lower level.

The aim of the tests is to work out what your maximum ability is. Or put another way, what the most challenging level you are capable of working at is.

Another thing that makes Capp Tests feel different is that they have no time limit (although the time you take to complete the test does effect the score so you still need to work as quickly as you can).

This takes a bit of the pressure off and can make taking these tests rather less stressful than others.

Finally, the variety of question types and the format of the questions in Capp Tests can be different to those used by more traditional test publishers.

Let’s take a closer look at this:

• Numerical Reasoning Tests

Traditionally numerical reasoning tests require candidates to select the correct answer from a number of potential options.

The Capp numerical reasoning test still does this, but it also requires candidates to rank potential answers or to type their answer into a free-text box.

This makes it harder to guess the correct answers.

• Verbal Reasoning Tests

Verbal reasoning tests typically give you a passage of text to read and then ask you whether a number of subsequent statements are true or false, based on the information contained in the passage.

This question type is included within the Capp Verbal Reasoning Test, but there are also a number of different question formats included.

This means that as well as testing verbal reasoning, the Capp test can also assess verbal dexterity, comprehension, interpretation, and adaptability.

As well as traditional multiple choice questions, the test also presents:

• Free text editing : This type of question requires you to type your answers directly into the question. You might be asked to correct spellings or grammar, or edit a passage of text.
• Bucket sort : You will be presented with two categories/styles of writing; your task is to place each item presented to the category/style of writing that it best fits.
• Drag and Drop : This type of question requires you to drag statements or words to the place that they best fit.
• Ranking : These questions can be quite subtle and require you to really understand the nuance of language and language use. You will be presented with a number of statements and asked to rank these based on some feature of the text, such as positivity.
• Selecting the most appropriate word to fill in the sentence : You will be presented with a passage of text with a number of blanks in it, for each blank space you must select the most appropriate word to fill the space from a drop down menu.

Critical Reasoning Tests

The Capp Critical Reasoning test evaluates your ability to think critically in a number of ways.

In each instance, a passage of information is presented followed by a series of statements, your task is to select the appropriate response from the drop down menu.

Questions focus around five areas:

• Inference: rating the probability of truth of inferences based on given information
• Recognition of assumptions: identifying unstated assumptions underlying given statements
• Deduction: determining whether conclusions follow logically from given information
• Interpretation: weighing evidence and deciding if generalisations or conclusions based on data are warranted
• Evaluation of arguments: evaluating the strength and relevance of arguments with respect to a particular question or issue.

Are you considering cheating on your upcoming SHL tests ?

In this full disclosure article, I’ll tell you why people cheat on tests, how people cheat, and whether or not it’s worth doing..

Don't cheat!

Practice... it's the only legitimate way to improve your scores, you'll sleep better at night and probably get better results in your tests too.

Still want to read about how to cheat on a test?

Numerical Reasoning Tests can be very tricky.

And when it comes to results, preparation and practice are key.

But that's easier said than done.

If you're researching this type of aptitude test for the first time or if you want to improve your numerical ability , perform better on tests and get more job offers this article will provide some practical strategies that you can use immediately .

For the best chance of success, read the article below slowly, work through the example questions , follow our tips and actionable advice and then start taking practice tests .

Ready to get started?

Let's go!...

Want to try a practice test before reading this article?

You can take our free numerical test right here:

Logical reasoning tests are a little different to your average psychometric test .

With this type of assessment, there are many different variations so it is sometimes difficult to determine which aspect of logical reasoning you will be assessed on.

With this guide, you’ll learn the difference between inductive and deductive reasoning tests , and some tips for maximising performance.

Designed to evaluate how you interpret patterns, shapes, numbers and other data to reach logical conclusions, the assessments are used across a number of different sectors at all levels of recruitment from entry right up to managerial positions.

The in tray exercise (also called an e-tray exercise ) is a popular assessment activity which employers use to evaluate the skills of applicants in a workplace situation.

If you have an In Tray exercise coming up as part of your interview process, this article will help you prepare.

Within these exercises, candidates will be presented with a given scenario, along with a set of tasks to complete which may include things like responding to email messages, reports or briefing documents.

Aptitude tests are short tests employers use to assess whether a candidate has the level of competency necessary for success in the role.

The tests are used to see if a candidate has the skills necessary to do the job.

Aptitude tests are standardized, for the most part, and the results of all the candidates are compared to each other to see which candidate may be the best for the job.

Aptitude tests provide employers with a quick way to assess a candidate’s ability to perform in high-pressure situations and think in critical ways as they would if they were on the job.

What Is a Situational Judgment Test?

A situational judgement test (SJT) is a psychometric test that is often used as part of the recruitment process for graduate and managerial positions as well as roles that are customer-facing in a wide range of industries.

The SJT is designed to assess how a candidate deals with work-related problems and situations, focusing on essential aptitudes , competencies and soft skills that are not always easy to evaluate in other ways.

Although SJTs are usually bespoke to the company (or in some cases, the specific role), they tend to follow the same basic structure.

Each question is formed by presenting a fictional yet realistic work-based scenario. This might be text-based, it may include some illustrations or it could be animated or acted out in a video.

Following the scenario, there will be several options that you can choose from, each giving a possible course of action to follow to solve the issue that is presented in the situation given.

The answer that you choose will be compared to the benchmark answers that the recruitment team is using – these represent the core competencies for the role, as well as alignment with company values.

SHL assessment tests are important steps in many job interviews and career advancement opportunities. Therefore, it is essential to have a comprehensive understanding of how the different types of SHL tests work and how you can prepare for them in order to get top scores.

In this article, we will provide an overview of how SHL assessments work, sample SHL test questions, tips on improving your test performance, and strategies for prepping and succeeding with any SHL test.

What Is an SHL Assessment Test?

SHL is a global assessment company that is well known and recognised as a leader in pre-employment psychometric tests; the tests that SHL publishes are used by 75% of the FTSE 100 and they are available in more than 40 languages.

So if you are applying for a new role (especially for a graduate position), you are likely to come across them in the recruitment process.

In addition, the company offers consultancy and management services via its TalentCentral platform.

The SHL assessment are a series of tests that can be delivered individually or in a battery, and some of them are bespoke to the company that is using them, making them an excellent way for the recruitment team to ensure that the applicants for a role have the basic competencies, personality traits, work behaviours and cognitive abilities to be successful.

Sind Sie auf der Suche nach kostenlosen psychometrischen Tests zur Übung?

Dann ist diese Seite genau das Richtige für Sie.

Was ist ein psychometrischer Test?

Psychometrische Tests (auch Eignungstests genannt) sind fester Bestandteil von Jobinterviews vieler Unternehmen auf der ganzen Welt.

Diese Tests bestehen normalerweise aus einer Reihe von zeitlich erfassten Fragen , die meist numerischen (mathematischen Fragen), verbalen (Fragen zum Leseverständnis) oder logischen (diagrammatischen Fragen) Ursprungs sind.

Testes psicométricos (também conhecidos como testes de aptidão) são uma parte comum do processo de entrevistas de emprego em muitas companhias no mundo todo.

Geralmente, esses testes consistem de uma série de questões com um certo tempo de resposta.

As questões costumam ser numéricas (questões matemáticas), verbais (compreensão textual) ou lógicas (questões de diagrama).

Testes SHL . Se você está lendo isso, há uma boa chance de você ter acabado de descobrir que fará um desses testes difíceis como parte de um processo de recrutamento em andamento.

Se você chegou tão longe e agora está se sentindo tenso para se sentar na frente de um ‘abstract quiz’, não se preocupe...

Nós cuidaremos de você.

El Razonamiento Inductivo está basado en patrones y es otra variante de las muchas pruebas psicométricas utilizadas por los empleadores como una forma de determinar la idoneidad de un candidato para sus roles.

En un nivel similar al del razonamiento esquemático , el razonamiento inductivo probará tu habilidad para aplicar la lógica y la razón para la resolución de problemas.

Cómo funcionan las pruebas inductivas

Dentro de la prueba se te presentará una serie de diagramas los cuales se vincularán mediante una regla subyacente.

Esta regla afectará el diseño del diagrama y tu tarea será identificar el patrón.

Bonificación: puedes obtener acceso ilimitado y gratuito a la práctica de prueba (durante 30 minutos) en nuestro sitio web asociado JobTestPrep: Clic aquí .

Por lo general, se espera que los candidatos seleccionen entre 4 y 6 posibles respuestas completas bajo condiciones de tiempo.

Las pruebas de razonamiento inductivo a menudo complementan otras pruebas como las de razonamiento verbal o numérico.

A veces las empresas requieren que complete una prueba de juicio situacional o un cuestionario de personalidad junto con la evaluación de razonamiento inductivo.

Los resultados de cada prueba se revisarán individualmente y luego colectivamente para determinar si tú serías una buena opción para la empresa.

¿Por qué los empleadores utilizan estas pruebas?

Algunas veces se las denomina prueba de razonamiento abstracto, las evaluaciones de razonamiento inductivo están diseñadas para evaluar tus habilidades en la resolución de problemas y el razonamiento lógico.

Cuando completes la prueba, los reclutadores buscarán tu capacidad para trabajar de manera efectiva con información desconocida para alcanzar una solución viable.

Las pruebas se utilizan a menudo para evaluar tu capacidad de pensar creativamente, aplicar habilidades analíticas y diseñar soluciones innovadoras, mientras que a menudo son un indicador de tu nivel general de inteligencia.

Como tal, es esencial que realices el trabajo preparatorio necesario antes de la prueba real para asegurarte de poder completarla exitosamente y crear una buena impresión.

La prueba de razonamiento inductivo es frecuentemente usada por empleadores corporativos; es común esperar que se complete al menos una prueba psicométrica como parte del proceso de reclutamiento.

Los empleadores utilizarán estas pruebas para ver la eficacia con la que trabajas bajo presión y tu enfoque de la evaluación.

Las pruebas de razonamiento inductivo son usadas predominantemente en los roles técnicos o aquellos que requieren una resolución frecuente de problemas y los empleadores las utilizan para evaluar cómo identificas patrones, con qué eficacia puedes identificar reglas y consistencias de datos y si puedes predecir la secuencia de objetos a medida que evolucionan.

En términos de evaluación psicométrica, el razonamiento inductivo, el razonamiento abstracto y el razonamiento esquemático son tres pruebas que a menudo se superponen con la evaluación. Los proveedores utilizan nombres diferentes para cada uno, lo que hace que las cosas sean un poco más confusas.

Estas pruebas ciertamente varían entre los empleadores y la etapa en el proceso de reclutamiento también será diferente.

Algunas empresas los utilizan como un ejercicio de selección previa a la entrevista para limitar un conjunto de candidatos, mientras que otras organizaciones pueden usarlos hacia el final del proceso de reclutamiento o como parte de los días de evaluación.

Contenido de la prueba de Razonamiento Inductivo

La mayoría de las pruebas de razonamiento inductivo presentan una serie de secuencia de palabras, ilustraciones o formas y te piden que decidas cuál es la siguiente.

Esto requiere prestar atención a los detalles, a la resolución de problemas y perseverancia para alcanzar la respuesta requerida, todo lo cual se evalúa en condiciones de tiempo, lo que agrega aún más presión.

La prueba en sí misma requerirá que compares varios elementos incluyendo colores y formas, o que los clasifiques basándote en cantidad o tamaño.

Como un ejemplo, se te proporcionará un juego de seis cuadros conteniendo una cantidad de formas y luego se te pedirá que elabores una secuencia lógica para cada cuadro.

Para obtener la respuesta correcta, deberías identificar un patrón tal como similitudes, diferencias o una combinación de ambos.

Estas tareas pueden parecer extremadamente complejas, por ello es importante realizar tantas prácticas de pruebas similares como sea posible antes de la prueba real y también tanta práctica como puedas antes de la entrevista o del día de evaluación.

Asegúrate de llegar a tiempo y haber dormido bien la noche anterior, de lo contrario, es posible que te falte la concentración y que parezca que no entiendes lo que te piden que hagas.

Una aproximación a las Pruebas de Razonamiento Inductivo

Cuando comienzas la prueba, lee la pregunta detenidamente y trata de observar solamente a un elemento de la forma a la vez.

Es muy fácil sentirse abrumado por el contenido de una evaluación de razonamiento inductivo, por lo que la mejor manera de abordarla es intentar y decidir el patrón, considerando específicamente el tamaño, la orientación y la ubicación de la forma interior.

Los patrones están diseñados para ser complicados en tomarte el tiempo y utilizar tu lógica para resolver el problema.

Si estás teniendo una particular dificultad en identificar un patrón, trata de observarlo desde el final en lugar del principio.

Esto puede resaltar de manera efectiva algo que quizás hayas omitido usando el método tradicional de revisar las formas.

Toma conciencia de la hora pero no mires el reloj, y no te asustes en la medida de lo posible; esto sólo hará las cosas más difíciles.

Las pruebas de razonamiento inductivo son creadas para ser completadas bajo presión, por lo que la práctica de completar las pruebas en condiciones de tiempo puede ayudar de manera significativa.

Practicar es una de las mejores maneras de prepararte mentalmente para cualquier prueba psicométrica y el razonamiento inductivo no es diferente a ello.

Nada te preparará mejor para la evaluación que realizar una cantidad de exámenes de práctica, muchos de las cuales puedes encontrar en línea gratuitamente.

Cuando te familiarizas con el formato de la prueba y te acostumbras a responder preguntas rápidamente y trabajar bajo presión, es mucho más probable que tengas éxito que si no realizas ningún trabajo de preparación o práctica anteriormente.

¿Qué son las pruebas psicométricas?

Las pruebas psicométricas (también conocidas como Pruebas de Aptitud ) son ahora una parte común de los procesos de selección y evanotluación, por lo tanto un requisito necesario para solicitar trabajo.

Si tú aún no has completado una, es muy probable que lo necesites en algún momento en el futuro. Con esto en mente, hemos preparado para ti la Guía actual para las pruebas psicométricas para explicar qué son, cómo se utilizan y cómo completarlas con éxito.

Antes de comenzar con el artículo a continuación, ten en cuenta que tenemos tres pruebas psicométricas de práctica disponibles para que las pruebes.

Las pruebas de razonamiento verbal están diseñadas para examinar tu nivel de comprensión del pasaje de un texto.

Estas pruebas son un ejemplo de una prueba de habilidad (a veces conocida como pruebas de aptitud) y son utilizadas por los empleadores en combinación con pruebas de razonamiento numérico y pruebas de razonamiento lógico .

Las pruebas de razonamiento verbal tienen como objetivo identificar tu capacidad máxima de comprensión, o en otras palabras, el párrafo de un texto más desafiante que tú podrás entender.

Numerische Tests können knifflig sein. Übung und die richtige Vorbereitung sind der Schlüssel zum Erfolg.

Aber das ist leichter gesagt als getan…

Wenn Du zum ersten Mal über diese Tests nachliest oder wenn Du nach Wegen suchst um deine Fähigkeiten zu verbessern, besser abzuschneiden und mehr Interviews und Jobangebote zu bekommen, ist dieser Artikel ideal für Dich.

Hier erfährst Du von Strategien die Du sofort praktisch einsetzen kannst.

Falls du einen Übungstest machen möchtest kannst du hier jederzeit einen der kostenlosen numerischen Tests ausprobieren. Dieser Test beinhaltet zehn Fragen (mit Antworten und ausführlichen Erklärungen).

Wie kann man sein Ergebnis so schnell und effektiv wie möglich verbessern , selbst bis in der 99% Bereich ?

Lies den Artikel am besten langsam durch, folge unseren Tipps und unseren Empfehlungen – so hast du die größten Erfolgschancen. Wenn du damit fertig bist kannst du einen unserer Übungstests kostenlos ausprobieren.

Bonus: Kostenloser uneingeschränkter Zugang zum Eignungs-Übungstest (für 30 Minuten) auf unserer Partner-Webseite JobTestPrep.

Microsoft is one of the world's most commonly used computer software.

If you're working in an office, you are almost certain to use applications such as Microsoft Word, Excel, Outlook or PowerPoint.

Therefore, it makes perfect sense that employers want to know that you are proficient in these applications as part of their hiring process.

If your job requires data analysis or compiling data streams, you will likely need to be adept at using Microsoft Excel.

In these circumstances, you may be asked to participate in an Excel assessment test so a hiring manager can confirm that you know how to make the most out of the program.

With this in mind, we will look at what you could expect from a Microsoft Excel test.

Then, we'll take you through a series of Microsoft Excel practice test questions, and we'll give you everything you need to know so you can prepare for the Excel assessment.

What Is a Cubiks Test?

The Cubiks tests were developed by the Cubiks assessment consultancy, which was founded in 2000.

In 2019, Cubiks was acquired by PSI Talent Management UK, an award-winning provider of psychometric assessments.

In 2022, PSI Services became Talogy.

Cubiks tests are available in more than 50 countries around the world. Many highly-regarded employers in the UK use Cubiks tests, including:

• The UK Civil Service
• National Audit Office
• National Health Service

Cubiks tests are designed to help employers and organisations with recruitment, employee development and talent management. They are well known for their intuitive interface and easy-to-interpret structure.

When applying for job roles, you may be asked to complete one or more types of Cubiks test as part of the screening and selection process.

If you are already working, your employer might ask you to sit a Cubiks test assessment as part of the career development programme or talent management process.

This article offers an overview of what to expect from the Cubiks test. It also includes some Cubiks online test example questions and tips on how to succeed when taking the Cubiks test.

The Korn Ferry assessment is a tool used in the recruiting process for leadership positions.

The tests assess candidates across a range of skills, including:

• Logic reasoning ability
• Numerical reasoning ability
• Verbal reasoning ability
• Personality traits

As a result, the Korn Ferry assessment allows businesses to secure the best talent and identify individuals to be promoted to management positions.

The Korn Ferry assessment is an evaluation tool used by companies across the globe to ensure they employ the best talent.

The assessment comprises a series of smaller tests focusing on:

• Reading comprehension
• Personality
• Leadership assessments

As well as a tool utilized during the interview process, the Korn Ferry assessments are often used when looking to promote team members into management positions.

This article will discuss the Korn Ferry assessment, explaining exactly what it involves and giving tips to enable the best chance of success.

If you are applying for an executive-level or management role, you might be expected to take an aptitude test as part of the recruitment process.

The Swift Executive Aptitude Test is a short assessment designed to measure specific aptitudes that are necessary for success in a leadership position.

In this article, you will discover more about the test, the structure of the assessment, and example questions.

You will also learn what you will need to bear in mind to be successful in the test, including tips about preparation and a breakdown of what to expect from the scoring.

This numerical reasoning practice test has 10 questions.

The test has a mixture of numerical questions that vary in difficulty. 

Answers and full explanations are provided after you have completed a question.  You should aim to complete the test within 10 minutes.

Make sure you read and fully understand each question before answering. Work quickly, but don't rush. You cannot afford to make mistakes on a real test.

What is a Verbal Reasoning Test?

A Verbal Reasoning Test is a type of cognitive assessment designed to evaluate an individual's ability to comprehend and analyze written information, make logical deductions and draw conclusions based on the presented text.

These tests are often used in various educational and employment settings to assess a person's verbal reasoning skills, which are essential for tasks that involve understanding and interpreting written or spoken language.

This inductive reasoning practice test has nine questions (and includes answers and full explanations).

This abstract reasoning practice test has 10 questions (and answers with full explanations).

For each question, choose which of the figures in the bottom line – A, B, C, D or E – completes the series in the top line.

The level of difficulty varies significantly, from easy to extremely hard. Items having the solution based on one rule are easy, while those with the solution based on four rules are extremely hard; the others are in between - medium and hard, respectively.

Your goal is to understand the logic of each question (the rules behind it). Do not despair if you can’t find the solution immediately, especially for the very hard questions!

What is a Cognitive Test?

A cognitive test is an assessment tool designed to measure an individual's cognitive abilities, which are the mental processes involved in acquiring, processing, storing and using information.

Cognitive assessments are used to evaluate various aspects of cognitive functioning, including memory, attention, problem-solving, reasoning, language comprehension, and more.

Cognitive function tests are commonly employed in several contexts, including education, clinical psychology, neuropsychology and employment assessment.

This cognitive ability practice test has been designed to help you prepare for the real thing.  

What Is a Deductive Reasoning Test?

A deductive reasoning test is a type of cognitive assessment that measures a person's ability to draw logical conclusions based on given information or premises.

Deductive reasoning is a form of logical thinking that involves moving from general statements or principles to specific conclusions. In other words, it is the process of applying a general rule or premise to a specific situation to determine a particular outcome.

In a deductive reasoning test, you are typically presented with a set of premises or statements that establish certain conditions or facts. You are then asked to use these premises to determine a valid conclusion.

The conclusions you reach must follow logically from the given premises, and the test assesses your ability to make accurate deductions based on the provided information.

Deductive reasoning tests are often used in educational settings, as part of standardized testing, and in various employment assessments.

They are designed to evaluate an individual's problem-solving skills, critical thinking ability, and their capacity to analyze information and reach logical conclusions.

These tests can take various formats, including multiple-choice questions, true or false questions or scenario-based questions where you need to determine the correct outcome based on the information provided.

Success in deductive reasoning tests often requires a strong understanding of logical principles and the ability to apply them effectively to specific situations.

What is Logical Reasoning?

Logical reasoning, often referred to as logical thinking or critical thinking, is a cognitive process that involves the ability to analyze information, identify patterns, make sound judgments and draw valid conclusions.

It is a fundamental skill that plays a crucial role in problem-solving, decision-making and rational thinking.

Logical reasoning involves breaking down complex information or situations into smaller, more manageable parts. It requires examining details and understanding the relationships between various elements.

What are the Types of Logical Reasoning Tests?

Logical reasoning tests come in various forms and are used by employers, educational institutions, and standardized testing organizations to assess an individual's ability to think critically and solve problems.

Here are some common types of logical reasoning tests:

Reading Comprehension: These tests assess your ability to understand and analyze written information, make inferences, and draw conclusions from passages of text.

Critical Thinking Tests: These tests evaluate your ability to analyze and evaluate arguments, identify assumptions, and assess the validity of statements or claims.

Analogical Reasoning Tests: Analogical reasoning involves recognizing relationships between words or concepts and applying these relationships to solve problems. For example, you might be asked to complete an analogy like "A is to B as C is to what?"

Numerical Computation: These tests assess your basic arithmetic skills, including addition, subtraction, multiplication, and division.

Numerical Sequences: These tests require you to identify patterns and relationships within number sequences and use them to predict the next number.

Data Interpretation: In these tests, you are presented with data in the form of tables, graphs, or charts, and you must interpret the information to answer questions.

• Abstract Reasoning Tests

Non-Verbal Reasoning: Abstract reasoning tests evaluate your ability to recognize patterns, shapes, and relationships among visual elements. They often involve series of diagrams or figures, and you must identify the logical rules governing them.

Inductive Reasoning: Inductive reasoning tests present you with a series of visual or abstract patterns and require you to identify the underlying rules and predict the next pattern in the sequence.

• Spatial Reasoning Tests

Spatial Awareness: These tests measure your ability to visualize and manipulate objects in three-dimensional space. You may be asked to complete puzzles, identify rotated or mirrored images, or solve spatial problems. Diagrammatic Reasoning Tests:

Diagram Interpretation: Diagrammatic reasoning tests use diagrams or symbols to present problems. You must analyze the diagrams to draw conclusions or identify patterns.

Syllogism and Logic Tests

Syllogisms: Syllogism tests present logical statements and ask you to determine whether a conclusion is valid based on the given premises.

Symbolic Logic: These tests involve working with formal logic symbols to evaluate logical arguments.

Inference and Deduction Tests

Inference Tests: Inference tests assess your ability to make logical deductions and draw conclusions based on a set of statements or information.

Deductive Reasoning: Deductive reasoning tests require you to apply deductive logic principles to solve problems and make decisions.

• Mechanical Reasoning Tests

Mechanical Understanding: These tests evaluate your knowledge of mechanical and physical concepts, such as gears, pulleys, levers, and basic physics principles.

• Cognitive Ability Tests

Cognitive Ability Tests: These assessments often include a combination of various reasoning types and are designed to measure overall cognitive abilities.

What are the Common Logic Tests Employers Use?

Employers often use a variety of logic tests to assess the cognitive abilities and problem-solving skills of job applicants. The specific logic tests used can vary depending on the nature of the job and the industry.

Here are some common logic tests that employers may use during the hiring process:

• Logical Deduction and Syllogism Tests
• Data Interpretation Tests
• Diagrammatic Reasoning Tests

This is a 10 question practice logical reasoning test . 

After you have given an answer to a question, the correct answer (and a full explanation of that answer) will be given.

What are the Topics Covered by a Logical Reasoning Test?

Syllogism, statements and assumptions, logical deduction, cause and effect, statements and conclusions, logical problems.

Set of 10 questions, along with correct answers and explanations for each.

Topics Covered:

General concepts, levers, springs, pulleys, area and volume, gears, inclined plane, basic electrical circuitry.

Difficulty Level:

Take a free practice mechanical reasoning test.

Situational awareness, evaluation of alternatives.

Take a Free Practice Situational Judgement Test

Block counting, 3D rotation, 2D rotation, reflection, broken shapes, transforming 2D to 3D, isometric view, difference in 2D versus 3D viewing.

What Is the Watson Glaser Critical Thinking Test?

The Watson-Glaser Critical Thinking Test, often referred to as the Watson-Glaser test, is a widely used assessment tool designed to evaluate an individual's critical thinking skills.

It is commonly administered as part of the hiring process for various professional and managerial positions, particularly in fields where critical thinking and problem-solving abilities are highly valued, such as law, finance and management.

This is a nine question diagrammatic reasoning practice test.

We recommend a time limit of nine minutes for this test. 

After you have given your answer to a question, you will be shown the correct answer and given a full explanation.

What is the Critical Thinking Test?

The Critical Thinking Test is a comprehensive evaluation designed to assess individuals' cognitive capacities and analytical prowess.

This formal examination, often referred to as the critical thinking assessment, is a benchmark for those aiming to demonstrate their proficiency in discernment and problem-solving.

In addition, this evaluative tool meticulously gauges a range of skills, including logical reasoning, analytical thinking, and the ability to evaluate and synthesize information.

This article will embark on an exploration of the Critical Thinking Test, elucidating its intricacies and elucidating its paramount importance. We will dissect the essential skills it measures and clarify its significance in gauging one's intellectual aptitude.

We will examine examples of critical thinking questions, illuminating the challenging scenarios that candidates encounter prompting them to navigate the complexities of thought with finesse.

Critical Thinking Practice Test

Before going ahead to take the critical thinking test, let's delve into the realm of preparation. This segment serves as a crucible for honing the skills assessed in the actual examination, offering candidates a chance to refine their analytical blades before facing the real challenge. Here are some skills that will help you with the critical thinking assessment: Logical Reasoning: The practice test meticulously evaluates your ability to deduce conclusions from given information, assess the validity of arguments, and recognize patterns in logic. Analytical Thinking: Prepare to dissect complex scenarios, identify key components, and synthesize information to draw insightful conclusions—a fundamental aspect of the critical thinking assessment. Problem-Solving Proficiency: Navigate through intricate problems that mirror real-world challenges, honing your capacity to approach issues systematically and derive effective solutions. What to Expect: The Critical Thinking Practice Test is crafted to mirror the format and complexity of the actual examination. Expect a series of scenarios, each accompanied by a set of questions that demand thoughtful analysis and logical deduction. These scenarios span diverse fields, from business and science to everyday scenarios, ensuring a comprehensive evaluation of your critical thinking skills. Examples of Critical Thinking Questions Scenario: In a business context, analyze the potential impacts of a proposed strategy on both short-term profitability and long-term sustainability. Question: What factors would you consider in determining the viability of the proposed strategy, and how might it affect the company's overall success? Scenario: Evaluate conflicting scientific studies on a pressing environmental issue.

Question: Identify the key methodologies and data points in each study. How would you reconcile the disparities to form an informed, unbiased conclusion?

Why Practice Matters

Engaging in the Critical Thinking Practice Test familiarizes you with the test format and cultivates a mindset geared towards agile and astute reasoning. This preparatory phase allows you to refine your cognitive toolkit, ensuring you approach the assessment with confidence and finesse.

We'll navigate through specific examples as we proceed, offering insights into effective strategies for tackling critical thinking questions. Prepare to embark on a journey of intellectual sharpening, where each practice question refines your analytical prowess for the challenges ahead.

This is a three question practice in-tray exercise.

If you get a question wrong, make sure you find out why and learn how to answer this type of question in the future. 

Take a Free Practice In-Tray Exercise

What Is the PwC Assessment Test?

When you apply for a coveted role at PwC, you will be asked to undertake a PwC assessment test as part of the recruitment process.

The PwC test are used to evaluate candidates on measurable skills, abilities, aptitudes and personality traits that are needed for success in the type (and level) of the role that you have applied for.

PwC is one of the Big Four accounting firms globally, and from their headquarters in London, England, they have offices in 157 countries, a presence in 742 locations, and they currently employ nearly 300,000 staff.

With roles available in various departments, from consulting to legal, operations to audit, and tax to technology, competition for advertised jobs is fierce, and the PwC assessments are recognised as being particularly challenging to help narrow down the candidate pool to those applicants who really have what it takes to be successful.

In fact, less than 50% of candidates will advance past the screening tests as the benchmark for a passing mark is very high.

'AON assessments' are the new name for the cut-e tests, and they are often used as pre-employment evaluations for different skills, aptitudes, competencies and personality traits for various roles across different industries.

The AON assessments are characterized by being very short online assessment tests, and in many cases, candidates will be required to take more than one as part of a recruitment process.

With so much content to cover in all the different types of tests, it can be difficult to know what to expect from the AON assessments, which is where this guide will help.

Below you will learn more about why AON assessments are used and which companies use them as part of their hiring process.

We will discuss some of the features that the assessments have in common, as well as the most popular tests that are used by recruiters.

There will be some example questions with answers to get you familiar with the type of content you will be facing in certain tests and some helpful information regarding the way the AON assessments are scored and how you can give yourself the best chance to demonstrate that you have what it takes to be successful.

What Is the AON Assessment Test?

AON is well-known as a global financial services firm, and they acquired the cut-e testing battery so that they can provide top-of-the-range candidate evaluation and personnel development tools based on a scientific framework and testing methodology.

The CogAT Grade 4 test is used to understand a student’s thinking and reasoning abilities. It is not a test of learned knowledge; rather, it is a diagnosis of how they learn.

The 4th Grade CogAT test measures reasoning ability in three key areas: verbal, non-verbal and quantitative.

The assessment is often used to identify students for gifted and talented education programs.

If your child has been selected to sit the CogAT test in 4th grade, it can be confusing to know what to do to help.

This article will help you to answer these questions:

• What is the CogAT test ?
• What skills is the test assessing?
• What is the format of the test?
• How can I help my child prepare?
• What skills can we practice?
• What is the scoring system?

When applying for a job application, you may find that, along with providing your CV and attending an interview, you will be required to complete an IKM assessment .

This assessment will serve as a supplement to your overall application. So, you must understand what it entails and how it contributes to your application.

This article will explain the specifics of the IKM assessment, why it is important and how you can prepare for it.

What Is IKM?

The International Knowledge Measurement Service (IKM) offers organizations various assessments for employees and candidates among various career disciplines.

Among other things, this assessment ensures that employees hold the necessary requirements to go through the organization’s recruitment process.

Employee candidates will take the IKM assessment online remotely (self-supervised) or with client-side supervision from the organization.

The IKM assessment uses adaptive testing, meaning the difficulty of questions is dynamically selected based on the employee candidate’s previous answers .

This ensures that the assessment questions are neither too difficult nor too easy, greatly reducing the testing time.

The CAT4 Level D is a cognitive ability test used by a number of UK secondary schools. Typically taken by pupils in Year 7, the CAT4 Level D tests a child’s verbal, non-verbal, quantitative and spatial reasoning skills to give an accurate picture of their learning potential.

The Delta Assessment Test is a group of online tests that forms part of the Delta Airlines hiring process.

If you are applying for job roles with Delta, you may be asked to complete one or more of the Delta Assessment Tests.

Your test results will help the hiring manager to decide whether you are suitable for the job role you have applied for.

The tests you are asked to take will vary according to the job role.

The Deloitte immersive online assessment is a psychometric aptitude-style test. It is used to identify a candidate’s strengths and weaknesses.

Questions vary but are likely to include situational judgment style questions that link to the roles at Deloitte.

Candidates are also tested on their numerical reasoning and presented with personality questions.

Competition is tough for jobs on the Crossover recruitment platform.

There are thousands of applicants for each role, and only the top 1% are offered a contract .

After a successful initial application, the first step is taking the Crossover Cognitive Aptitude Test (CCAT).

To help you prepare, this article covers the following:

• How Crossover works
• The recruitment process
• What to expect in the CCAT
• The scoring system
• Tips to help you prepare

The Federal Bureau of Investigation (FBI) is the domestic intelligence and security service of the USA.

The agency investigates serious offenses such as terrorism, public corruption, cyber-attacks, and violent and organized crime.

The FBI's mission is to protect the American people and uphold the American Constitution.

The FBI has over 37,000 employees across hundreds of locations in the US.

To work for the FBI, you must fulfill specific criteria which include:

• Be a US citizen
• Be able to obtain an FBI Top Secret clearance
• Pass the FBI polygraph examination
• Pass the FBI Phase 1 test
• Adhere to the FBI drug policy

Roles available at the FBI include computer scientists, nurses, engineers, technicians, contract specialists, and of course, police officers.

It is important to note that the recruitment process can take over one year, so you must be willing to wait several months for the chance of your dream role.

In this FBI Phase 1 test prep guide, we will delve into the role of FBI special agents – upholders of the law that seek out cybercrime and infiltrate organized attacks such as terrorism.

When applying to be a special agent, you are required to take the FBI Phase 1 test .

What Is the FBI Phase 1 Test?

The FBI Phase 1 test is an assessment that evaluates your personality and suitability for a role as a Special Agent at the FBI.

The test is conducted online and is split into five parts.

As the second stage of the process, the FBI Phase 1 test is done after the successful completion of a written application.

The test is designed to assess several skills and qualities that are required for a role as an FBI special agent.

These include critical thinking, logical reasoning and personality. The test will also assess your background experiences.

Your answers are then compared to the benchmark of what is suitable for an FBI agent.

The five sections of the FBI Phase 1 test are:

• Logical reasoning
• Figural reasoning
• Personality Test
• Preferences and interests
• Situational responses

The assessment takes three hours to complete.

When applying for roles at the FBI, long waiting times are typical. The full special agent recruitment process can take over 20 months to complete.

If this is your dream job, it is certainly worth the wait as it is one of the most attractive career paths within any government agency.

To reflect this, the recruitment process is challenging and designed to reduce the number of candidates who could move on to the next stage.

This ensures that only the very best move through the application phases. In fact, only 30% of candidates can pass the FBI Phase 1 test.

You may have taken a personality test before, but the FBI Phase 1 test questions are framed and marked in a different way to other assessments.

Therefore, you should ensure you use FBI Phase 1 test practice questions and prepare in advance of the test.

It can be hard to plan for, but this is essential to get into the top 30% of successful candidates.

If you pass the FBI Phase 1 test, you will undergo background checks and receive an invitation to a regional meet-and-greet interview.

The main purpose of the CogAT Test grade 3 is to find out if a third grader is showing signs of being very smart.

Most of the questions on the test are about verbal, numerical and non-verbal reasoning. It's meant to show how a child might compare to other kids his or her own age. The CogAT grade 3 test can also be used to make individualized learning plans for kids.

The CogAT (Cognitive Abilities Test) is a standardized test used to measure children's cognitive abilities in the 3rd grade – age 9.

This test assesses a range of cognitive abilities, including verbal, quantitative and nonverbal reasoning. The CogAT is often used to identify gifted children and help educators develop appropriate educational plans.

This article will give insights and tips into how your child could pass the CogAT Test for 3rd grade students.

The MAP Test 2nd grade is a computerized test taken by children in the 2nd grade. It is designed to evaluate what the children already know and what they are ready to learn.

The test includes three sections:

Schools may not administer all three sections and may instead focus on one or two sections to measure pupils’ progress in those subjects.

The NEO Personality Inventory is a psychometric tool used to evaluate personality traits.

It is acknowledged globally and is used by recruiters and employers before hiring and, more broadly, to evaluate career potential.

The NEO Personality Inventory test is heavily associated with the 'Five-Factor Model' (which you may also know as the 'Big Five Personality Test') to identify personality traits.

It is widely believed that each person's personality can be broken down into five main categories. The NEO PI personality test looks at each of these five categories separately to create an understanding of who you are.

In this article, we'll look at the NEO PI test, why employers use it, and what you could expect if invited to participate in a NEO Personality Inventory test.

The Air Traffic Controller (ATC) Test, also known as the Air Traffic Skills Assessment (ATSA) is an exam used as part of the air traffic controller hiring process. It is a challenging assessment consisting of seven subtests designed to evaluate an applicant's aptitude for the role.

Becoming an air traffic controller is a challenging and rewarding career that requires extensive training. The Air Traffic Controller Test (previously known as the Air Traffic Selection and Training (AT-SAT) exam) is an important part of the selection process. 

The Air Traffic Skills Assessment (ATSA) measures a candidate's ability to handle the demands of the job. 

In this article, you’ll find example questions, a guide and tips for preparing for the ATSA exam.

This article relates specifically to the ATC test used in the US. Candidates in other countries may be expected to take a different version of the test. 

What is the CliftonStrengths test? This online assessment analyzes your personality and strengths for personal and professional development. You can purchase the basic test from Gallup for $19.99 and get a basic understanding of your top five personality themes. Or take the comprehensive version for $59.99 and receive a report that ranks all 34 themes and highlights your areas of excellence as well as your blind spots.

When applying for a job, you may find that the recruitment process consists of many different steps. There is the initial application form to start and usually an interview to finish. In the middle, there may be an assessment – an aptitude, intelligence or personality test.

The CliftonStrengths test is one assessment used by employers during the onboarding process. It was previously known as the CliftonStrengthsFinder.

In this guide, you will learn about the CliftonStrengths personality test and how it is used in recruitment.

The police psychological exam is a crucial part of the hiring process for law enforcement agencies. It is a personality test that confirms how suitable an applicant is for working in the police. The police psych test is used by most law enforcement agencies across the United States, although key details may differ from state to state.

What Is the Police Psychological Exam?

The police psychological exam is a series of tests and assessments administered to individuals who are seeking to become police officers.

The purpose of the exam is to evaluate a candidate's psychological fitness for the job and identify any potential psychological issues that may interfere with the candidate's ability to perform police work.

In this comprehensive guide , you’ll discover everything you need to know about the Capital One assessment and interview process.

These are designed to help the company select the best candidates for its team. To increase your chance of getting hired, it's important to be prepared.

Find out what to expect, how to prepare and the skills and qualities Capital One hiring managers are looking for in a candidate.

What Is the Capital One Assessment Test?

Capital One is an established financial services company with a focus on technology and innovation.

To become an employee, or ‘associate’, at Capital One you'll need to pass a series of online assessments and interviews .

The Capital One hiring process is as follows:

CogAT stands for Cognitive Abilities Test. These tests are normally administered by a classroom teacher or instructor, although some schools employ a specialist or test proctor to administer the test.

Many parents are interested in learning more about helping their children to succeed academically.

Achieving a high CogAT score could mean your child is eligible to join gifted or talented programs designed to enhance their development and learning.

In other schools, it is used as a tool to identify a pupil’s individual strengths or predict their future academic performance.

The CogAT test for 2nd grade is a cognitive ability test aimed at children around the age of eight years old.

It is often used as a pre-admission exam by gifted and talented schools and programs. It is designed to evaluate pupils’ cognitive abilities, including basic linguistic and math skills.

The test is made up of three sections or batteries:

• Non-verbal battery
• Verbal battery
• Quantitative battery

On the CogAT test 2nd grade, candidates are required to read the test questions instead of listening to the questions being read by the test proctor.

If you are looking for ideas on how to prepare your child for the CogAT test 2nd grade, read on to learn more.

What Is CogAT Test 2nd Grade?

The CogAT (Cognitive Abilities Test) was developed by Riverside Publishing, which is part of Houghton Mifflin Harcourt.

It is designed to assess problem-solving and reasoning skills in the following areas:

• Quantitative

Research has shown that high levels of ability in these three areas is linked to academic success.

If your child is considered potentially talented or gifted, they may be asked to sit a CogAT as part of the program entrance process.

Different CogAT tests are available for different age groups, from Kindergarten (K) up to grade 12.

In this article, you can find more information on the CogAT test 2nd grade. The CogAT test is used by schools across the US to help them identify exceptionally gifted pupils.

Each of the test levels corresponds to the age of the pupil sitting the test. For example, if your child is in grade 6 (aged 12), they will be sitting the Level 12 version of the test. Occasionally, schools may choose to administer a higher level CogAT to talented or gifted pupils; however, this is unusual.

Second grade pupils being considered for gifted programs will usually sit the CogAT Level 8 test. This test is made up of 154 questions and takes 122 minutes to complete.

Many schools use the CogAT Test 6th Grade to assess the non-verbal, verbal and quantitative abilities of sixth-grade students.

The Level 12 CogAT test is a useful tool for checking a student’s individual academic strengths and weaknesses. It can also be used as a screening assessment for entry into the gifted and talented program.

What Is the CogAT Test 6th Grade?

'CogAT' is an acronym for Cognitive Aptitude Test .

CogAT tests are usually administered at school by a teacher or instructor, although some schools employ test proctors and specialists to administer the tests.

This guide is designed to support you and your child through the CogAT Test 6th Grade. You can use it to find out what to expect from the test and tips on how to prepare for it.

We have also included information on the purpose of the test and how to interpret your child’s results.

The Procter and Gamble Assessment Test describes a series of pre-employment screening tests used by Procter and Gamble (P&G).

If you have applied for a job at P&G, you will be expected to sit these tests as part of the hiring process.

Each of the different tests is designed to assess a specific aptitude that is required for a job role at P&G.

In this article, you can learn more about the different tests used by Procter and Gamble. We have also provided tips on how to prepare for the assessments.

This guide includes useful tips and Renaissance Star testing sample questions to help students prepare for the test and feel confident on test day.

You can find detailed information on interpreting and understanding your Renaissance Star Test scores in our dedicated article .

What Is the 6th Grade MAP Test?

The MAP Growth test system was created by educators from Oregon and Washington who established the Northwest Evaluation Association (NWEA) back in 1973.

Their goal was to create an assessment that could accurately measure and track academic progress in children to ensure they graduated high school with all the essential skills and knowledge they required.

In 2000, the first MAP Growth Test was published.

The test is administered in all grades and is based on a set of learning principles known as the Common Core Principles .

The CCAT test grade 3 is a standardized assessment administered to grade 3 students in Canada.

It measures verbal, quantitative and non-verbal reasoning skills and is used to identify a student's learning potential, typically for admission to gifted educational programs.

The CCAT test grade 3 is an assessment commonly used by schools in Canada.

If you’re the parent or guardian of a child preparing for the test, this CCAT grade 3 guide will tell you everything you need to know.

What Is the CCAT Test Grade 3?

The CCAT test (Canadian Cognitive Abilities Test) is a standardized assessment administered to students in grade levels K-12 in the Canadian educational system.

Rather than a measure of academic achievement, the test assesses a child's ability to learn, reason, and problem-solve.

The Independent School Entrance Examination (ISEE) test is used by many independent and magnet schools in the US and overseas as an admission test for children across the entire school age range, but more commonly from year five upwards.

It assesses a child’s academic levels of reasoning across math and literacy in comparison to children of the same age, the norm for that school grade and other applicants to the school.

Created and administered by the Educational Records Bureau (ERB), the ISEE test is available to be taken online or in a pen and paper format.

What Are the ISEE Levels?

There are four levels of the ISEE test.

• ISEE primary for entry into years two to four
• ISEE lower level for entry into years five to six
• ISEE middle level for entry into years seven to eight
• ISEE upper level for entry into years nine to 12

Each level of the ISEE test is created to be relevant to a specific school age group, increasing in complexity with each year and level.

An employer’s recruitment process can include a wide range of assessments and interviews for the candidate to take that indicate to the employer how an individual might fare in the job.

One common way to measure job performance though is by getting candidates to take the PI Cognitive Assessment, which measures mental ability and critical thinking skills.

This article will look in detail at the assessment, its format, who uses it, example questions and PI Cognitive Assessment tips on how to be successful when taking it.

The Raven’s Progressive Matrices is a test that is often used as part of the recruitment process for high-level management and analytical roles.

In this article, you will learn more about the test, its history and background, as well as the different types of tests that are available and what you can expect if you are going to be taking the test.

You will also find some example questions that you can expect to see in each type of test and get helpful pointers that you can use to prepare and do well in the assessment.

If you are applying for a role with the United States Postal Service (USPS) , you will usually be asked to complete at least one of four 477 Virtual Entry Assessments as part of the recruitment process.

These exams are used to evaluate various skills, aptitudes, personality traits and work preferences, which can show whether you have what it takes to be successful in the role in the future.

The USPS 477 Exam is sometimes referred to as the CS VEA, which relates to customer service.

An iReady level score of 3.00 or over means the student is working at or above the level required to meet the standard for their grade.

The level score is calculated in line with expectations when the test was administered, not in comparison to the expected score by the end of the school year.

What Are the iReady Diagnostic Scores?

The iReady diagnostic test is administered to US school children in grades K to eight.

The purpose of this school assessment test is to help parents and teachers check a student’s academic process at the beginning, middle and end of each school year.

It is a computer-adaptive test, which means the questions are adjusted to become more difficult if a series of correct answers is given.

As a result, the test is designed to challenge the skill level of the student sitting the test, as well as assess their strengths and opportunities for growth.

If a student answers a few questions in a row incorrectly, the questions that follow will be easier.

Many people find i-Ready Diagnostic scores difficult to interpret.

As a child progresses through each academic year and moves up the year groups, their expected score will change.

The average score increases year on year, too.

In this article, you can learn more about the different types of iReady diagnostic scores, how these scores are displayed, and how to interpret them to better understand a student’s iReady test performance.

There are two types of HESI Exam:

• The Admissions (A2) test
• The Exit exam

The minimum passing score for the Admissions test is usually between 75 and 80 for each section, although this varies between schools.

The composite score range for the Admissions (A2) test is 750 to 900, with 900 being the maximum possible score.

The HESI Exit Exam score ranges between 0 to 1,500. 850 is considered to be an acceptable score, although HESI recommends a minimum score of 900.

If you want to sit your NCLEX licensing exam, you will need to achieve a score of at least 850 on the HESI Exit Exam.

HESI is an acronym for Health Education Systems Incorporated .

As a company, HESI administers exams and provides study material to help prepare students for the NCLEX professional licensure exam.

If you want to work as a nurse in the US, many nursing and healthcare programs use HESI tests to screen prospective students and determine suitability and readiness for specific study routes.

In this article, you can learn more about the HESI score ranges and passing scores required for each of these tests and what impact your HESI results may have on acceptance into your preferred nursing program.

Administered at college and university level, the Accuplacer test is used by some educational institutions to determine how prepared a student is for the next steps in their academic career.

This guide looks specifically at Accuplacer test scores – how they are awarded and what they mean – so you can better understand how your Accuplacer score might impact your learning experience.

Accuplacer test scores are a set of metrics that evaluate a student's knowledge and skills in specific subject areas including reading, writing and math.

The CogAT Kindergarten Test is an assessment designed to measure a child's abilities in various cognitive areas.

It plays a critical role in identifying a child's strengths and weaknesses and determining their readiness for advanced academic programs.

In this comprehensive study guide for 2024, you will explore the purpose, format, and structure of the CogAT Kindergarten Test.

Additionally, you will get valuable insights on how to prepare your child for the test, sample questions to familiarize yourself with the test content, strategies for success and answers to frequently asked questions.

Understanding the CogAT Kindergarten Test: Purpose, Format, and Structure

The purpose of the CogAT Kindergarten Test is to assess a child's cognitive abilities in areas such as verbal, quantitative, and nonverbal reasoning.

By evaluating these different components, the test provides educators and parents with valuable information about a child's potential and can help guide educational decisions.

The ATI TEAS Test , also known as the Test of Essential Academic Skills, is an important exam for students looking to pursue a career in the healthcare field. The most recent version is the ATI TEAS 7.

This comprehensive exam assesses a student's knowledge in various areas, including reading, math, science and English language usage.

If you're planning to take the ATI TEAS Test in 2024, it's essential to understand what the exam entails and how to best prepare for it.

In this article, we'll cover everything you need to know about the 2024 ATI TEAS Test.

The ATI TEAS 7 Math Test is a crucial component of the ATI TEAS exam, which is widely used by nursing and allied health schools to assess prospective students' academic readiness for their programs.

In this comprehensive guide, you will delve into various aspects of the TEAS Maths 7 Test, including what it entails, when it is taken, ATI TEAS math practice test questions to help you prepare, and tips for success.

So, let's dive right in!

The 1st Grade CogAT test is an important assessment that measures a child's cognitive abilities. It is designed to identify a child's strengths and weaknesses in areas such as verbal, quantitative, and non-verbal reasoning.

This article will provide you with a comprehensive guide on understanding and preparing for the 1st Grade CogAT Test.

The CogAT (Cognitive Abilities Test) for Kindergarten is an assessment designed to evaluate the cognitive development and problem-solving abilities of young children.

Typically, this version of the test is tailored to children around five to six years old who are attending kindergarten.

The test is typically used for educational placement, identifying gifted and talented students, and understanding a child's cognitive strengths and weaknesses. It can be administered individually or in groups, and is often used by schools to tailor instruction to better meet the educational needs of their students.

Understanding the results of the CogAT can help educators and parents support the child's learning and development more effectively, by identifying areas where the child excels or may need additional focus.

In this article, you’ll find practice CoGAT Kindergarten practice test questions and tips to help your child prepare for the big day.

The Cognitive Abilities Test (CogAT) 5th Grade Level is a crucial assessment tool for students between 10 and 11 years old.

Designed to measure verbal, nonverbal, and quantitative abilities, this standardized test plays a pivotal role in identifying students for gifted programs.

In this article, you’ll learn what the CogAT 5th grade test is, which subjects are tested, along with example questions and how best to prepare.

What Is the CogAT 5 Grade Test?

The Cognitive Abilities Test (CogAT) is a widely used standardized test designed to assess your child’s cognitive abilities in various areas.

The CogAT 5th Grade Level is specifically tailored for students in the 5th grade and measures their abilities in three main cognitive areas:

• Quantitative Reasoning
• Non-Verbal Reasoning

The MAP Test Grade 7 tests students’ proficiency in mathematics, reading and language usage.

Developed by the Northwest Evaluation Association (NWEA), it measures individual growth over time, adapting question difficulty based on responses.

This online test lasts around two to three hours, and the results are used to inform teaching or gauge students' ability levels.

Scoring is based on the RIT (Rasch Unit) scale, indicating a student's instructional level and growth potential in each subject area.

MAP Grade 7 Sample Question

The State of Texas Assessments of Academic Readiness (STAAR) test is a standardized assessment issued to public school students in Texas in grades 3 to 12.

Below you’ll find a range of STAAR test practice questions to help you prepare – whether you’re a parent coaching a child through their exam prep or a high school student revising for a test of your own.

For more info on the STAAR Test, read our dedicated article.

The STAR Early Literacy Test is an assessment tool used to measure children’s early literacy skills. It forms part of the wider Renaissance STAR (Standardized Test for the Assessment of Reading) assessment system by Renaissance Learning.

The STAR Early Literacy Assessment is mostly used to test students from pre-kindergarten to grade 3.

The test is designed to assess the following areas of early literacy:

• Phonemic awareness
• General vocabulary
• Comprehension
• Reading ability
• Early numeracy skills

STAR Early Literacy is a computer-adaptive test. This means that the difficulty of the questions adjusts according to a student’s responses.

The adaptive element of the test allows for more precise results and a better insight into a student’s overall literacy skills.

Word games are a great way to help your child prepare for the STAR Early Literacy Test.

You should also encourage your child to read daily.

You may wish to build this into their routine at certain times of the day. For example, reading before going to bed is often a good way to unwind.

If you are looking for other ways to help your child prepare, you can help them practice their time management skills, talk to them about maintaining a positive attitude towards the test and ensure they are getting sufficient rest.

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The Wechsler Intelligence Scale for Children (WISC-V) is a commonly used assessment for judging a child's intelligence. More than that, it can help to understand their reasoning and thinking abilities to support their development.

Here’s everything you need to know about this test.

The Wechsler Intelligence Scale for Children - Fifth Edition (WISC-V) is an individually administered and extensive evaluation tool used to assess children's reasoning and general thinking abilities.

It's typically given to children between ages 6 and 16.

After completing a test, children are awarded a Full-Scale Intelligence Quotient (IQ) score, along with age-based scores and rankings in several cognitive function fields.

Here we’ll provide an all-around study guide for parents whose children are required or scheduled to take the WISC-V test.

We’ll also include a comprehensive explanation of how it is constructed, its key features, tips for preparing, and a few example questions.

Let’s take a look!

The STAR assessments utilize a scoring system comprising scaled scores ranging from 0 to 1,400.

These scores reflect a student's proficiency level in subjects such as reading and math.

Benchmark categories provide descriptive labels for performance levels, while percentile rank compares a student's performance to a national reference group.

Additionally, grade equivalent scores and domain scores offer insights into grade-level equivalence and specific skill areas.

The STAR Assessment can play a crucial role in evaluating your child’s academic ability and guiding educational strategies.

Understanding its scoring system, test format and significance is important for parents and educators alike.

This article aims to provide comprehensive insights into the STAR Assessment, including its purpose, score interpretation and effective strategies to help children excel in these standardized tests.

The CogAT raw score represents how many questions were answered correctly on the CogAT test. This information is used to create the Universal Scale Score (between 100 and 150), which you will see on your child’s CogAT score report.

Here is an image of a typical score report:

With the MAP Growth Test used in many schools across the United States, MAP (Measures of Academic Progress) scores are an important part of your child’s life.

The MAP testing scores chart a student’s academic growth in a way that highlights areas of excellence and improvement.

It is essential that you understand how NWEA MAP scores are calculated so you can best support your child throughout their learning journey.

This guide will explain how to find and improve your child’s NWEA Map Scores.

The main three sections for the Upper and Middle level tests have a maximum score of 800. They have a total scaled score that ranges between 1,500 to 2,400.

Navigating the SSAT involves understanding its scoring system.

In this guide, you can explore the SSAT Score Chart and understand score ranges and percentile ranking and how they matter in private school admissions.

It's a comprehensive resource for decoding SSAT scores and making informed decisions about your child’s education.

What Is the SSAT Test?

The SSAT stands for the Secondary School Admission Test. The SSAT was first administered in 1957.

It is a standardized test designed for students seeking admission to private middle and high schools.

The primary purpose of the SSAT is to assess the skills and knowledge of students applying to independent or private schools.

It aims to provide an accurate measure of a student's academic abilities and readiness for a challenging curriculum.

As with other careers, joining the US military comes with its own set of recruitment processes, one of which is taking the ASVAB test .

If you’ve been looking to pursue a career in the US military, then it might be a test you’ve become familiar with or heard of before. It is an exam a recruiter will advise you to take prior to joining the armed forces.

The ASVAB , otherwise known as the Armed Services Vocational Aptitude Battery , is a test the armed services use to determine which part of the US military you will be most suited to join.

Within this article we will discuss what your ASVAB score means and what score counts as a good ASVAB score .

Good ASVAB Score Defined

Whether you’re looking to join the Coast Guard, Army, Marine Corps or another sector within the US military, each branch will require its candidates to score a minimum amount to qualify for that specific area.

It is important to note that there is no single ASVAB score , and you will normally receive a variety of different scores on your final report.

The Microsoft Codility Test evaluates coding skills and algorithmic thinking.

Designed to streamline Microsoft’s recruitment process, the Microsoft Codility Test assesses candidates' ability to solve real-world problems efficiently. 

Candidates can prepare using coding practice platforms and mastering programming languages. It's an integral tool in selecting skilled software engineers for Microsoft's diverse roles.

The Smarter Balanced Assessment Consortium Test, known as the SBAC test, is a standardized assessment of English and math used by schools in participating states.

Administered to students in grades K to 12, it measures grade level proficiency and academic progress through computer-adaptive testing and performance tasks.

The Smarter Balanced Test is an educational tool developed and administered by the Smarter Balanced Assessment Consortium (SBAC), hence the abbreviation SBAC test.

In this article we explore what the test involves, what the results mean and how to help a student prepare for their SBAC assessment.

What Is the SBAC Test?

The SBAC assessment is a set of standardized tests that evaluate how well students are performing in the subjects of English Language Arts (ELA) and mathematics.

These assessments are taken by students ranging from elementary school to high school in multiple states across the US.

The tests are developed and managed by the Smarter Balanced Assessment Consortium (SBAC), a collaborative group of states working together.

FireTEAM Test Prep: Top Tips:

• Master time management
• Brush up on basic concepts
• Diversify your reading
• Play observational and memory games
• Assess your communication style
• Prioritize rest and sleep

If you're considering a career in firefighting, taking the FireTEAM test is a pivotal step that can open doors to various fire departments across the US.

This article covers everything you need to know to put in a strong performance, including an overview of its format, practice questions and FireTEAM test tips to help you create an effective study plan.

A career in the fire service is a challenging – but extremely rewarding – journey. Such an important, high-pressure job requires a high level of physical, mental and emotional skills.

As well as the necessary personality traits, you generally need a high school diploma or GED. If you have a college degree, you have a better chance of securing a role in the fire service.

You will also be required to take a series of assessments that evaluate your physical and mental strength. One of the assessments used by Californian fire departments is the FCTC Written Test. To become a firefighter in California, you must pass this entry-level test.

In this guide, we will explore what the FCTC Written Test includes and how you can prepare for success.

To successfully enlist in the US Marine Corps, certain standards must be met. Marines require both physical and mental strength as well as discipline, determination and the ability to overcome obstacles. This is sometimes referred to as the ‘Marine Mindset’.

One of the ways candidates who wish to enlist will be assessed is by taking a test known as the Armed Services Vocational Aptitude Battery (ASVAB).

A good score on the test suggests that a candidate possesses the mental skillset to be successful in the military.

Marines need to be able to make quick, accurate decisions and adapt to and overcome threats and obstacles on the battlefield.

The PiCAT test is a commonly used assessment tool for those applying to military positions, such as those in the US Navy or the US Army.

This article explores the PiCAT test in more detail. We look at the test format to familiarize individuals with what the Navy PiCAT and Army PiCAT test covers.

Preparation is vital to performing to the best of your ability in the PiCAT test.

The article includes PiCAT practice test questions, answers to help you prepare, and tips to give you the best opportunity to approach the test positively.

The Mettl tests are developed by the world's largest assessment provider, Mercer Mettl.

The tests have been designed to analyze various competencies, including verbal, logical and numerical reasoning.

Alongside, the Mettl assessments evaluate candidates' personalities and working styles, establishing whether they are an accurate fit for the role and the broader company.

The Mettl tests are a comprehensive recruitment tool provided by Mercer Mettl – the world's largest assessment provider.

Moreover, the Mettl tests are designed to assess various skills, including numerical , verbal and abstract reasoning.

The assessments are also constructed to understand candidates' behaviors and personality types.

This guide explains everything you need to know about the Mettl test, including tips on how to pass the test in 2024.

What Is the Mettl Test?

As mentioned, the Mettl test is a comprehensive recruitment tool designed to test a range of skills.

It allows employers to ensure they recruit the most suitable candidates for the role.

Mastering the Pipefitter Test is crucial for those entering the field.

This guide provides valuable insights, a pipefitter sample test and strategies to conquer the examination.

Discover expert tips to excel in your pipefitting career by navigating the challenges of this important assessment.

What Is the Pipefitter Assessment Test?

The Pipefitter test is an important evaluation tool for individuals aspiring to secure roles as pipefitters in the construction and industrial sectors.

Qualifications and certifications necessary for such positions can vary by state. This makes the pipefitter assessment test a valuable method of demonstrating skills and knowledge.

The National Center for Construction Education and Research (NCCER) administers the most popular pipefitter assessment test, designed to assess the potential skills of candidates.

It covers the principles related to the installation and maintenance of both high and low-pressure pipe systems.

In addition, it focuses on how these are used across various sectors, including manufacturing, electricity generation and climate control systems in buildings.

The i-Ready Diagnostic Test is an internet-based adaptive diagnostic test linked to the i-Ready educational learning program.

Students from kindergarten to grade 12 take the test three times each year. The test is divided into two subtests:

i-Ready test results are used to help teaching staff create a personalized learning plan according to a student’s strengths and weaknesses.

What Is the i-Ready Diagnostic Test?

The i-Ready Diagnostic Test is a computer-adaptive, untimed assessment for students between grades K and 12.

Administered by Curriculum Associates , teachers can use it to monitor a student’s ability and progress throughout the school year.

In most cases, the i-Ready Diagnostic Test is administered three times each year. It is split into two subtests: math and reading.

The HSBC Online Immersive Assessment contains 38 questions over five subtests. The test includes a combination of behavioural questions and cognitive ability exercises.

It is an untimed assessment, but most candidates can answer all test questions within 50 minutes.

Some people find the test difficult, but adequate preparation will stand you in good stead to pass the assessment.

What Is the HSBC Hiring Process Like?

HSBC is a major global bank and financial institution. It offers services via three global businesses and serves millions of customers daily.

The hiring process at HSBC comprises four key stages:

• Initial Screening and Application
• HSBC Online Immersive Assessment
• Online Job Simulation Assessment

What Is the Electronic Data Processing Test?

The Electronic Data Processing Test (EDPT) is a pre-employment test taken by military candidates who want to transfer to IT or computer programming roles within the Marine Corps or Air Force.

The EDPT test is one of the most challenging pre-employment tests currently on the market with a pass rate of around 10%.

It is 90 minutes long and has 120 multiple-choice questions. This means you have around 45 seconds to answer each question.

While the minimum ASVAB score varies between military branches, the minimum acceptable score is 31.

However, as the majority of candidates score between 30 and 70, you want to aim for a percentile rank of at least 60.

The ASVAB Test Score Report is a valuable document that provides detailed information about your aptitudes, skills, and qualifications for military service.

It includes Career Exploration Scores to guide career choices, individual scores on ASVAB subtests to assess specific abilities and the critical AFQT score that determines your eligibility for enlistment.

Understanding the information presented in this report is essential for making informed decisions about your military career options.

What Is in the ASVAB Test Score Report?

The ASVAB (Armed Services Vocational Aptitude Battery) Test Score Report provides a comprehensive overview of your performance on the ASVAB test, which is a critical step in the military enlistment process.

The report helps you and military recruiters assess your aptitudes, skills, and potential for various military occupations.

What Is the MMPI Assessment?

The Minnesota Multiphasic Personality Inventory (MMPI) is one of the most widely used assessment tools used to help clinically diagnose mental health disorders.

Originally developed in the late 1930s, it is used by mental health professionals, lawyers and even in some cases by employers when they are hiring for positions that are considered to be high-risk, such as working in the police, in nuclear power plants or in air traffic control.

The MMPI is a self-reporting tool that is administered by professionals, and during the assessment, you will be asked to answer hundreds of true/false questions, which help paint a picture of your mental health and your personality traits.

As a diagnosis tool, the MMPI is considered to be clinically accurate. It has been updated multiple times over the years to make it more relevant, especially in terms of cultural sensitivity.

The MMPI offers results that show on a scale what symptoms a person has, and what mental health problems that could be indicative of.

In addition, the MMPI is usually used in tandem with other diagnosis tools to provide a clear picture of a person's mental health.

What Is the ACCUPLACER Reading Comprehension Test?

The Accuplacer Reading Comprehension test is part of a suite of assessments that are used to evaluate students prior to entry at college.

While the Accuplacer test battery is not used to determine whether a student will achieve a placement at college, the results are used to ensure that the student is studying at an appropriate level and is ready for education at this level.

Created by the College Board, which is a not-for-profit organization that is also responsible for creating assessments like the SATs, the Accuplacer tests are designed to offer better opportunities to students and make entry to top colleges accessible to all.

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How to Tackle Exam Questions

Learn more about how to tackle different kinds of exams and exam questions.

We cover the following topics on exam preparation on this page:

• Quantitative Questions
• Multiple Choice Questions
• Essay Questions

First, Let’s Think About De-Coding Different Types of Exam Questions

It’s helpful to understand the kinds of question that are asked on a exam, because the response you need to come up with depends on the type of question. Knowing about different types of exam questions can help you activate appropriate strategies for formulating answers and reduce exam-taking anxiety.

Exam questions generally fall into one of three categories: 1

“Green Light”

• Go right ahead!
• These are factual questions, and the answers are straight-forward. You either know the answer or you don’t; it’s right there in your head or it’s not.
• Some green light questions can be very difficult, and your ability to recall details is often tested with this typeof question.
• Study for this type of question by using recitation, making flash cards, quizzing yourself or a study partner, etc.
• If you don’t know the answer to a green light question right away, circle it and move on; often the answer will pop into your head later on during the exam.

“Yellow Light”

• These questions are more detailed than green light questions, but are based on the same idea: you either know the answer or you don’t.
• Often you’ll have to put multiple or “green light” details together.
• Similar strategies work for yellow and green questions, but with yellow light questions you’ll need to recall many ideas, concepts, formulas, etc., just to answer one question.

• These questions ask you to make inferences or apply your knowledge to new situations, which is sometimes called “critical thinking”.
• You need to know the material being covered to answer these questions at the “green light” level, but the exam question is not asking you to simply regurgitate it. You will need to take what you know and use it in ways you have not yet used it.
• This type of question sometimes flummoxes students, because they are surprised to they are being asked a question that wasn’t exactly covered in class. Remember that with red light questions you are not supposed to already know the answer. You have to come up with the answer yourself, it is not already in your head. (You will need to know the basic information, though, to be able to answer this type of question.)
• Red light questions are asked more frequently in college than in high school.
• To study for red light questions, make diagrams or concept maps that link ideas or topics from the course together. Think about how what you’re learning relates to what you’ve learned in other classes. Sit down with friends or classmates and talk about how one might use information from the class in a job setting.

See this link for a pdf of  Decoding exam questions.

How to Tackle: Problem-Solving and Quantitative Questions

Study for problem-based exams by practicing (new!) problems

As you work on the problems, remember:

• DO let yourself be stuck.* (yes, we mean that!)
• DON’T sneak a peak at the answer if you get stuck. (keep trying!)
• Check your answer only after you’ve put something–anything–down. Think partial credit, which is better than no credit if you freeze when you get stuck on hard problems on the test.

* You need to get your “stuck” muscles stronger so you know what to do on tests when you feel stuck.

Watch: LSC’s Mike Chen Shares “The Key to Problem-Solving Tests”

Taking problem-based exams

1. Understand the problem: Determine what you are supposed to find, what you need to find it, and what the unknown is (and if there is extra information). Consider whether drawing a sketch will help. Also – note each part of the question. Not answering each part is an easy way to lose points.

2. Determine a way to solve the problem: Write down all that is given or known. Draw a sketch when appropriate to show relations. Write down all relevant formulas.

3. Carry out the procedure you have devised: For numerical problems, try and estimate an answer first. This will help you to check your work later. Neat, careful work keeps you from making mistakes, and allows you to find them when you do make them (show your units!!). Additionally, when the instructor can see your work clearly, he or she may give you partial credit for what you do know, even if your ultimate answer is incorrect.

4. Check your Answers: This requires the same quality of thought originally used to solve the problem. Is your answer what you thought it would be in your original estimate? Is it a quantity that makes sense? Is your answer in the correct units? If your answer does not seem reasonable, rework the problem.

How to Tackle: Multiple Choice Questions

1. Read the stem: First, read the stem and make sure you understand what it is getting at. Look out for double negatives or other twists in wording before you consider the answer.

2. Try to come up with the correct answer: Before you look at the answer choices, try to come up with the correct answer. This will help you to rule out choices that are similar to the correct answer. Now read and consider each option carefully.

3. Look for clues in the stem: Look for clues in the stem that suggest the correct answer or rule out any choices. For example, if the stem indicates that the answer is plural you can rule out any answers that are singular. The basic rule is: the correct answer must make sense grammatically with the stem. Options which fail this exam can be ruled out.

4. Cross off any options you know are incorrect: As you rule out options cross them off with your pencil. This will help you focus on the remaining choices and eliminates the chance of returning to an item and selecting an option you had already eliminated.

5. Come back to items you were unsure of: Put a mark next to any questions you are unsure of. If you complete the entire exam with time to spare, review these questions – you will often get clues (or even answers) from other questions.

Take a look at some additional information on difficult “ Multiple Choice Tests ” (opens a PDF).

How to Tackle: Essay Questions

The best way to  prepare  for essay tests is to practice writing essays.

• Anticipate questions : Make outlines of possible essay topics using your course materials so you know you’ve got a good grasp of what might be on the test. Then recreate your outlines from memory (unless it’s an open-notes test).
• Practice writing  at least one full essay; be mindful of the time you spend practicing and think about how much time you will have during the exam. It is also important to think about  how  you are organizing the information you are including in your essay — for example, if you are asked to compare and contrast two theories as they relate to an issue, you might want to define each of them, describe the issue, and then compare and contrast them.
• If your exam is closed book,  memorize key events, facts, and names  that you will need to support your argument. If it is open-notes, then make sure you develop good outlines.

When you are  taking  essay tests:

• Manage your time  well. As with all exams, if there are multiple essay questions, be sure to look at them all at the beginning (taking note of the points each is worth), and prioritize the order you answer the questions.
• Read the directions  carefully. Ask yourself honestly: are you answering the  actual  question on the test, or the question you  want  to be on the test?  (tip: instructors know when you aren’t really answering the exact question, so make sure you are addressing the actual question and don’t just write random information that is unrelated to the question.)
• Before you write the essay,  decide on your argument  and  quickly list your supporting evidence  (it is ok to do a brain dump of all the important information that you want to include so that you have it handy when you begin writing).
• Make a quick outline  of what you are going to write to organize your thoughts and arguments.
• Write! And, make your point right away – you don’t want to get to the end of a timed essay test with your amazing argument still unmade!
• If you have time, go back and quickly  proof-read  your essay for errors.

You might want to take a look at some “ Words to Watch for in an Essay ” (opens a PDF).

References:

1 Taffy E. Raphael, Teaching Question Answer Relationships, Revisited, The Reading Teacher, Vol. 39, No. 6 (Feb., 1986), pp. 516-522.

Ellis, D. (1998). Becoming a Master Student. Houghton Mifflin: Boston

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30 Problem Solving Maths Questions And Answers For GCSE

Martin Noon

Problem solving maths questions can be challenging for GCSE students as there is no ‘one size fits all’ approach. In this article, we’ve compiled tips for problem solving, example questions, solutions and problem solving strategies for GCSE students. 

Since the current GCSE specification began, there have been many maths problem solving exam questions which take elements of different areas of maths and combine them to form new maths problems which haven’t been seen before. 

While learners can be taught to approach simply structured problems by following a process, questions often require students to make sense of lots of new information before they even move on to trying to solve the problem. This is where many learners get stuck.

How to teach problem solving

6 tips to tackling problem solving maths questions, 10 problem solving maths questions (foundation tier), 10 problem solving maths questions (foundation & higher tier crossover), 10 problem solving maths questions (higher tier).

In the Ofsted maths review , published in May 2021, Ofsted set out their findings from the research literature regarding the sort of curriculum and teaching that best supports all pupils to make good progress in maths throughout their time in school.

Regarding the teaching of problem solving skills, these were their recommendations:

• Teachers could use a curricular approach that better engineers success in problem-solving by teaching the useful combinations of facts and methods, how to recognise the problem types and the deep structures that these strategies pair to.
• Strategies for problem-solving should be topic specific and can therefore be planned into the sequence of lessons as part of the wider curriculum. Pupils who are already confident with the foundational skills may benefit from a more generalised process involving identifying relationships and weighing up features of the problem to process the information. 
• Worked examples, careful questioning and constructing visual representations can help pupils to convert information embedded in a problem into mathematical notation.
• Open-ended problem solving tasks do not necessarily mean that the activity is the ‘ideal means of acquiring proficiency’. While enjoyable, open ended problem-solving activities may not necessarily lead to improved results.  

Are you a KS2 teacher needing more support teaching reasoning, problem solving & planning for depth ? See this article for FREE downloadable CPD

There is no ‘one size fits all’ approach to successfully tackling problem solving maths questions however, here are 6 general tips for students facing a problem solving question:

• Read the whole question, underline important mathematical words, phrases or values.
• Annotate any diagrams, graphs or charts with any missing information that is easy to fill in.
• Think of what a sensible answer may look like. E.g. Will the angle be acute or obtuse? Is £30,000 likely to be the price of a coat?
• Tick off information as you use it.
• Draw extra diagrams if needed.
• Look at the final sentence of the question. Make sure you refer back to that at the end to ensure you have answered the question fully.

There are many online sources of mathematical puzzles and questions that can help learners improve their problem-solving skills. Websites such as NRICH and our blog on SSDD problems have some great examples of KS2, KS3 and KS4 mathematical problems.

Read more: KS2 problem solving and KS3 maths problem solving

In this article, we’ve focussed on GCSE questions and compiled 30 problem solving maths questions and solutions suitable for Foundation and Higher tier students. Additionally, we have provided problem solving strategies to support your students for some questions to encourage critical mathematical thinking . For the full set of questions, solutions and strategies in a printable format, please download our 30 Problem Solving Maths Questions, Solutions & Strategies.

30 Problem Solving Maths Questions, Solutions & Strategies

Help your students prepare for their maths GCSE with these free problem solving maths questions, solutions and strategies

These first 10 questions and solutions are similar to Foundation questions. For the first three, we’ve provided some additional strategies.

In our downloadable resource, you can find strategies for all 10 Foundation questions .

1) L-shape perimeter 

Here is a shape:

Sarah says, “There is not enough information to find the perimeter.”

Is she correct? What about finding the area?

• Try adding more information – giving some missing sides measurements that are valid. 
• Change these measurements to see if the answer changes.
• Imagine walking around the shape if the edges were paths. Could any of those paths be moved to another position but still give the same total distance?

The perimeter of the shape does not depend on the lengths of the unlabelled edges.

Edge A and edge B can be moved to form a rectangle, meaning the perimeter will be 22 cm. Therefore, Sarah is wrong.

The area, however, will depend on those missing side length measurements, so we would need more information to be able to calculate it.

2) Find the missing point

Here is a coordinate grid with three points plotted. A fourth point is to be plotted to form a parallelogram. Find all possible coordinates of the fourth point.

• What are the properties of a parallelogram?
• Can we count squares to see how we can get from one vertex of the parallelogram to another? Can we use this to find the fourth vertex?

There are 3 possible positions.

3) That rating was a bit mean!

The vertical line graph shows the ratings a product received on an online shopping website. The vertical line for 4 stars is missing.

If the mean rating is 2.65, use the information to complete the vertical line graph.

Strategies 

• Can the information be put into a different format, either a list or a table?
• Would it help to give the missing frequency an algebraic label, x ?
• If we had the data in a frequency table, how would we calculate the mean?
• Is there an equation we could form?

Letting the frequency of 4 star ratings be x , we can form the equation \frac{45+4x}{18+x} =2.65

Giving x=2 

4) Changing angles

The diagram shows two angles around a point. The sum of the two angles around a point is 360°.

Peter says “If we increase the small angle by 10% and decrease the reflex angle by 10%, they will still add to 360°.”

Explain why Peter might be wrong.

Are there two angles where he would be correct?

Peter is wrong, for example, if the two angles are 40° and 320°, increasing 40° by 10% gives 44°, decreasing 320° by 10% gives 288°. These sum to 332°.

10% of the larger angle will be more than 10% of the smaller angle so the sum will only ever be 360° if the two original angles are the same, therefore, 180°.

5) Base and power

The integers 1, 2, 3, 4, 5, 6, 7, 8 and 9 can be used to fill in the boxes. 

How many different solutions can be found so that no digit is used more than once?

There are 8 solutions.

6) Just an average problem 

Place six single digit numbers into the boxes to satisfy the rules.

The mean in maths is 5  \frac{1}{3}

The median is 5

The mode is 3.

How many different solutions are possible?

There are 4 solutions.

2, 3, 3, 7, 8, 9

3, 3, 4, 6, 7, 9

3, 3, 3, 7, 7, 9

3, 3, 3, 7, 8, 8

7) Square and rectangle  

The square has an area of 81 cm 2 . The rectangle has the same perimeter as the square.

Its length and width are in the ratio 2:1.

Find the area of the rectangle.

The sides of the square are 9 cm giving a perimeter of 36 cm. 

We can then either form an equation using a length 2x and width x . 

Or, we could use the fact that the length and width add to half of the perimeter and share 18 in the ratio 2:1. 

The length is 12 cm and the width is 6 cm, giving an area of 72 cm 2 .

8) It’s all prime

The sum of three prime numbers is equal to another prime number.

If the sum is less than 30, how many different solutions are possible?

There are 6 solutions. 

2 can never be used as it would force two more odd primes into the sum to make the total even.

9) Unequal share

Bob and Jane have £10 altogether. Jane has £1.60 more than Bob. Bob spends one third of his money. How much money have Bob and Jane now got in total?

Initially Bob has £4.20 and Jane has £5.80. Bob spends £1.40, meaning the total £10 has been reduced by £1.40, leaving £8.60 after the subtraction.

10) Somewhere between

Fred says, “An easy way to find any fraction which is between two other fractions is to just add the numerators and add the denominators.” Is Fred correct?

Solution 

Fred is correct. His method does work and can be shown algebraically which could be a good problem for higher tier learners to try.

If we use these two fractions \frac{3}{8} and \frac{5}{12} , Fred’s method gives us \frac{8}{20} = \frac{2}{5}

\frac{3}{8} = \frac{45}{120} , \frac{2}{5} = \frac{48}{120} , \frac{5}{12} = \frac{50}{120} . So \frac{3}{8} < \frac{2}{5} < \frac{5}{12}

The next 10 questions are crossover questions which could appear on both Foundation and Higher tier exam papers. We have provided solutions for each and, for the first three questions, problem solving strategies to support learners.

11) What’s the difference?

An arithmetic sequence has an nth term in the form an+b .

4 is in the sequence.

16 is in the sequence.

8 is not in the sequence.

-2 is the first term of the sequence.

What are the possible values of a and b ?

• We know that the first number in the sequence is -2 and 4 is in the sequence. Can we try making a sequence to fit? Would using a number line help?
• Try looking at the difference between the numbers we know are in the sequence.

If we try forming a sequence from the information, we get this:

We can now try to fill in the missing numbers, making sure 8 is not in the sequence. Going up by 2 would give us 8, so that won’t work.

The only solutions are 6 n -8 and 3 n -5.

12) Equation of the hypotenuse

The diagram shows a straight line passing through the axes at point P and Q .

Q has coordinate (8, 0). M is the midpoint of PQ and MQ has a length of 5 units.

Find the equation of the line PQ .

• We know MQ is 5 units, what is PQ and OQ ?
• What type of triangle is OPQ ?
• Can we find OP if we know PQ and OQ ?
• A line has an equation in the form y=mx+c . How can we find m ? Do we already know c ?

PQ is 10 units. Using Pythagoras’ Theorem OP = 6

The gradient of the line will be \frac{-6}{8} = -\frac{3}{4} and P gives the intercept as 6.

13) What a waste

Harry wants to cut a sector of radius 30 cm from a piece of paper measuring 30 cm by 20 cm. 

What percentage of the paper will be wasted?

• What information do we need to calculate the area of a sector? Do we have it all?
• Would drawing another line on the diagram help find the angle of the sector?

The angle of the sector can be found using right angle triangle trigonometry.

The angle is 41.81°.

This gives us the area of the sector as 328.37 cm 2 .

The area of the paper is 600 cm 2 .

The area of paper wasted would be 600 – 328.37 = 271.62 cm 2 .

The wasted area is 45.27% of the paper.

14) Tri-polygonometry

The diagram shows part of a regular polygon and a right angled triangle. ABC is a straight line. Find the sum of the interior angles of the polygon.

Finding the angle in the triangle at point B gives 30°. This is the exterior angle of the polygon. Dividing 360° by 30° tells us the polygon has 12 sides. Therefore, the sum of the interior angles is 1800°.

15) That’s a lot of Pi

A block of ready made pastry is a cuboid measuring 3 cm by 10 cm by 15 cm. 

Anne is making 12 pies for a charity event. For each pie, she needs to cut a circle of pastry with a diameter of 18 cm from a sheet of pastry 0.5 cm thick.

How many blocks of pastry will Anne need to buy?

The volume of one block of pastry is 450 cm 3 . 

The volume of one cylinder of pastry is 127.23 cm 3 .

12 pies will require 1526.81 cm 3 .

Dividing the volume needed by 450 gives 3.39(…). 

Rounding this up tells us that 4 pastry blocks will be needed.

16) Is it right?

A triangle has sides of (x+4) cm, (2x+6) cm and (3x-2) cm. Its perimeter is 80 cm.

Show that the triangle is right angled and find its area.

Forming an equation gives 6x+8=80

This gives us x=12 and side lengths of 16 cm, 30 cm and 34 cm.

Using Pythagoras’ Theorem

16 2 +30 2 =1156 

Therefore, the triangle is right angled.

The area of the triangle is (16 x 30) ÷ 2 = 240 cm 2 .

17) Pie chart ratio

The pie chart shows sectors for red, blue and green. 

The ratio of the angles of the red sector to the blue sector is 2:7. 

The ratio of the angles of the red sector to the green sector is 1:3. 

Find the angles of each sector of the pie chart.

Multiplying the ratio of red : green by 2, it can be written as 2:6. 

Now the colour each ratio has in common, red, has equal parts in each ratio.

The ratio of red:blue is 2:7, this means red:blue:green = 2:7:6.

Sharing 360° in this ratio gives red:blue:green = 48°:168°:144°.

18) DIY Simultaneously

Mr Jones buys 5 tins of paint and 4 rolls of decorating tape. The total cost was £167.

The next day he returns 1 unused tin of paint and 1 unused roll of tape. The refund amount is exactly the amount needed to buy a fan heater that has been reduced by 10% in a sale. The fan heater normally costs £37.50.

Find the cost of 1 tin of paint.    

The sale price of the fan heater is £33.75. This gives the simultaneous equations

p+t = 33.75 and 5 p +4 t = 167.

We only need the price of a tin of paint so multiplying the first equation by 4 and then subtracting from the second equation gives p =32. Therefore, 1 tin of paint costs £32. 

19) Triathlon pace

Jodie is competing in a Triathlon. 

A triathlon consists of a 5 km swim, a 40 km cycle and a 10 km run. 

Jodie wants to complete the triathlon in 5 hours. 

She knows she can swim at an average speed of 2.5 km/h and cycle at an average speed of 25 km/h. There are also two transition stages, in between events, which normally take 4 minutes each.

What speed must Jodie average on the final run to finish the triathlon in 5 hours?

Dividing the distances by the average speeds for each section gives times of 2 hours for the swim and 1.6 hours for the cycle, 216 minutes in total. Adding 8 minutes for the transition stages gives 224 minutes. To complete the triathlon in 5 hours, that would be 300 minutes. 300 – 224 = 76 minutes. Jodie needs to complete her 10 km run in 76 minutes, or \frac{19}{15} hours. This gives an average speed of 7.89 km/h.

20) Indices

a 2x × a y =a 3

(a 3 ) x ÷ a 4y =a 32

Find x and y .

Forming the simultaneous equations

Solving these gives

This final set of 10 questions would appear on the Higher tier only. Here we have just provided the solutions. Try asking your learners to discuss their strategies for each question.  

21) Angles in a polygon

The diagram shows part of a regular polygon.

A , B and C are vertices of the polygon. 

The size of the reflex angle ABC is 360° minus the interior angle.

Show that the sum of all of these reflex angles of the polygon will be 720° more than the sum of its interior angles.

Each of the reflex angles is 180 degrees more than the exterior angle: 180 + \frac{360}{n}

The sum of all of these angles is n (180 + \frac{360}{n} ). 

This simplifies to 180 n + 360

The sum of the interior angles is 180( n – 2) = 180 n – 360

The difference is 180 n + 360 – (180 n -360) = 720°

22) Prism and force (Non-calculator)

The diagram shows a prism with an equilateral triangle cross-section.

When the prism is placed so that its triangular face touches the surface, the prism applies a force of 12 Newtons resulting in a pressure of \frac{ \sqrt{3} }{4} N/m^{2}

Given that the prism has a volume of 384 m 3 , find the length of the prism.

Pressure = \frac{Force}{Area}

Area = 12÷ \frac{ \sqrt{3} }{4} = 16\sqrt{3} m 2

Therefore, the length of the prism is 384 ÷ 16\sqrt{3} = 8\sqrt{3} m

23) Geometric sequences (Non-calculator)

A geometric sequence has a third term of 6 and a sixth term of 14 \frac{2}{9}

Find the first term of the sequence.

The third term is ar 2 = 6

The sixth term is ar 5 = \frac{128}{9}

Diving these terms gives r 3 = \frac{64}{27}

Giving r = \frac{4}{3}

Dividing the third term twice by \frac{4}{3} gives the first term a = \frac{27}{8}

24) Printing factory

A printing factory is producing exam papers. When all 10 of its printers are working, it can produce all of the exam papers in 12 days.

For the first two days of printing, 3 of the printers are broken.

At the beginning of the third day it is discovered that 2 more printers have broken down, so the factory continues to print with the reduced amount of printers for 3 days. The broken printers are repaired and now all printers are available to print the remaining exams.

How many days in total does it take the factory to produce all of the exam papers?

If we assume one printer prints 1 exam paper per day, 10 printers would print 120 exam papers in 12 days. Listing the number printed each day for the first 5 days gives:

Day 5: 5 

This is a total of 29 exam papers.

91 exam papers are remaining with 10 printers now able to produce a total of 10 exam papers each day. 10 more days would be required to complete the job.

Therefore, 15 days in total are required.

25) Circles

The diagram shows a circle with equation x^{2}+{y}^{2}=13 .

A tangent touches the circle at point P when x=3 and y is negative.

The tangent intercepts the coordinate axes at A and B .

Find the length AB .

Using the equation  x^{2}+y^{2}=13 to find the y value for P gives y=-2 .

The gradient of the radius at this point is - \frac{2}{3} , giving a tangent gradient of \frac{3}{2} .

Using the point (3,-2) in y = \frac {3}{2} x+c gives the equation of the tangent as y = \frac {3}{2} x – \frac{13}{2}

Substituting x=0 and y=0 gives A and B as (0 , -\frac {13}{2}) and ( \frac{13}{3} , 0)

Using Pythagoras’ Theorem gives the length of AB as ( \frac{ 13\sqrt{13} }{6} ) = 7.812.

26) Circle theorems

The diagram shows a circle with centre O . Points A, B, C and D are on the circumference of the circle. 

EF is a tangent to the circle at A . 

Angle EAD = 46°

Angle FAB = 48°

Angle ADC = 78°

Find the area of ABCD to the nearest integer.

The Alternate Segment Theorem gives angle ACD as 46° and angle ACB as 48°.

Opposite angles in a cyclic quadrilateral summing to 180° gives angle ABC as 102°.

Using the sine rule to find AC will give a length of 5.899. Using the sine rule again to find BC will give a length of 3.016cm.

We can now use the area of a triangle formula to find the area of both triangles.

0.5 × 5 × 5.899 × sin (46) + 0.5 × 3.016 × 5.899 × sin (48) = 17 units 2 (to the nearest integer).

27) Quadratic function

The quadratic function f(x) = -2x^{2} + 8x +11 has a turning point at P .

Find the coordinate of the turning point after the transformation -f(x-3) .

There are two methods that could be used. We could apply the transformation to the function and then complete the square, or, we could complete the square and then apply the transformation.

Here we will do the latter.

This gives a turning point for f(x) as (2,19).

Applying -f(x-3) gives the new turning point as (5,-19).

28) Probability with fruit

A fruit bowl contains only 5 grapes and n strawberries.

A fruit is taken, eaten and then another is selected.

The probability of taking two strawberries is \frac{7}{22} .

Find the probability of taking one of each fruit. 

There are n+5 fruits altogether.

P(Strawberry then strawberry)= \frac{n}{n+5} × \frac{n-1}{n+4} = \frac{7}{22}

This gives the quadratic equation 15n^{2} - 85n - 140 = 0

This can be divided through by 5 to give 3n^{2} - 17n- 28 = 0

This factorises to (n-7)(3n + 4) = 0

n must be positive so n = 7.

The probability of taking one of each fruit is therefore, \frac{5}{12} × \frac{7}{11} + \frac {7}{12} × \frac {5}{11} = \frac {70}{132}

29) Ice cream tub volume

An ice cream tub in the shape of a prism with a trapezium cross-section has the dimensions shown. These measurements are accurate to the nearest cm.

An ice cream scoop has a diameter of 4.5 cm to the nearest millimetre and will be used to scoop out spheres of ice cream from the tub.

Using bounds find a suitable approximation to the number of ice cream scoops that can be removed from a tub that is full.

We need to find the upper and lower bounds of the two volumes. 

Upper bound tub volume = 5665.625 cm 3

Lower bound tub volume = 4729.375 cm 3

Upper bound scoop volume = 49.32 cm 3  

Lower bound scoop volume = 46.14 cm 3  

We can divide the upper bound of the ice cream tub by the lower bound of the scoop to get the maximum possible number of scoops. 

Maximum number of scoops = 122.79

Then divide the lower bound of the ice cream tub by the upper bound of the scoop to get the minimum possible number of scoops.

Minimum number of scoops  = 95.89

These both round to 100 to 1 significant figure, Therefore, 100 scoops is a suitable approximation the the number of scoops.

30) Translating graphs

 The diagram shows the graph of y = a+tan(x-b ).

The graph goes through the points (75, 3) and Q (60, q).

Find exact values of a , b and q .

The asymptote has been translated to the right by 30°. 

Therefore, b=30

So the point (45,1) has been translated to the point (75,3). 

Therefore, a=2

We hope these problem solving maths questions will support your GCSE teaching. To get all the solutions and strategies in a printable form, please download the complete resource .

Looking for additional support and resources at KS3? You are welcome to download any of the secondary maths resources from Third Space Learning’s resource library for free. There is a section devoted to GCSE maths revision with plenty of maths worksheets and GCSE maths questions . There are also maths tests for KS3, including a Year 7 maths test , a Year 8 maths test and a Year 9 maths test Other valuable maths practice and ideas particularly around reasoning and problem solving at secondary can be found in our KS3 and KS4 maths blog articles. Try these fun maths problems for KS2 and KS3, SSDD problems , KS3 maths games and 30 problem solving maths questions . For children who need more support, our maths intervention programmes for KS3 achieve outstanding results through a personalised one to one tuition approach.

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Unit 7: Medium: Problem solving and data analysis

About this unit.

This unit tackles the medium-difficulty problem solving and data analysis questions on the SAT Math test. Work through each skill, taking quizzes and the unit test to level up your mastery progress.

Ratios, rates, and proportions: medium

• Ratios, rates, and proportions | SAT lesson (Opens a modal)
• Ratios, rates, and proportions — Basic example (Opens a modal)
• Ratios, rates, and proportions — Harder example (Opens a modal)
• Ratios, rates, and proportions: medium Get 3 of 4 questions to level up!

Unit conversion: medium

• Unit conversion | Lesson (Opens a modal)
• Units — Basic example (Opens a modal)
• Units — Harder example (Opens a modal)
• Unit conversion: medium Get 3 of 4 questions to level up!

Percentages: medium

• Percentages | Lesson (Opens a modal)
• Percents — Basic example (Opens a modal)
• Percents — Harder example (Opens a modal)
• Percentages: medium Get 3 of 4 questions to level up!

Center, spread, and shape of distributions: medium

• Center, spread, and shape of distributions | Lesson (Opens a modal)
• Center, spread, and shape of distributions — Basic example (Opens a modal)
• Center, spread, and shape of distributions — Harder example (Opens a modal)
• Center, spread, and shape of distributions: medium Get 3 of 4 questions to level up!

Data representations: medium

• Data representations | Lesson (Opens a modal)
• Key features of graphs — Basic example (Opens a modal)
• Key features of graphs — Harder example (Opens a modal)
• Data representations: medium Get 3 of 4 questions to level up!

Scatterplots: medium

• Scatterplots | Lesson (Opens a modal)
• Scatterplots — Basic example (Opens a modal)
• Scatterplots — Harder example (Opens a modal)
• Scatterplots: medium Get 3 of 4 questions to level up!

Linear and exponential growth: medium

• Linear and exponential growth | Lesson (Opens a modal)
• Linear and exponential growth — Basic example (Opens a modal)
• Linear and exponential growth — Harder example (Opens a modal)
• Linear and exponential growth: medium Get 3 of 4 questions to level up!

Probability and relative frequency: medium

• Probability and relative frequency | Lesson (Opens a modal)
• Table data — Basic example (Opens a modal)
• Table data — Harder example (Opens a modal)
• Probability and relative frequency: medium Get 3 of 4 questions to level up!

Data inferences: medium

• Data inferences | Lesson (Opens a modal)
• Data inferences — Basic example (Opens a modal)
• Data inferences — Harder example (Opens a modal)
• Data inferences: medium Get 3 of 4 questions to level up!

Evaluating statistical claims: medium

• Evaluating statistical claims | Lesson (Opens a modal)
• Data collection and conclusions — Basic example (Opens a modal)
• Data collection and conclusions — Harder example (Opens a modal)
• Evaluating statistical claims: medium Get 3 of 4 questions to level up!

The resources on this page will hopefully help you teach AO2 and AO3 of the new GCSE specification - problem solving and reasoning.

This brief lesson is designed to lead students into thinking about how to solve mathematical problems. It features ideas of strategies to use, clear steps to follow and plenty of opportunities for discussion.

The PixiMaths problem solving booklets are aimed at "crossover" marks (questions that will be on both higher and foundation) so will be accessed by most students. The booklets are collated Edexcel exam questions; you may well recognise them from elsewhere. Each booklet has 70 marks worth of questions and will probably last two lessons, including time to go through answers with your students. There is one for each area of the new GCSE specification and they are designed to complement the PixiMaths year 11 SOL.

These problem solving starter packs are great to support students with problem solving skills. I've used them this year for two out of four lessons each week, then used Numeracy Ninjas as starters for the other two lessons.  When I first introduced the booklets, I encouraged my students to use scaffolds like those mentioned here , then gradually weaned them off the scaffolds. I give students some time to work independently, then time to discuss with their peers, then we go through it as a class. The levels correspond very roughly to the new GCSE grades.

Some of my favourite websites have plenty of other excellent resources to support you and your students in these assessment objectives.

@TessMaths has written some great stuff for BBC Bitesize.

There are some intersting though-provoking problems at Open Middle.

I'm sure you've seen it before, but if not, check it out now! Nrich is where it's at if your want to provide enrichment and problem solving in your lessons.

MathsBot  by @StudyMaths has everything, and if you scroll to the bottom of the homepage you'll find puzzles and problem solving too.

I may be a little biased because I love Edexcel, but these question packs are really useful.

The UKMT has a mentoring scheme that provides fantastic problem solving resources , all complete with answers.

I have only recently been shown Maths Problem Solving and it is awesome - there are links to problem solving resources for all areas of maths, as well as plenty of general problem solving too. Definitely worth exploring!

Succeed at Exams

• Study for Exams
• Set Up Your Study Environment
• Write Online Exams
• Write In-Person Exams
• Manage Exam Stress
• Multiple Choice Exams
• Multiple Choice Sample Questions
• Short-Answer Exams
• Prepare for Essay Exams
• Write Essay Exams

What is a problem-solving exam?

What are some strategies for studying for problem-solving exams, what are some strategies for writing problem-solving exams, what can i do after the exam.

• Analyze Exam Errors

Ask Us: Chat, email, visit or call

More help: Studying

• Book Studying Appointments
• Problem-solving exams come in a variety of formats, from multiple choice, to short answer, to long calculations.
• They frequently test your ability to apply the problem-solving skills you’ve learned in lectures, labs, and readings to new types of questions.
• Pay attention to example problems emphasized in class, the text, and assignments, especially those that appear in more than one of these places.
• Don’t assume, however, that the same or similar problems will appear on the exam. The exam will likely test your ability to apply what you’ve learned about solving problems to new types of questions, rather than your ability to memorize and regurgitate examples you’ve already seen.
• Focus on the process the instructor used for solving the problem.  Think about your own problem-solving strategies.
• Practise, practise, practise! The more problems, and more importantly, the more types of problems you solve, the better prepared you’ll be.
• Look for connections between concepts and equations and note how to choose the correct equation in complex practice problems.
• Generate your own test questions with a study group or partner. Practise answering questions within a limited time frame.
• Review previous tests, quizzes, or midterms, and figure out why you lost marks before.
• Look over the entire exam before beginning and budget your time according to how much each question is worth.  Leave enough time to read over your answers at the end of the exam.
• Before starting, find a blank page on your exam and write down equations, concepts, and constants that you memorized.
• Do the easy questions first to warm up your brain and calm exam nerves.
• Read the questions carefully and rephrase them in your own words.
• Keep track of all units. Convert values to keep the units consistent. Be aware of +/- signs.
• Clearly mark assumptions, if they are necessary, and place them at or near the beginning of the solution whenever possible.
• It can be helpful to look over your exam if you get it back to see where you have gone wrong, and what you have done well. If your instructor doesn’t routinely return exams, ask if you can see your exam to learn from your errors.
• Use this information to help you study more effectively next time.
• Check out the error analysis LibGuide to help you go over feedback.
• << Previous: Write Essay Exams
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• Last Updated: Apr 25, 2024 1:41 PM
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How Good Is Your Problem Solving?

© iStockphoto Entienou

Use a systematic approach.

Good problem solving skills are fundamentally important if you're going to be successful in your career.

But problems are something that we don't particularly like.

They're time-consuming.

They muscle their way into already packed schedules.

They force us to think about an uncertain future.

And they never seem to go away!

That's why, when faced with problems, most of us try to eliminate them as quickly as possible. But have you ever chosen the easiest or most obvious solution – and then realized that you have entirely missed a much better solution? Or have you found yourself fixing just the symptoms of a problem, only for the situation to get much worse?

To be an effective problem-solver, you need to be systematic and logical in your approach. This quiz helps you assess your current approach to problem solving. By improving this, you'll make better overall decisions. And as you increase your confidence with solving problems, you'll be less likely to rush to the first solution – which may not necessarily be the best one.

Once you've completed the quiz, we'll direct you to tools and resources that can help you make the most of your problem-solving skills.

How Good Are You at Solving Problems?

Instructions.

For each statement, click the button in the column that best describes you. Please answer questions as you actually are (rather than how you think you should be), and don't worry if some questions seem to score in the 'wrong direction'. When you are finished, please click the 'Calculate My Total' button at the bottom of the test.

Your last quiz results are shown.

You last completed this quiz on , at .

Score Interpretation

Answering these questions should have helped you recognize the key steps associated with effective problem solving.

This quiz is based on Dr Min Basadur's Simplexity Thinking    problem-solving model. This eight-step process follows the circular pattern shown below, within which current problems are solved and new problems are identified on an ongoing basis. This assessment has not been validated and is intended for illustrative purposes only. 

Figure 1 – The Simplexity Thinking Process

Reproduced with permission from Dr Min Basadur from "The Power of Innovation: How to Make Innovation a Part of Life & How to Put Creative Solutions to Work" Copyright ©1995

Below, we outline the tools and strategies you can use for each stage of the problem-solving process. Enjoy exploring these stages!

Step 1: Find the Problem

(Questions 7, 12)

Some problems are very obvious, however others are not so easily identified. As part of an effective problem-solving process, you need to look actively for problems – even when things seem to be running fine. Proactive problem solving helps you avoid emergencies and allows you to be calm and in control when issues arise.

These techniques can help you do this:

• PEST Analysis   helps you pick up changes to your environment that you should be paying attention to. Make sure too that you're watching changes in customer needs and market dynamics, and that you're monitoring trends that are relevant to your industry.
• Risk Analysis   helps you identify significant business risks.
• Failure Modes and Effects Analysis   helps you identify possible points of failure in your business process, so that you can fix these before problems arise.
• After Action Reviews   help you scan recent performance to identify things that can be done better in the future.
• Where you have several problems to solve, our articles on Prioritization   and Pareto Analysis   help you think about which ones you should focus on first.

Step 2: Find the Facts

(Questions 10, 14)

After identifying a potential problem, you need information. What factors contribute to the problem? Who is involved with it? What solutions have been tried before? What do others think about the problem?

If you move forward to find a solution too quickly, you risk relying on imperfect information that's based on assumptions and limited perspectives, so make sure that you research the problem thoroughly.

Step 3: Define the Problem

(Questions 3, 9)

Now that you understand the problem, define it clearly and completely. Writing a clear problem definition forces you to establish specific boundaries for the problem. This keeps the scope from growing too large, and it helps you stay focused on the main issues.

A great tool to use at this stage is CATWOE   . With this process, you analyze potential problems by looking at them from six perspectives, those of its Customers; Actors (people within the organization); the Transformation, or business process; the World-view, or top-down view of what's going on; the Owner; and the wider organizational Environment. By looking at a situation from these perspectives, you can open your mind and come to a much sharper and more comprehensive definition of the problem.

Cause and Effect Analysis   is another good tool to use here, as it helps you think about the many different factors that can contribute to a problem. This helps you separate the symptoms of a problem from its fundamental causes.

Step 4: Find Ideas

(Questions 4, 13)

With a clear problem definition, start generating ideas for a solution. The key here is to be flexible in the way you approach a problem. You want to be able to see it from as many perspectives as possible. Looking for patterns or common elements in different parts of the problem can sometimes help. You can also use metaphors   and analogies to help analyze the problem, discover similarities to other issues, and think of solutions based on those similarities.

Traditional brainstorming   and reverse brainstorming   are very useful here. By taking the time to generate a range of creative solutions to the problem, you'll significantly increase the likelihood that you'll find the best possible solution, not just a semi-adequate one. Where appropriate, involve people with different viewpoints to expand the volume of ideas generated.

Don't evaluate your ideas until step 5. If you do, this will limit your creativity at too early a stage.

Step 5: Select and Evaluate

(Questions 6, 15)

After finding ideas, you'll have many options that must be evaluated. It's tempting at this stage to charge in and start discarding ideas immediately. However, if you do this without first determining the criteria for a good solution, you risk rejecting an alternative that has real potential.

Decide what elements are needed for a realistic and practical solution, and think about the criteria you'll use to choose between potential solutions.

Paired Comparison Analysis   , Decision Matrix Analysis   and Risk Analysis   are useful techniques here, as are many of the specialist resources available within our Decision-Making section . Enjoy exploring these!

Step 6: Plan

(Questions 1, 16)

You might think that choosing a solution is the end of a problem-solving process. In fact, it's simply the start of the next phase in problem solving: implementation. This involves lots of planning and preparation. If you haven't already developed a full Risk Analysis   in the evaluation phase, do so now. It's important to know what to be prepared for as you begin to roll out your proposed solution.

The type of planning that you need to do depends on the size of the implementation project that you need to set up. For small projects, all you'll often need are Action Plans   that outline who will do what, when, and how. Larger projects need more sophisticated approaches – you'll find out more about these in the Mind Tools Project Management section. And for projects that affect many other people, you'll need to think about Change Management   as well.

Here, it can be useful to conduct an Impact Analysis   to help you identify potential resistance as well as alert you to problems you may not have anticipated. Force Field Analysis   will also help you uncover the various pressures for and against your proposed solution. Once you've done the detailed planning, it can also be useful at this stage to make a final Go/No-Go Decision   , making sure that it's actually worth going ahead with the selected option.

Step 7: Sell the Idea

(Questions 5, 8)

As part of the planning process, you must convince other stakeholders that your solution is the best one. You'll likely meet with resistance, so before you try to “sell” your idea, make sure you've considered all the consequences.

As you begin communicating your plan, listen to what people say, and make changes as necessary. The better the overall solution meets everyone's needs, the greater its positive impact will be! For more tips on selling your idea, read our article on Creating a Value Proposition   and use our Sell Your Idea   Bite-Sized Training session.

Step 8: Act

(Questions 2, 11)

Finally, once you've convinced your key stakeholders that your proposed solution is worth running with, you can move on to the implementation stage. This is the exciting and rewarding part of problem solving, which makes the whole process seem worthwhile.

This action stage is an end, but it's also a beginning: once you've completed your implementation, it's time to move into the next cycle of problem solving by returning to the scanning stage. By doing this, you'll continue improving your organization as you move into the future.

Problem solving is an exceptionally important workplace skill.

Being a competent and confident problem solver will create many opportunities for you. By using a well-developed model like Simplexity Thinking for solving problems, you can approach the process systematically, and be comfortable that the decisions you make are solid.

Given the unpredictable nature of problems, it's very reassuring to know that, by following a structured plan, you've done everything you can to resolve the problem to the best of your ability.

This site teaches you the skills you need for a happy and successful career; and this is just one of many tools and resources that you'll find here at Mind Tools. Subscribe to our free newsletter , or join the Mind Tools Club and really supercharge your career!

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Comments (220)

• Over a month ago Sonia_H wrote Hi PANGGA, This is great news! Thanks for sharing your experience. We hope these 8 steps outlined will help you in multiple ways. ~Sonia Mind Tools Coach
• Over a month ago PANGGA wrote Thank you for this mind tool. I got to know my skills in solving problem. It will serve as my guide on facing and solving problem that I might encounter.
• Over a month ago Sarah_H wrote Wow, thanks for your very detailed feedback HardipG. The Mind Tools team will take a look at your feedback and suggestions for improvement. Best wishes, Sarah Mind Tools Coach

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• When you’re studying, be sure to work in a way that tests and extends your knowledge: just having read the textbook or jumping to the solutions can give you a false sense of knowing the information.
• Study problems out of sequence: mixing problem types when you’re preparing will help you in an exam situation where questions come from different parts of the course.
• If you’re not allowed aid sheets in the exam, think about what you’d wish to have in the exam room, and work on memorizing it. For instance, in the first few minutes of an exam, you can write out a list of equations and associated instructional verbs to make sure you have them while you’re problem solving.
• Write problems and solutions out in full: double-check that you haven’t made any transcription errors, and do every step on paper so that you can double-check your answers and earn partial marks.

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• Problem Solving I: Frequent Solver (Richard Zajchowski for McMaster University)
• Problem Solving II: Concepts (Richard Zajchowski for McMaster University)
• Problem Solving III: Decision Steps (Richard Zajchowski for McMaster University)

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GMAT Quant Questions: Problem Solving

Note: GMAT Quant questions cover Problem Solving, and so much more. Be sure to use our GMAT Practice Test to test your knowledge of these concepts.

On the GMAT Quantitative section, the Problem Solving questions are just the familiar five-choice multiple choice math problems you have seen on every standardized test since well before puberty.  Here, you have discovered a veritable treasure chest of Problem Solving sample questions.  

Below is a link to thirty-two different articles on this blog, each with at least two Problem Solving questions.  The sample GMAT Problem Solving questions are often at the top of the article, although sometimes they are further down in the text.  The total number of sample Problem Solving problems available from this page is far more than 37, the total number of math questions you will see on a full Quantitative section of the GMAT. 

In each blog, the solutions & explanations to the sample questions are at the ends of the articles.  (If the topic is less than crystal clear for you, you may find the article itself enlightening.)

1. Problems with Averages

https://magoosh.com/gmat/math/gmat-averages-and-sums-formulas/

2. Distance, Rate, Time

https://magoosh.com/gmat/math/word-problems/gmat-distance-and-work-rate-formula/

3. Permutations & Combinations

https://magoosh.com/gmat/math/gmat-permutations-and-combinations/

4. Factors & Prime Factorizations ( five practice PS questions at the bottom of the article )

https://magoosh.com/gmat/math/arithmetic/gmat-math-factors/

5. Advanced Geometric Solids

https://magoosh.com/gmat/math/geometry/gmat-math-advanced-geometric-solids/

6. Estimation questions

https://magoosh.com/gmat/math/the-power-of-estimation-for-gmat-quant/

7. Difficult Dice Questions

https://magoosh.com/gmat/math/basics/gmat-probability-difficult-dice-questions/

8. Difference of Two Squares

https://magoosh.com/gmat/math/algebra/gmat-quant-difference-of-two-squares/

9. Sequences ( five PS practice questions scattered through article )

https://magoosh.com/gmat/math/word-problems/sequences-on-the-gmat/

10. Remainders

https://magoosh.com/gmat/math/basics/gmat-quant-thoughts-on-remainders/

11. Work & Work Rate

https://magoosh.com/gmat/2012/gmat-work-rate-questions/

12. Circle & Line Diagrams

https://magoosh.com/gmat/math/geometry/circle-and-line-diagrams-on-the-gmat/

13. Polygons

https://magoosh.com/gmat/math/geometry/polygons-and-regular-polygons-on-the-gmat/

14. Set Problems, with Double Matrix Method

https://magoosh.com/gmat/math/word-problems/gmat-sets-double-matrix-method/

15. Set Problems, with Venn Diagrams

https://magoosh.com/gmat/math/word-problems/gmat-sets-venn-diagrams/

16. Scale Factor & Percent Change

https://magoosh.com/gmat/math/geometry/scale-factors-on-the-gmat-percent-increases-and-decreases/

17. Standard Deviation

https://magoosh.com/gmat/math/standard-deviation-on-the-gmat/

18. Radicals

https://magoosh.com/gmat/math/algebra/simplifying-radical-expressions-on-the-gmat/

19. Function Notation

https://magoosh.com/gmat/math/arithmetic/function-notation-on-the-gmat/

20. Algebraic Factoring

https://magoosh.com/gmat/math/algebra/algebra-on-the-gmat-how-to-factor/

21. Hard Factorial Problems

https://magoosh.com/gmat/math/arithmetic/gmat-factorials/

22. Backsolving from the answers

https://magoosh.com/gmat/math/gmat-plugging-in-strategy-always-start-with-answer-choice-c/

23. Distance in the x-y plane

https://magoosh.com/gmat/math/geometry/gmat-coordinate-geometry-distance-between-two-points/

24. Pythagoras !

https://magoosh.com/gmat/math/geometry/pythagorean-triplets-to-memorize-for-the-gmat/

25. Lines in the x-y plane

https://magoosh.com/gmat/math/geometry/gmat-math-lines-slope-in-the-x-y-plane/

26. Tricks for Calculating Combinations

https://magoosh.com/gmat/math/gmat-math-calculating-combinations/

27. Parallel & Perpendicular Lines and Midpoints in the x-y plane

https://magoosh.com/gmat/math/geometry/gmat-math-midpoints-and-parallel-vs-perpendicular-lines/

28. Probability: AND & OR Rules

https://magoosh.com/gmat/2012/gmat-math-probability-rules/

29. Probability: “at least” statements

https://magoosh.com/gmat/math/basics/gmat-math-the-probability-at-least-question/

30. Probability: counting problems

https://magoosh.com/gmat/math/gmat-probability-and-counting-techniques/

31. Hard counting problems

https://magoosh.com/gmat/math/word-problems/gmat-counting-with-restrictions/

32. Probability: geometric probability

https://magoosh.com/gmat/math/geometry/geometric-probability-on-the-gmat/

Also check out these GMAT Probability questions .

Other GMAT Practice Questions

Magoosh has practice materials for all of the GMAT question types in GMAT Quantitative  and in GMAT Verbal. Look at the table below, and click the links for more practice!

And make sure you do practice questions that cover the most common GMAT Quant concepts too.

Addendum to the table: A special note on Sentence Correction questions

Sentence Correction questions are the very shortest questions on the test, both in terms of word count and time. Ideally, you should complete any SC question in less than one minute. Make sure you set your speed for this question type carefully. And be aware that Sentence Correction questions do NOT have their own subsection in GMAT Verbal; instead, SC is mixed in with Critical Reasoning and Reading Comprehension on the GMAT.

Mike served as a GMAT Expert at Magoosh, helping create hundreds of lesson videos and practice questions to help guide GMAT students to success. He was also featured as “member of the month” for over two years at GMAT Club . Mike holds an A.B. in Physics (graduating magna cum laude ) and an M.T.S. in Religions of the World, both from Harvard. Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike’s Youtube video explanations and resources like What is a Good GMAT Score? and the GMAT Diagnostic Test .

View all posts

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Self-Assessment • 20 min read

How Good Is Your Problem Solving?

Use a systematic approach..

By the Mind Tools Content Team

Good problem solving skills are fundamentally important if you're going to be successful in your career.

But problems are something that we don't particularly like.

They're time-consuming.

They muscle their way into already packed schedules.

They force us to think about an uncertain future.

And they never seem to go away!

That's why, when faced with problems, most of us try to eliminate them as quickly as possible. But have you ever chosen the easiest or most obvious solution – and then realized that you have entirely missed a much better solution? Or have you found yourself fixing just the symptoms of a problem, only for the situation to get much worse?

To be an effective problem-solver, you need to be systematic and logical in your approach. This quiz helps you assess your current approach to problem solving. By improving this, you'll make better overall decisions. And as you increase your confidence with solving problems, you'll be less likely to rush to the first solution – which may not necessarily be the best one.

Once you've completed the quiz, we'll direct you to tools and resources that can help you make the most of your problem-solving skills.

How Good Are You at Solving Problems?

Instructions.

For each statement, click the button in the column that best describes you. Please answer questions as you actually are (rather than how you think you should be), and don't worry if some questions seem to score in the 'wrong direction'. When you are finished, please click the 'Calculate My Total' button at the bottom of the test.

Answering these questions should have helped you recognize the key steps associated with effective problem solving.

This quiz is based on Dr Min Basadur's Simplexity Thinking problem-solving model. This eight-step process follows the circular pattern shown below, within which current problems are solved and new problems are identified on an ongoing basis. This assessment has not been validated and is intended for illustrative purposes only.

Below, we outline the tools and strategies you can use for each stage of the problem-solving process. Enjoy exploring these stages!

Step 1: Find the Problem (Questions 7, 12)

Some problems are very obvious, however others are not so easily identified. As part of an effective problem-solving process, you need to look actively for problems – even when things seem to be running fine. Proactive problem solving helps you avoid emergencies and allows you to be calm and in control when issues arise.

These techniques can help you do this:

PEST Analysis helps you pick up changes to your environment that you should be paying attention to. Make sure too that you're watching changes in customer needs and market dynamics, and that you're monitoring trends that are relevant to your industry.

Risk Analysis helps you identify significant business risks.

Failure Modes and Effects Analysis helps you identify possible points of failure in your business process, so that you can fix these before problems arise.

After Action Reviews help you scan recent performance to identify things that can be done better in the future.

Where you have several problems to solve, our articles on Prioritization and Pareto Analysis help you think about which ones you should focus on first.

Step 2: Find the Facts (Questions 10, 14)

After identifying a potential problem, you need information. What factors contribute to the problem? Who is involved with it? What solutions have been tried before? What do others think about the problem?

If you move forward to find a solution too quickly, you risk relying on imperfect information that's based on assumptions and limited perspectives, so make sure that you research the problem thoroughly.

Step 3: Define the Problem (Questions 3, 9)

Now that you understand the problem, define it clearly and completely. Writing a clear problem definition forces you to establish specific boundaries for the problem. This keeps the scope from growing too large, and it helps you stay focused on the main issues.

A great tool to use at this stage is CATWOE . With this process, you analyze potential problems by looking at them from six perspectives, those of its Customers; Actors (people within the organization); the Transformation, or business process; the World-view, or top-down view of what's going on; the Owner; and the wider organizational Environment. By looking at a situation from these perspectives, you can open your mind and come to a much sharper and more comprehensive definition of the problem.

Cause and Effect Analysis is another good tool to use here, as it helps you think about the many different factors that can contribute to a problem. This helps you separate the symptoms of a problem from its fundamental causes.

Step 4: Find Ideas (Questions 4, 13)

With a clear problem definition, start generating ideas for a solution. The key here is to be flexible in the way you approach a problem. You want to be able to see it from as many perspectives as possible. Looking for patterns or common elements in different parts of the problem can sometimes help. You can also use metaphors and analogies to help analyze the problem, discover similarities to other issues, and think of solutions based on those similarities.

Traditional brainstorming and reverse brainstorming are very useful here. By taking the time to generate a range of creative solutions to the problem, you'll significantly increase the likelihood that you'll find the best possible solution, not just a semi-adequate one. Where appropriate, involve people with different viewpoints to expand the volume of ideas generated.

Tip: Don't evaluate your ideas until step 5. If you do, this will limit your creativity at too early a stage.

Step 5: Select and Evaluate (Questions 6, 15)

After finding ideas, you'll have many options that must be evaluated. It's tempting at this stage to charge in and start discarding ideas immediately. However, if you do this without first determining the criteria for a good solution, you risk rejecting an alternative that has real potential.

Decide what elements are needed for a realistic and practical solution, and think about the criteria you'll use to choose between potential solutions.

Paired Comparison Analysis , Decision Matrix Analysis and Risk Analysis are useful techniques here, as are many of the specialist resources available within our Decision-Making section . Enjoy exploring these!

Step 6: Plan (Questions 1, 16)

You might think that choosing a solution is the end of a problem-solving process. In fact, it's simply the start of the next phase in problem solving: implementation. This involves lots of planning and preparation. If you haven't already developed a full Risk Analysis in the evaluation phase, do so now. It's important to know what to be prepared for as you begin to roll out your proposed solution.

The type of planning that you need to do depends on the size of the implementation project that you need to set up. For small projects, all you'll often need are Action Plans that outline who will do what, when, and how. Larger projects need more sophisticated approaches – you'll find out more about these in the article What is Project Management? And for projects that affect many other people, you'll need to think about Change Management as well.

Here, it can be useful to conduct an Impact Analysis to help you identify potential resistance as well as alert you to problems you may not have anticipated. Force Field Analysis will also help you uncover the various pressures for and against your proposed solution. Once you've done the detailed planning, it can also be useful at this stage to make a final Go/No-Go Decision , making sure that it's actually worth going ahead with the selected option.

Step 7: Sell the Idea (Questions 5, 8)

As part of the planning process, you must convince other stakeholders that your solution is the best one. You'll likely meet with resistance, so before you try to “sell” your idea, make sure you've considered all the consequences.

As you begin communicating your plan, listen to what people say, and make changes as necessary. The better the overall solution meets everyone's needs, the greater its positive impact will be! For more tips on selling your idea, read our article on Creating a Value Proposition and use our Sell Your Idea Skillbook.

Step 8: Act (Questions 2, 11)

Finally, once you've convinced your key stakeholders that your proposed solution is worth running with, you can move on to the implementation stage. This is the exciting and rewarding part of problem solving, which makes the whole process seem worthwhile.

This action stage is an end, but it's also a beginning: once you've completed your implementation, it's time to move into the next cycle of problem solving by returning to the scanning stage. By doing this, you'll continue improving your organization as you move into the future.

Problem solving is an exceptionally important workplace skill.

Being a competent and confident problem solver will create many opportunities for you. By using a well-developed model like Simplexity Thinking for solving problems, you can approach the process systematically, and be comfortable that the decisions you make are solid.

Given the unpredictable nature of problems, it's very reassuring to know that, by following a structured plan, you've done everything you can to resolve the problem to the best of your ability.

This assessment has not been validated and is intended for illustrative purposes only. It is just one of many Mind Tool quizzes that can help you to evaluate your abilities in a wide range of important career skills.

If you want to reproduce this quiz, you can purchase downloadable copies in our Store .

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McKinsey PST: Question Types, Study Plan & Mock Tests

The McKinsey Problem Solving Test (McKinsey PST) is a very crucial part of the McKinsey recruitment process. It is where most of the applicant pool is eliminated, and yet there are so few resources to help you prepare for it. Fortunately, you’ve found the ultimate guide to nail the test with an unbelievable level of detail!

Table of Contents

McKinsey PST overview

What is the mckinsey pst.

The McKinsey Problem Solving Test (or PST) is a paper-based test used at McKinsey & Company to select candidates for the case interviews. The PST is conducted after resume screening; it has 6 types of question, testing the candidate on 3 crucial problem-solving skills – data interpretation, mental calculations and logical reasoning.

McKinsey PST passing score / Acceptance rate

McKinsey has never officially stated the passing score or acceptance rate for the PST. However, these numbers can be estimated using reports from test-takers, with passing score being around 70%, and acceptance rate at roughly 30-35% (1 in every 3 candidates will pass).

Does McKinsey still use the PST?

Currently, the McKinsey PST is being replaced by the new Problem-Solving Game. However, the transition is not complete globally. In addition, the new Problem-Solving Game still retains the core principles from the old test, so preparing for the PST is still relevant.

Why do they need PST?

It’s very similar to what we have here! McKinsey believes that the gap between CV screening and in-person case interviews is too big. The firm may miss many good candidates with bad resumes or may interview too many candidates who don’t live up to their resumes.

At the end of the day, in-person interviews are expensive, and the Problem Solving Test provides a cost-effective solution.

Who has to take the McKinsey PST?

Every candidate who passes the resume screening round has to take the McKinsey PST – if they apply for the management consulting track. Some report indicates that MBA applicants might be waived from the test – however, this is rare and you should confirm with the target office HR.

What does PST look like?

26 questions, 1 hour, paper-based, and no calculator! The test has 26 multiple choice questions set within the context of 3 business cases. A candidate has exactly 60 minutes to finish the test. He will be provided with a watch, pencils, scratch paper, and the test is in a paper-based format. No calculator is allowed. No personal assistant is allowed. Just you and the test!

As the business landscape is changing, candidate recruitment has become increasingly complex. This requires another way of presenting PST content for McKinsey. They have changed the format into gamification and planned to implement this method to all McKinsey offices within 2020. Visit the mock game designed exclusively for MConsultingPrep followers!

PST vs. GMAT vs. SAT?

If you are new to PST, you may hear the myth that PST is similar to the Math section in GMAT or SAT. In fact, being excellent in SAT Math does help with quantitative calculation in PST, however, the context is different. The SAT Math section includes only simple calculations in simple context; meanwhile, logic in business problems is highly emphasized in PST.

Why is this test so challenging?

• You will not have enough time to properly think through each question.

If you are going to read every single word in the case background and do every calculation “asked”, you will not be able to finish the test. You will need to know how to work through stress and pressure, how to give out “high-probability” answers instead of “exactly-right” ones, and how to painlessly skip questions.

• You will be judged by a machine (or if by a person, they will try to be like a machine).

I myself feel much more comfortable in an in-person case interview, where I will be fine as long as I have the right tactics. The interviewers generally allow candidates to make a few mistakes here and there, to slow down the process if needed, and to ask for help when necessary. In the PST, the result is all that matters. There will be no mercy granted. If you don’t get enough correct answers, you are out.

• On top of those, the questions themselves are hard!

A huge amount of logical and analytical reasoning is required. You will need to really grasp the logical fundamentals of how management consultants solve problems, e.g: the difference between a conclusion vs a hypothesis; etc.

How to prepare for the McKinsey PST?

Step 1 : Seek confirmation from the target office if you must take the PST

Step 2: Get familiar with official sample tests from McKinsey

Step 3 : Learn the logic of each question type, common mistakes, and how to answer correctly

Step 4: Practice mental math to improve calculation speed and accuracy

Step 5 : Practice speed reading and data selection

Step 6 : Practice answering individual question type under time pressure

Step 7 : Do one mock test with simulated test conditions

Step 8 : Review the test and your performance

Step 9 : Return to step 3, 4, 5, 6 to for further practice on weakness

Step 10 : Do mock test again, repeat until you can confidently hit 90% or more

McKinsey PST question types

Some emailed me and asked what they should do if there were 3 days left until the PST. I would still suggest you follow our spirit of learning. When you have little time, choose which question you want to prioritize, tackle it carefully and decide how deep you will go into it. If I were in your shoes, I would use this prioritization table

In addition to the above, I would suggest you practice your math in these last days. The learning curve at the beginning is usually high for anything, including  Mental Math . Doing better math can significantly improve your test score. It reduces simple mistakes (which can still cost you points) and allows you to have more time for other questions.

McKinsey PST study plan

These are the same steps I took to pass the PST years ago, and the basis for my product – the PST Comprehensive Package which has helped countless candidates pass this notoriously difficult consulting test.

Step 1. Answer the questions correctly

You are recommended to first answer all the test questions correctly without time pressure. Before, you need to break down all the questions into 6 question types as below. Besides, it is necessary to understand how these questions are constructed, what are their logical foundation, and even how the wrong choices are made.

Step 2. Answer the questions quickly

There will be no turning point that indicates you it is about time to move to the second step, but you should gradually try to answer the questions both correctly and quickly. Once getting all the correct answers without clocking, you should put yourself under time constraint. If you don’t know how to increase your speed, you have better to start with 3 tips below:

#1. Increase your reading speed.

The PST contains 3 business cases with various number and case context, which requires you to read as fast as possible (of course correctly). Many candidates cannot finish their PST because of being overwhelmed in text. The Princeton intensive program is helpfulto increase your speed by 2 times faster without difficulties.

#2. Increase your calculator speed.

Half of the test involves math, which have no way to improve but practice rigorously. The more you practice, the better you gain. If you haven’t found any efficient tips, try our method to score well with Mental Math!

#3. Embrace test-hacking tips.

After years of coaching students to MBB, I have collected wonderful tips and tricks to nail your test with less effort! Find out some of those tricks as below or check out the McKinsey PST Comprehensive for more detail!

Reading facts

Reading-facts is the most common question type in the McKinsey PST (38%) and the BCG Potential Test (up to 100%). These questions test your ability to understand the facts/data itself. There will be no inferring, logic, hypothesizing, or creativity needed. Instead, proficiency in chart reading and calculations will be handy here. See the picture below for an illustration.

QUESTION FORMAT

The following are a few examples of typical question formats:

• Which of the following values is the best estimate of…?
• Which of the following statements is valid based on the data…?
• Which of the following can be concluded from Exhibit…?

Sometimes even though the word “conclude” is used, questions don’t require any logical reasoning, just your ability to read facts and perform basic calculations. In these cases, I still classify these questions into the reading-facts category.

SAMPLE QUESTION

This question is written based on an official McKinsey practice PST.

Which of the following statements is valid based on the data in Table 1?

A) Soccer revenue was more than $325 thousand five years ago

B) Tennis revenue grew by no less than 1.2% in each of the last five years

C) The total revenue of Saigon League did not grow at all in the last five years

D) If the growth rate in the last 5 years is maintained, Soccer revenue will be more than $420K 5 years from now.

You will see that no tricky logical reasoning is needed here. All you need in order to answer these questions is the ability to read the table and perform calculations correctly.

COMMON MISTAKES

A good way to determine the correct option is to investigate if the other three are wrong. Now there are two ways you can be wrong in this type of PST question: (1) Incorrect calculation and (2) Misread the facts/ data

Type #2 is harder to understand, so I will dive deeper into that here. Let’s look at the sample question above. Hope you got D, the correct choice.

Example 1: How you can misread the data – Why A is wrong

If you overlook the phrase “Average annual” on column 3′s title, then Soccer revenue 5 years ago would be: $342.8 k / (100% + 4.5%) = $328 k, which is more than $325 thousand. Revenue grew at an average rate of 4.5% in EACH of the last 5 years. It is NOT 4.5% over the whole period of 5 years.

Example 2: How you can misread the data – Why B is wrong

If you overlook the phrase “Average” in column 3′s title, then it seems like the growth rate for each of the last 5 years is exactly 1.2%, no more, no less. B, therefore, seems correct. However, as indicated in the table, 1.2% is just an average figure, which means there are years with a lower or higher growth rate.

Example 3: How you can misread the data – Why C is wrong

If you overlook the second column of the table (Revenue this year column), then it seems like the average overall growth rate for Saigon League is 0% (4.5% + 3.3% + 1.2% – 9% = 0%), which makes C correct. However, different lines have different sizes. Even though Golf had negative growth of 9%, it is a relatively small line so its impact on the overall rate is small as well.

Hope that you will not make this mistake in your real PST. Again, PST is a simple test… when you have enough time!

PREPARATION GUIDE

Skill #1: Calculation

We have a detailed article on Consulting Math and how to strengthen your quantitative proficiency.

Skill #2: Chart/exhibit/table reading

Always take a moment to read and understand every single chart or graph you encounter in your everyday life.After all, practice makes perfect.

You can also improve your reading speed through an amazing speed reading program by Princeton University .

Skill #3: Attention to details

The devil is in the details. It’s the little things that can make or break a project, and no true consultants would let themselves be caught unaware.

Develop a habit in daily life. Have the mindset that I am not going to miss any stupid details.

For every practice question you get in this type, make sure you understand not only why an answer is right, but also why an answer is wrong, exactly like what I did above.

PRACTICE QUESTIONS

Which of the following statements is valid based on the data provided on Graph 3 above?

A) The Service-to-Agriculture ratio increased by more than 3 times between 1995 and 2007

B) Service GDP in 1995 is more than Industry GDP in 2007

C) Agriculture is where GDP value dropped the most between 1995 and 2007

D) In 2007, Service GDP is no less than 6 times Agriculture GDP

Correct answer: D

If you want to practice more, check out my PST Comprehensive Package for questions and answers!

Fact-based conclusion

Once you get into consulting, you will probably hear the term “fact-based” a million times a day. Consulting is the business of making conclusions based on facts. Consultants face tons of different problems throughout the course of any project: from the top to the granular level, from function to function, from industry to industry, etc. Fact-based conclusion is such a fundamental aspect of consulting that it weighs in heavily on the PST.

Fact-based conclusion questions test your ability to draw and recognize sound and logical conclusions based on a set of data/facts provided. See the picture below for an illustration.

• Which of the following statements is a valid conclusion based on …?
• Which of the following statements can be concluded from …?

The McKinsey team has an interview with the Chief Operating Officer of the New Bingham Mine, Salt Lake City. During the interview, the following facts have been gathered:

• The factory must have at least one safety inspector 24 hours a day, seven days a week, in accordance with Federal and State labor regulations.
• To maximize operational efficiency, there must be exactly 10 line workers operating the mine.
• The mine operates from 8 am until 5 pm, Monday to Sunday.
• The mine employs 4 safety inspectors and 16 line workers to make 20 workers in total.
• The total weekly labor cost for the Bingham Mine is $16,000.

Which of the following statements is a valid conclusion?

A. One-fifth of the total labor cost for the mine is for safety inspectors.

B. At least one safety inspector must work more than 40 hours per week.

C. Line workers do not work more than 40 hours per week.

D. The majority of the mine’s labor cost is for line workers.

A – Fit-well but not fact-based

There are 4 inspectors out of 20 employees so it seems like the cost of the inspectors can very well be 1/5 of total labor cost. But a missing piece of data to conclude that is: does each person get a similar total income?

C – Fit well but not fact-based

The mine opens for 9 hours per day, 7 days per week, and there must be 10 line workers at a time, so it is 630 man-hours per week at the line positions. There are 16 line workers, so on average each of them only needs to work 39 hours per week. This seems to fit very well with the proposed conclusion: line workers do not work more than 40 hours per week. However, a missing piece of data to conclude is: does every line worker work the same amount of time (if not, there can be some who work over 40 hours while others work less)?

D – Fit well but not fact-based

Similar to A, there are more line workers, so it seems like the total cost for line workers is more than the total cost for safety inspectors. But a missing piece of data needed to conclude is: does each worker get paid the same amount?

=> Only B is proven true by the provided facts

There are 24 * 7 = 168 inspector hours needed in a week, equaling 42 hours per week per inspector. So there must be one who works more than 40 hours.

Identifying proven true conclusions is an important foundation to master all conclusion-related questions. However, most conclusion-related questions in the McKinsey Problem Solving Test will be given in other formats. In this section, we will learn about the two types of twists: (1) False conclusions and (2) Conclusions reversed . Let’s start with the first one.

TWIST TYPE 1: FALSE CONCLUSION

Any proposed conclusion must fall into one of the following three groups: Proven True, Proven False, and Unproven. This twist is when a question asks you to identify the False Conclusion instead of the True Conclusion.

• Which of the following statements is FALSE based on …?
• Which of the following statements is FALSE based on … ?

METHODOLOGY

A proposed conclusion is proven false when you can point out at least one instance where the conclusion is wrong. Similarly, with true conclusion questions, unproven conclusions should also not be selected.

Notice that proven FALSE conclusions are NOT conclusions not proven TRUE. A conclusion will stay unproven until it is proved to be TRUE or FALSE.

Which of the following statements is FALSE based on Table 1?

A. A, Inc. had lower average economic growth in the last five years than D, LTD.

B. A, Inc. had higher average economic growth in the last five years than D, LTD.

C. Investment risk rating is based on the difference between maximum and minimum revenue growth in the past five years.

D. Potential rating is based on the maximum recent revenue.

Of A and B, A seems to be false and B seems to be true. However, both of them are unproven. The maximum and minimum figures are not enough to conclude the average.

We don’t know if C is right or not, but we know that it is not proven false. In the provided data, there is no instance where the larger difference between maximum and minimum recent revenue growth indicates smaller risk (and vice versa).

With D, we know for sure that it is proven false because we can point out an instance where the assertion conflicts with the data (B Corp. vs. D, LTD.).

TWIST TYPE 2: CONCLUSIONS REVERSED

Very often, conclusion questions in the McKinsey Problem Solving Test are given in a reversed format. You will be given the conclusion first and asked to pick what facts/ data would be enough to come up with that conclusion.

The key to answering this type of question is to recognize which proposed fact makes the stated conclusion proven or unproven.

This question is written based on an official McKinsey practice PST:

FOCUS Travel is a premium Russian tourism company, offering tours to South East Asian countries. Facing the economic downturn, FOCUS revenue has been hurt badly. While the CFO (Chief Finance Officer) proposed an overall price cut to stay competitive, the CMO (Chief Marketing Officer) is concerned that a price reduction would negatively impact the premium perception of the brand, which drives a lot of sales.

Which of the following statements, if TRUE, would best support the CMO’s assertion?

A. In a recent survey, FOCUS’s customers quoted “price” as the most important indicator in choosing travel agencies in a list of ten factors.

B. In a recent survey, FOCUS’s customers quoted “price” as the most important indicator of quality in a list of ten factors.

C. In a recent survey, there were customers who said they would not buy FOCUS’s services if there was a 10% price increase.

D. In a recent survey, there were customers who said they would not buy FOCUS’s services if there was a 10% price decrease.

In this question, the “conclusion” has been given to us: Price reduction will negatively impact the premium perception, which will in turn negatively impact sales.

Of the four proposed answers, which facts are enough to prove the provided “conclusion” above?

A: This fact is only enough to conclude that price will impact sales. Not enough to prove that price reduction will negatively impact sales.

C: This fact is irrelevant.

D: This fact is not enough to conclude that price reduction will negatively impact sales because not all customers say so. The word “there were” can be understood as either a minority or a majority. It is only enough to conclude the proposed conclusions when “there were” is replaced with “the majority of” or “all“ .

With B, we can logically infer that price reduction will negatively impact the quality perception, which in turn will hurt to sales.

3.3. Root-cause reason

This question gives you a particular set of facts/data and asks you to identify what could be the cause for them. When doing a real consulting project, we consultants have to find out the root-cause reason. There may be various reasons that can cause the current situation, but the root-cause reason will help us tackle and solve it more efficiently. You can see the picture below for an illustration.

The following are a few examples of typical root-cause reason question format:

• Which of the following reasons, if TRUE, will help explain the Facts …?
• Which of the following does NOT explain the Facts …?
• Which of the following points is NOT a valid reason for the Facts …?

Only B is proven true by the provided facts

Facts provided: Visits to the website MConsultingPrep were relatively low last month.

Root-cause Reason Question: What reasons, if TRUE, would help explain the low traffic to MConsultingPrep last month?

The correct answers can be any of the following:

1. The quality of contents has been bad

2. Because of technical issues, some visitors could not access the website

3. Last month was December when the overall demand for job prep materials is lowest in the year

4. Other new consulting prep blogs opened recently

Fact-based Conclusion Question: What can be concluded from the data provided?

All of the statements above can be the reason for the stated fact, but NONE of them can be concluded from it.

An example of a statement that can be concluded: Because the conversion rate stayed constant over the years, revenue last month was relatively low.

What makes a statement NOT a potential reason for a particular fact?

There are two ways a statement cannot be the potential reason: (1) Wrong Subject and (2) Wrong Trend.

• A statement is (1) Wrong on Subject when the subject is irrelevant, which means the statement has zero effect on the phenomenon mentioned in the stated fact.
• A statement is (2) Wrong on Trend when the direction is reversed, which usually means the statement has a reversed effect on the phenomenon mentioned in the stated fact

Illustrative example Let’s continue with the simple example above. The Stated Fact: Visits to the MConsultingPrep blog were relatively low last month. (1) Example of a “Wrong Subject” statement: “Some new Investment Banking Prep blogs opened recently” Here the subject “Investment Banking Prep blogs” is irrelevant to the stated fact. The statement (1) will have zero effect on the stated fact. (2) Example of a “Wrong Trend” statement: “Some other existing Consulting Prep blogs closed recently” Here, even though the subject “Consulting Prep blogs” is relevant, the trend is reversed. The exit of Consulting Blogs will increase visits to MConsultingPrep. Therefore, statement (2) will have an opposite effect on the stated fact.

PRACTICE QUESTION

Fletcher is a major Steel producer in the Pacific continent. It has markets in New Zealand, Australia and other South East Asia countries. Of many types of steels, re-bar (reinforced bar) is typically used in high-rises and big construction projects.

There are three main groups of steel consumers in New Zealand:

• Homeowners purchase steel at retail sizes for purposes of self-constructing and self-renovating their homes
• Scaled private construction companies, who often contracts large construction projects and steel orders
• State-owned Enterprises (SOE), who build government’s projects such as roads, bridges, schools, hospitals, etc. (SOEs usually have bargaining power since steel providers need governments’ permissions in order to be legally used in particular countries.)

Table 1 below shows the size of re-bar steel market (in billions of $US)

Which of the following statements, if TRUE, best explains why future trends for South East Asia sales differ from sales in the other two markets?

A) South East Asia population is expected to grow strongest, which lead to high steel demand from individual homeowners.

B) South East Asia economy will be heavily based on SOE, so will the construction market.

C) South East Asia economy will shift toward privatization, so will the construction market.

D) Developed markets of New Zealand and Australia will have the most advanced steel production technology and facilities.

Correct answer: C

Word Problem

Word Problem is a quantitative question where the answer cannot be calculated directly from the data provided. Usually, we have to set up one or more equations in order to solve this kind of question. Word Problem questions in the McKinsey PST and Case Interviews are just the word problems we usually see in schools, GMAT… but put into business contexts. The method to solve them, therefore, is the same.

Table 1: Data on the Washing Room of Jean Valjean Restaurant

Suppose the restaurant opens 350 days a year. There are 3 meal shifts per day, 1 shift lasts 3 hours, 1 customer uses an average of 5 dishes per visit, and currently the restaurant hosts 530 customers on average daily.

What percentage of increase in the number of daily visits would be required in order to make purchasing the machines financially beneficial?

Step 1 . Convert data/facts into manageable and standardized format and units (only needed for complex questions).

Step 2 . Set up an equation with one (or more) unknown variables, i.e. X, Y, Z, etc.

Tips: Don’t worry about having to make the variable as the question asked. Just set up the equation in a way that makes the most sense to you as long as the variables can be easily converted to the asked variable. It will save much more time and helps you avoid silly mistakes.

Step 3 . Solve the equation and get the answer.

METHODOLOGY ILLUSTRATION

Let’s solve the sample question above together.

Step 1: This is a very complex question with many non-standardized and not ready-to-use data. If I am going to tackle this question on my PST, I would convert the provided figures and write them out on a table as follows.

Notice that I have converted all the necessary data points into the same unit of “Franc per day”.

The only data point not fully converted is the Labor cost in Manual Process (measured by the “per dish” variable), yet I want to make sure that I go as far as I can.

See how simple the problem is now!

Step 2: Now that we have very manageable data, let’s go ahead and set up an equation that will help us find the answer. The asked variable here is: what percent increase in current daily visits does Jean Valjean need?

As mentioned above, it is NOT necessary to put the variable question is looking for in the equation. In this case, doing so will result in a very awkward and complicated equation.

Instead, I set up the equation that makes the most sense to me (do note that there is more than one way to set up equations). Let Y be the “break-even size” (measured by people). I can easily calculate the percentage asked for after getting the break-even size.

Cost per day of Manual Process = Cost per day of Machine Process

Washing cost + Set up cost = Washing cost + Set up cost + other cost

Y x 5 dishes x 0.1 Franc + 30 Franc = 270 Franc + 90 Franc + 200 Franc

After executing step 1 and step 2, the problem becomes a lot easier. Now we have:

0.5 Y = 530

Y = 2 x 530

Once we have Y (the new “break-even” visit volume) of 2 * 530, we can quickly convert Y into the asked variable: What percent increase of 530 customers/day does Jean Valjean need?

The final answer is C.

Client Interpretation

In every consulting project, communication with the clients’ top-level (usually the Chairman or CEO) is always important. During my time with McKinsey, we usually hear an update every one or two weeks from our Project Director (usually a partner) on his meeting with the clients’ top level. Messages from those meetings are important on-going steers for the project. No surprise it makes up an entire question category in the Problem Solving Test.

Client Interpretation questions test your ability to read, understand, and interpret the messages the client is trying to convey in the case question or description. To some extent, this is very similar to GMAT verbal questions.

• Which of the following best summarizes the CEO’s concerns?
• Which of the following statements best describes the thoughts of the CEO regarding…?
• Based on the opinion of the head of the Department, which of the following statements is valid?
• Which of the following statements best describes the CEO’s aims for the McKinsey research?

Case context:

Mommy said she saw some dirty clothes on the dining table. She is also quite shocked to see Kevin’s toys in every room throughout the house. She even complains about how much time it takes her every night to clean up Kevin’s mess. “I will have to have a very straightforward conversation with Kevin tonight!”, said mom

Which of the following statements best describes the Mom’s concern?

A. Mom is not happy about too many of Kevin’s toys sitting on the dining table

B. Mom does not expect to see that many of Kevin’s toys in the house

C. Mom does not like to be responsible for anyone’s mess

D. Mom is too busy these days

E. Mom wants to talk to Kevin

F. Mom wants Kevin to be tidier

In this example, we continuously get small data points, all leading to one bottom-line, not explicitly mentioned but can be reasonably interpreted:

Kevin is too messy and mom doesn’t like that!

Notice that, the bottom-line here is not explicitly stated but it IS the bottom-line. All 4 sentences in the case context are small pieces of data leading to that final “so-what”. Having this “so-what” in mind, you can just skim through the answer and quickly pick F without concern about other choices.

In case you are curious about how other choices are “wrong-choice” …

Choices B and E are in fact right according to the case context, but not the bottom-line.

Choices A is simple wrong according to the case context (Tip #2)

Choices C and D are neither right or wrong according to the case context. There are not enough “evidence” to be reasonably interpreted using common sense.

TIPS AND TRICKS

Tip #1: Read the case description before going to multiple choices!

Normally the strategy of scanning through the answers first before going back to the case description works when you have a very long case description and don’t know where to look for the right information. Scanning through the answers helps you get a more focused read on the case description. However, the client’s assertion is typically found in a very short and specific part of the case description. So once you realize it’s a Client Interpretation question, go back to the case description and find that very specific part of the client’s assertion. Make sure you understand it very well. Then the rest of the work is just determining which of the four choices has the same meaning as the original assertion.

Tip #2: Cross out some obviously wrong choices …

… by recognizing a few words or short phrases that make a choice incorrectly reflect the client’s assertion. Sometimes, you can do this very quickly and effectively. If not, please see tips #3.

Tip #3: Catch the bottom-line, the “so-what” of client’s assertion

Client’s expression as quoted in the case context is always a bit blur and confusing. That is very realistic of what you may encounter in the real consulting work. It also makes these question types challenging. But in almost every situation, there is always one “so-what”, stated explicitly or implicitly. The trick here is to catch that so-what, ignore the noise, and go straight for the answer choice. Most of the time, the wrong choices DO contain a part of the client’s assertion, but either not the whole idea or the main, the bottom-line, the most important one!

Using this method, you can fly and land straight to the correct choice, not having to care too much about how wrong choices are made of. But if you are curious, some of the most common wrong-choice types:

• Choice that is simply wrong according to the client’s assertion (Tip #2 above).
• Choice that is in fact right, but is a minor point, NOT the bottom-line of the client’s assertion.
• Choice that seems to be right, but cannot be reasonably interpreted by common sense (not by scientifically supporting logic like in other question types).

Gangnam Market is a convenience-stores chain mainly in the Gangnam district, Seoul, Korea. Though it has been losing money almost every year since 2000, Gangnam Market secures a good deal of strategic locations in the highly populated Gangnam district. Recently, Gangnam Market was acquired by Lotte Mart in its aspiration to expand to the mini-market market. Lotte right away sets up a transformation project to get Gangnam Market back on track. The CEO of Gangnam Market states that aggressive transformation targets are fine for newly acquired stores with a similar operation model with Lotte’s big stores, but he hopes that the parent company is realistic about the convenience-stores model Gangnam has been operating with.

Which of the following statements best reflect the concerns of Gangnam Market’s CEO?

A) He is concerned that Gangnam Market will never be able to transform itself into Lotte system because Gangnam Market only presents in a specific geographic location

B) He is concerned that Lotte Mart sets transformation milestones that are too aggressive and not realistic for newly acquired companies like Gangnam Market

C) He is concerned that Lotte Mart’s transformation milestones are not realistic for companies with different operational model from Lotte Mart like Gangnam Market

D) He is concerned that Lotte Mart’s transformation targets are too high for Gangnam Market because it has been losing money for a while

Formulae questions are generally like word problems in PST where you don’t have to provide the actual numerical results, just the formulae containing letters representing input variables. Normally, the question will provide input variables in letter format and you will be asked to provide the right formulae in letter format (e.g. it takes the process center T hours to process each file. If the speed is doubled, it takes T/2 hours to process each file). This is one of the easiest PST question types on the McKinsey PST. Let’s make sure you don’t lose points on any question of this type in your exam!

Table 3.6.1: Labor Cost and Processing Data – Holcim Missouri plant

Which of the following formulae accurately calculates the annual cement output per worker?

A. (c x p) / (b + w)

B. (c x p) / [(b + w) x 12]

C. 144 x (c x p) / (b + w)

D. 12 x (c x p) / (b + w)

FORMULAE FOR SUCCESS IN FORMULAE QUESTIONS

Formula 1: Calculate first before looking at the given option

A popular technique for multiple-choice questions is to read the answers first before coming back to the facts. However, that technique would not help you with Formulae Questions. The reason for this is that, often, the end-result formula has already been simplified (e.g. canceling out the same variable on both numerator and denominator) as much as possible. It gives you neither the path to get there nor any hints on how to solve the problem. For instance, when you look at the four options in the example above, does any of them give you a sense of what it represents or how to get there? What does (c x p) represent? What do you get by multiplying Cement output by Monthly labor income?

Formula 2: Divide the problem into smaller pieces (take one step at a time)

This is the universal tip for everybody in the consulting industry, and it also works great here! Often, the result cannot be directly calculated from the provided variables. However, if you take an extra step in-between, the problem becomes a lot easier. Let’s solve the sample question above together to illustrate this point. I broke the problem into smaller steps as below:

• Step 1: Annual cement output per worker = Total annual cement output / Total number of workers
• Step 2: Since we already have Total annual cement output of (c), the next step is to calculate the total number of workers. Total number of workers = Total labor cost / Salary of 1 worker Both Total labor cost and salary are provided. Bingo!
• Step 3: Simplify the final formulae

Formula 3: Get the reading-facts tools right

In some aspects, the formulae question is also a tweaked version of reading-facts questions. You still need to read some facts and perform some calculations (with letters instead of real numbers). Therefore, it is important to master those reading-facts tools and apply them here.

Illustration of a usual mistake: Now come back to Step 2 above and explicitly solve it.

Step 2: Total number of workers = Total labor cost / Salary of 1 worker = (b + w) / p

Step 3: Annual cement output per worker = c / [(b + w) / p] = (c x p) / (b + w)]

Chosen choice: A

Unfortunately, A is NOT the correct answer, because the above calculation doesn’t take into account the difference in units – the salary is on a monthly basis whereas the total labor cost is on an annual basis. If you convert the unit, the final choice should be D.

No matter how beautifully you have tackled the problem, you will not get any credit if small mistakes like this slip through the crack. Make sure you don’t get blindsided by this kind of pitfall!

VICEM is a leading cement company in South East Asia. The following data regarding its business and production has been gathered.

Table 3.6.2: VICEM Business and Production data

Clinker factor is defined as the amount of clinker needed to produce 100 units of cement.

Which of the following formulas calculates the amount of clinker (in tons) needed to purchase in a year?

A) [(s x f) / 100] – c

B) [(p – s) / 100] – c

C) (p x f) – c

D) [(p x f) / 100] – c

 ANSWER KEY

McKinsey PST sample test

Download McKinsey PST practice test (PDF): TOYO case .

More free materials like this can be found in our Prospective Candidate Starter Pack – a collection of beginner’s materials to consulting resume, screening tests and case interviews. 

Scoring in the McKinsey PSG/Digital Assessment

The scoring mechanism in the McKinsey Digital Assessment

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Problem solving test: Pre-employment screening assessment to hire the best candidates

Summary of the problem solving test.

This Problem Solving test evaluates candidates’ ability to define problems and analyze data and textual information to make correct decisions. This test helps you identify candidates who use analytical skills to evaluate and respond to complex situations.

Covered skills

Creating and adjusting schedules, interpreting data and applying logic to make decisions, prioritizing and applying order based on a given set of rules, analyzing textual and numerical information to draw conclusions, use the problem solving test to hire.

Any role that involves managing constantly shifting variables with tight deadlines. This may include administrative assistants, project managers, planners, and people working in hospitality or sales.

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About the Problem Solving test

Effective problem-solving requires a broad skill set that enables individuals, teams, and businesses to advance towards stated objectives. It involves the ability to define a problem, to break it down into manageable parts, to develop approaches to solve the (sub)problem using creativity and analytical thinking, and to execute flawlessly.

This problem solving test allows you to identify candidates who display these abilities. The test presents candidates with typical problem-solving scenarios like scheduling on the basis of a diverse set of conditions, identifying the right sequence of actions based on a number of business rules, and drawing conclusions based on textual and numerical information.

The test requires candidates to identify the right answers to the questions in a limited amount of time. Successful candidates can quickly identify the key elements of the problem and work through the problem at speed without making mistakes. This is a great test to include to check candidates' overall analytical skills.

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The global IT industry has benefited from Anirban’s talents for over two decades. With a flawless reputation that precedes him, Anirban has earned a status as a sought-after agile project manager and consultant. He’s worked internationally as a Senior Project Manager with companies such as Ericsson, IBM, and T-Mobile.

Anirban’s love for learning helps him keep his skills sharp. He holds an MBA and a degree in engineering, is a certified Scrum Master, and has certifications in Prince2 and ITIL.

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Why problem-solving is a crucial skill

We’ve all been thrown a curveball at work. An unexpected problem crops up and we need to make a plan to solve it. This is called problem-solving and it’s an important skill in most job roles because employees will encounter difficult or complex situations or problems that need to be solved.

Interestingly, unlike some career skills, problem-solving translates to both an individual’s personal and professional lives, making it crucial to potential success. But this may make it harder for recruiters to find the right candidate for a job where problem-solving skills are needed. In this case, a problem-solving test can help you find the best candidate capable of handling situations that influence business functions.

Problem-solving in the workplace

In business, problem-solving relies on a candidate’s ability to create processes that mitigate or remove obstacles that prevent the company from achieving its goals. Consequently, these issues or situations can create a gap between desired outcomes and actual results. This means that problem-solving plays an important role in how employees meet this challenge and work through it.

Roles such as project management, administrative assistance, and planning work with changing circumstances and tight deadlines on a day-to-day basis. When recruiting for these roles, finding candidates who have good problem-solving skills is crucial to their success in the role.

To gain insight into a candidate’s skill in this area, you can use a problem-solving test. Through expert formulation, a skill-specific test can help you understand a candidate’s level of proficiency. And testing your applicants before you start the interview process can highlight the candidates with the skills most relevant to the role.

A process-driven skill

In the workplace, there are important steps that can contribute to a candidate’s ability to successfully solve problems. Let’s take a look:

Identify the problem

Problem-solving begins with accurately identifying the problem. This determining factor looks at whether a candidate can find the origin and the implications of the problem. It includes:

• Differentiating between fact and opinion

• Compiling data to determine the problem

• Identifying underlying causes

• Recognizing which processes are affected• Pinpointing the process standard

By accurately identifying the problem, individuals can proceed to the next step to solve the problem.

Determine alternative solutions

Once an individual has established the source of the problem, they can determine alternative solutions. The goal of plotting solutions to the problem is to remedy it and realign it with business goals. A creative problem-solving test may identify whether an individual has the competency to determine solutions. Key competencies in seeking solutions include:

• Establishing alternative solutions that align with business goals

• Determining whether a problem needs short- or long-term solutions

• Evaluating how solutions may impact on resources; and determining if there are any barriers to implementing the solutions.

Although any problem can have multiple solutions, the simplest or fastest one may not always be the best course of action. This is where solution comparison comes into play.

Compare solutions and plot a course

Once all possible solutions are determined, it is important to compare them. This involves evaluating each solution without bias to determine the optimal solution to the problem.

Through the evaluation process, the individual should rule out options that do not align with company goals, may take too much time and/or resources, or are unrealistic in their approach.

Some considerations when determining the best solution include the likelihood of solution implementation, whether all parties involved will accept the solution, and how it fits in with business goals. Additionally, it is important to note that the goal of the optimal solution is to solve the problem without causing additional or unanticipated problems.

In essence, problem-solving is about finding solutions that cause as little disruption as possible and correcting a project’s course.

Implement the solution

The last stage in problem-solving is the implementation of the final step. This step focuses on the remedial solution and requires continuous evaluation to ensure its effective implementation. For you as a recruiter, knowing if a candidate can find a solution as well as implement it may be important to the goals of the role.

Continually evaluating the solution will give the individual insight into whether the project goals are aligned, whether all stakeholders accept the new solution and whether the outcomes are managed effectively.

Considerations for recruiters

When hiring for a role in which problem-solving skills are crucial, it may be beneficial to test a candidate’s ability to define problems and analyze data and textual information to make decisions that best serve the business. Some of the considerations for a problem-solving test include:

Schedules are living documents that need to adapt as eventualities come into play. Candidates should be able to understand what they can realistically achieve with the time and how to adjust schedules to account for variable outcomes.

Data-driven decision-making should inform a course of action before an individual commits to it. For recruiters, this means candidates should have an aptitude for aligning data with business goals and making actionable decisions.

By using prioritization rules and supporting information, candidates can determine which project tasks take priority. This system aims to optimize resources for project delivery.

Examining textual and numerical information to reveal patterns, relationships, and trends can tell the candidate what connection exists among variables. Conclusions can then be drawn from the data to gain an accurate assessment of the overall situation.

When broken down, problem-solving is a skill that relies on a variety of disciplines to achieve success. Although this skill is transferable to many job roles, determining candidates’ proficiency can be difficult, so it can be beneficial to recruiters to use a problem-solving test to review candidates’ aptitude when recruiting for a role.

Using a pre-formulated problem-solving test will enable you to quickly assess your candidates and help you recruit the best person for the role.

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15 Common Problem-Solving Interview Questions

In an interview for a big tech company, I was asked if I’d ever resolved a fight — and the exact way I went about handling it. I felt blindsided, and I stammered my way through an excuse of an answer.

It’s a familiar scenario to fellow technical job seekers — and one that risks leaving a sour taste in our mouths. As candidate experience becomes an increasingly critical component of the hiring process, recruiters need to ensure the problem-solving interview questions they prepare don’t dissuade talent in the first place. 

Interview questions designed to gauge a candidate’s problem-solving skills are more often than not challenging and vague. Assessing a multifaceted skill like problem solving is tricky — a good problem solver owns the full solution and result, researches well, solves creatively and takes action proactively. 

It’s hard to establish an effective way to measure such a skill. But it’s not impossible.

We recommend taking an informed and prepared approach to testing candidates’ problem-solving skills . With that in mind, here’s a list of a few common problem-solving interview questions, the science behind them — and how you can go about administering your own problem-solving questions with the unique challenges of your organization in mind.

Key Takeaways for Effective Problem-Solving Interview Questions

• Problem solving lies at the heart of programming. 
• Testing a candidate’s problem-solving skills goes beyond the IDE. Problem-solving interview questions should test both technical skills and soft skills.
• STAR, SOAR and PREP are methods a candidate can use to answer some non-technical problem-solving interview questions.
• Generic problem-solving interview questions go a long way in gauging a candidate’s fit. But you can go one step further by customizing them according to your company’s service, product, vision, and culture. 

Technical Problem-Solving Interview Question Examples

Evaluating a candidates’ problem-solving skills while using coding challenges might seem intimidating. The secret is that coding challenges test many things at the same time — like the candidate’s knowledge of data structures and algorithms, clean code practices, and proficiency in specific programming languages, to name a few examples.

Problem solving itself might at first seem like it’s taking a back seat. But technical problem solving lies at the heart of programming, and most coding questions are designed to test a candidate’s problem-solving abilities.

Here are a few examples of technical problem-solving questions:

1. Mini-Max Sum  

This well-known challenge, which asks the interviewee to find the maximum and minimum sum among an array of given numbers, is based on a basic but important programming concept called sorting, as well as integer overflow. It tests the candidate’s observational skills, and the answer should elicit a logical, ad-hoc solution.

2. Organizing Containers of Balls  

This problem tests the candidate’s knowledge of a variety of programming concepts, like 2D arrays, sorting and iteration. Organizing colored balls in containers based on various conditions is a common question asked in competitive examinations and job interviews, because it’s an effective way to test multiple facets of a candidate’s problem-solving skills.

3. Build a Palindrome

This is a tough problem to crack, and the candidate’s knowledge of concepts like strings and dynamic programming plays a significant role in solving this challenge. This problem-solving example tests the candidate’s ability to think on their feet as well as their ability to write clean, optimized code.

4. Subarray Division

Based on a technique used for searching pairs in a sorted array ( called the “two pointers” technique ), this problem can be solved in just a few lines and judges the candidate’s ability to optimize (as well as basic mathematical skills).

5. The Grid Search 

This is a problem of moderate difficulty and tests the candidate’s knowledge of strings and searching algorithms, the latter of which is regularly tested in developer interviews across all levels.

Common Non-Technical Problem-Solving Interview Questions 

Testing a candidate’s problem-solving skills goes beyond the IDE . Everyday situations can help illustrate competency, so here are a few questions that focus on past experiences and hypothetical situations to help interviewers gauge problem-solving skills.

1. Given the problem of selecting a new tool to invest in, where and how would you begin this task? 

Key Insight : This question offers insight into the candidate’s research skills. Ideally, they would begin by identifying the problem, interviewing stakeholders, gathering insights from the team, and researching what tools exist to best solve for the team’s challenges and goals. 

2. Have you ever recognized a potential problem and addressed it before it occurred? 

Key Insight: Prevention is often better than cure. The ability to recognize a problem before it occurs takes intuition and an understanding of business needs. 

3. A teammate on a time-sensitive project confesses that he’s made a mistake, and it’s putting your team at risk of missing key deadlines. How would you respond?

Key Insight: Sometimes, all the preparation in the world still won’t stop a mishap. Thinking on your feet and managing stress are skills that this question attempts to unearth. Like any other skill, they can be cultivated through practice.

4. Tell me about a time you used a unique problem-solving approach. 

Key Insight: Creativity can manifest in many ways, including original or novel ways to tackle a problem. Methods like the 10X approach and reverse brainstorming are a couple of unique approaches to problem solving. 

5. Have you ever broken rules for the “greater good?” If yes, can you walk me through the situation?

Key Insight: “Ask for forgiveness, not for permission.” It’s unconventional, but in some situations, it may be the mindset needed to drive a solution to a problem.

6. Tell me about a weakness you overcame at work, and the approach you took. 

Key Insight: According to Compass Partnership , “self-awareness allows us to understand how and why we respond in certain situations, giving us the opportunity to take charge of these responses.” It’s easy to get overwhelmed when faced with a problem. Candidates showing high levels of self-awareness are positioned to handle it well.

7. Have you ever owned up to a mistake at work? Can you tell me about it?

Key Insight: Everybody makes mistakes. But owning up to them can be tough, especially at a workplace. Not only does it take courage, but it also requires honesty and a willingness to improve, all signs of 1) a reliable employee and 2) an effective problem solver.

8. How would you approach working with an upset customer?

Key Insight: With the rise of empathy-driven development and more companies choosing to bridge the gap between users and engineers, today’s tech teams speak directly with customers more frequently than ever before. This question brings to light the candidate’s interpersonal skills in a client-facing environment.

9. Have you ever had to solve a problem on your own, but needed to ask for additional help? How did you go about it? 

Key Insight: Knowing when you need assistance to complete a task or address a situation is an important quality to have while problem solving. This questions helps the interviewer get a sense of the candidate’s ability to navigate those waters. 

10. Let’s say you disagree with your colleague on how to move forward with a project. How would you go about resolving the disagreement?

Key Insight: Conflict resolution is an extremely handy skill for any employee to have; an ideal answer to this question might contain a brief explanation of the conflict or situation, the role played by the candidate and the steps taken by them to arrive at a positive resolution or outcome. 

Strategies for Answering Problem-Solving Questions

If you’re a job seeker, chances are you’ll encounter this style of question in your various interview experiences. While problem-solving interview questions may appear simple, they can be easy to fumble — leaving the interviewer without a clear solution or outcome. 

It’s important to approach such questions in a structured manner. Here are a few tried-and-true methods to employ in your next problem-solving interview.

1. Shine in Interviews With the STAR Method

S ituation, T ask, A ction, and R esult is a great method that can be employed to answer a problem-solving or behavioral interview question. Here’s a breakdown of these steps:

• Situation : A good way to address almost any interview question is to lay out and define the situation and circumstances. 
• Task : Define the problem or goal that needs to be addressed. Coding questions are often multifaceted, so this step is particularly important when answering technical problem-solving questions.
• Action : How did you go about solving the problem? Try to be as specific as possible, and state your plan in steps if you can.
• Result : Wrap it up by stating the outcome achieved. 

2. Rise above difficult questions using the SOAR method

A very similar approach to the STAR method, SOAR stands for S ituation, O bstacle, A ction, and R esults .

• Situation: Explain the state of affairs. It’s important to steer clear of stating any personal opinions in this step; focus on the facts.
• Obstacle: State the challenge or problem you faced.
• Action: Detail carefully how you went about overcoming this obstacle.
• Result: What was the end result? Apart from overcoming the obstacle, did you achieve anything else? What did you learn in the process? 

3. Do It the PREP Way

Traditionally used as a method to make effective presentations, the P oint, R eason, E xample, P oint method can also be used to answer problem-solving interview questions.  

• Point : State the solution in plain terms. 
• Reasons: Follow up the solution by detailing your case — and include any data or insights that support your solution. 
• Example: In addition to objective data and insights, drive your answer home by contextualizing the solution in a real-world example.
• Point : Reiterate the solution to make it come full circle.

How to Customize Problem-Solving Interview Questions 

Generic problem-solving interview questions go a long way in gauging a candidate’s skill level, but recruiters can go one step further by customizing these problem-solving questions according to their company’s service, product, vision, or culture. 

Here are some tips to do so:

• Break down the job’s responsibilities into smaller tasks. Job descriptions may contain ambiguous responsibilities like “manage team projects effectively.” To formulate an effective problem-solving question, envision what this task might look like in a real-world context and develop a question around it.  
• Tailor questions to the role at hand. Apart from making for an effective problem-solving question, it gives the candidate the impression you’re an informed technical recruiter. For example, an engineer will likely have attended many scrums. So, a good question to ask is: “Suppose you notice your scrums are turning unproductive. How would you go about addressing this?” 
• Consider the tools and technologies the candidate will use on the job. For example, if Jira is the primary project management tool, a good problem-solving interview question might be: “Can you tell me about a time you simplified a complex workflow — and the tools you used to do so?”
• If you don’t know where to start, your company’s core values can often provide direction. If one of the core values is “ownership,” for example, consider asking a question like: “Can you walk us through a project you owned from start to finish?” 
• Sometimes, developing custom content can be difficult even with all these tips considered. Our platform has a vast selection of problem-solving examples that are designed to help recruiters ask the right questions to help nail their next technical interview.

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Top 20 Problem Solving Interview Questions (Example Answers Included)

Mike Simpson 0 Comments

By Mike Simpson

When candidates prepare for interviews, they usually focus on highlighting their leadership, communication, teamwork, and similar crucial soft skills . However, not everyone gets ready for problem-solving interview questions. And that can be a big mistake.

Problem-solving is relevant to nearly any job on the planet. Yes, it’s more prevalent in certain industries, but it’s helpful almost everywhere.

Regardless of the role you want to land, you may be asked to provide problem-solving examples or describe how you would deal with specific situations. That’s why being ready to showcase your problem-solving skills is so vital.

If you aren’t sure who to tackle problem-solving questions, don’t worry, we have your back. Come with us as we explore this exciting part of the interview process, as well as some problem-solving interview questions and example answers.

What Is Problem-Solving?

When you’re trying to land a position, there’s a good chance you’ll face some problem-solving interview questions. But what exactly is problem-solving? And why is it so important to hiring managers?

Well, the good folks at Merriam-Webster define problem-solving as “the process or act of finding a solution to a problem.” While that may seem like common sense, there’s a critical part to that definition that should catch your eye.

What part is that? The word “process.”

In the end, problem-solving is an activity. It’s your ability to take appropriate steps to find answers, determine how to proceed, or otherwise overcome the challenge.

Being great at it usually means having a range of helpful problem-solving skills and traits. Research, diligence, patience, attention-to-detail , collaboration… they can all play a role. So can analytical thinking , creativity, and open-mindedness.

But why do hiring managers worry about your problem-solving skills? Well, mainly, because every job comes with its fair share of problems.

While problem-solving is relevant to scientific, technical, legal, medical, and a whole slew of other careers. It helps you overcome challenges and deal with the unexpected. It plays a role in troubleshooting and innovation. That’s why it matters to hiring managers.

How to Answer Problem-Solving Interview Questions

Okay, before we get to our examples, let’s take a quick second to talk about strategy. Knowing how to answer problem-solving interview questions is crucial. Why? Because the hiring manager might ask you something that you don’t anticipate.

Problem-solving interview questions are all about seeing how you think. As a result, they can be a bit… unconventional.

These aren’t your run-of-the-mill job interview questions . Instead, they are tricky behavioral interview questions . After all, the goal is to find out how you approach problem-solving, so most are going to feature scenarios, brainteasers, or something similar.

So, having a great strategy means knowing how to deal with behavioral questions. Luckily, there are a couple of tools that can help.

First, when it comes to the classic approach to behavioral interview questions, look no further than the STAR Method . With the STAR method, you learn how to turn your answers into captivating stories. This makes your responses tons more engaging, ensuring you keep the hiring manager’s attention from beginning to end.

Now, should you stop with the STAR Method? Of course not. If you want to take your answers to the next level, spend some time with the Tailoring Method , too.

With the Tailoring Method, it’s all about relevance. So, if you get a chance to choose an example that demonstrates your problem-solving skills, this is really the way to go.

We also wanted to let you know that we created an amazing free cheat sheet that will give you word-for-word answers for some of the toughest interview questions you are going to face in your upcoming interview. After all, hiring managers will often ask you more generalized interview questions!

Click below to get your free PDF now:

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FREE BONUS PDF CHEAT SHEET: Get our " Job Interview Questions & Answers PDF Cheat Sheet " that gives you " word-word sample answers to the most common job interview questions you'll face at your next interview .

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Top 3 Problem-Solving-Based Interview Questions

Alright, here is what you’ve been waiting for: the problem-solving questions and sample answers.

While many questions in this category are job-specific, these tend to apply to nearly any job. That means there’s a good chance you’ll come across them at some point in your career, making them a great starting point when you’re practicing for an interview.

So, let’s dive in, shall we? Here’s a look at the top three problem-solving interview questions and example responses.

1. Can you tell me about a time when you had to solve a challenging problem?

In the land of problem-solving questions, this one might be your best-case scenario. It lets you choose your own problem-solving examples to highlight, putting you in complete control.

When you choose an example, go with one that is relevant to what you’ll face in the role. The closer the match, the better the answer is in the eyes of the hiring manager.

EXAMPLE ANSWER:

“While working as a mobile telecom support specialist for a large organization, we had to transition our MDM service from one vendor to another within 45 days. This personally physically handling 500 devices within the agency. Devices had to be gathered from the headquarters and satellite offices, which were located all across the state, something that was challenging even without the tight deadline. I approached the situation by identifying the location assignment of all personnel within the organization, enabling me to estimate transit times for receiving the devices. Next, I timed out how many devices I could personally update in a day. Together, this allowed me to create a general timeline. After that, I coordinated with each location, both expressing the urgency of adhering to deadlines and scheduling bulk shipping options. While there were occasional bouts of resistance, I worked with location leaders to calm concerns and facilitate action. While performing all of the updates was daunting, my approach to organizing the event made it a success. Ultimately, the entire transition was finished five days before the deadline, exceeding the expectations of many.”

2. Describe a time where you made a mistake. What did you do to fix it?

While this might not look like it’s based on problem-solving on the surface, it actually is. When you make a mistake, it creates a challenge, one you have to work your way through. At a minimum, it’s an opportunity to highlight problem-solving skills, even if you don’t address the topic directly.

When you choose an example, you want to go with a situation where the end was positive. However, the issue still has to be significant, causing something negative to happen in the moment that you, ideally, overcame.

“When I first began in a supervisory role, I had trouble setting down my individual contributor hat. I tried to keep up with my past duties while also taking on the responsibilities of my new role. As a result, I began rushing and introduced an error into the code of the software my team was updating. The error led to a memory leak. We became aware of the issue when the performance was hindered, though we didn’t immediately know the cause. I dove back into the code, reviewing recent changes, and, ultimately, determined the issue was a mistake on my end. When I made that discovery, I took several steps. First, I let my team know that the error was mine and let them know its nature. Second, I worked with my team to correct the issue, resolving the memory leak. Finally, I took this as a lesson about delegation. I began assigning work to my team more effectively, a move that allowed me to excel as a manager and help them thrive as contributors. It was a crucial learning moment, one that I have valued every day since.”

3. If you identify a potential risk in a project, what steps do you take to prevent it?

Yes, this is also a problem-solving question. The difference is, with this one, it’s not about fixing an issue; it’s about stopping it from happening. Still, you use problem-solving skills along the way, so it falls in this question category.

If you can, use an example of a moment when you mitigated risk in the past. If you haven’t had that opportunity, approach it theoretically, discussing the steps you would take to prevent an issue from developing.

“If I identify a potential risk in a project, my first step is to assess the various factors that could lead to a poor outcome. Prevention requires analysis. Ensuring I fully understand what can trigger the undesired event creates the right foundation, allowing me to figure out how to reduce the likelihood of those events occurring. Once I have the right level of understanding, I come up with a mitigation plan. Exactly what this includes varies depending on the nature of the issue, though it usually involves various steps and checks designed to monitor the project as it progresses to spot paths that may make the problem more likely to happen. I find this approach effective as it combines knowledge and ongoing vigilance. That way, if the project begins to head into risky territory, I can correct its trajectory.”

17 More Problem-Solving-Based Interview Questions

In the world of problem-solving questions, some apply to a wide range of jobs, while others are more niche. For example, customer service reps and IT helpdesk professionals both encounter challenges, but not usually the same kind.

As a result, some of the questions in this list may be more relevant to certain careers than others. However, they all give you insights into what this kind of question looks like, making them worth reviewing.

Here are 17 more problem-solving interview questions you might face off against during your job search:

• How would you describe your problem-solving skills?
• Can you tell me about a time when you had to use creativity to deal with an obstacle?
• Describe a time when you discovered an unmet customer need while assisting a customer and found a way to meet it.
• If you were faced with an upset customer, how would you diffuse the situation?
• Tell me about a time when you had to troubleshoot a complex issue.
• Imagine you were overseeing a project and needed a particular item. You have two choices of vendors: one that can deliver on time but would be over budget, and one that’s under budget but would deliver one week later than you need it. How do you figure out which approach to use?
• Your manager wants to upgrade a tool you regularly use for your job and wants your recommendation. How do you formulate one?
• A supplier has said that an item you need for a project isn’t going to be delivered as scheduled, something that would cause your project to fall behind schedule. What do you do to try and keep the timeline on target?
• Can you share an example of a moment where you encountered a unique problem you and your colleagues had never seen before? How did you figure out what to do?
• Imagine you were scheduled to give a presentation with a colleague, and your colleague called in sick right before it was set to begin. What would you do?
• If you are given two urgent tasks from different members of the leadership team, both with the same tight deadline, how do you choose which to tackle first?
• Tell me about a time you and a colleague didn’t see eye-to-eye. How did you decide what to do?
• Describe your troubleshooting process.
• Tell me about a time where there was a problem that you weren’t able to solve. What happened?
• In your opening, what skills or traits make a person an exceptional problem-solver?
• When you face a problem that requires action, do you usually jump in or take a moment to carefully assess the situation?
• When you encounter a new problem you’ve never seen before, what is the first step that you take?

Putting It All Together

At this point, you should have a solid idea of how to approach problem-solving interview questions. Use the tips above to your advantage. That way, you can thrive during your next interview.

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SnapXam is an AI-powered math tutor that can help students better understand different types of math, from calculus to trigonometry.  After entering the math problem, the tool quickly presents the final answer, as well as a step-by-step solution that shows how to work out the problem.

The unique AI math problem solver also provides access to informative YouTube videos that students can watch to learn more about different concepts in math. 

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• Geared toward older students. 
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Completing math assignments can be a long and tedious process. Having access to the best math AI tools can help eliminate the stress and frustration that come with not understanding math problems. For convenience, efficiency, and unmatched accuracy, try some of the top math AI tools like Mathful for free today!

This is a guest post, created for informational purposes only, and should not be considered as professional advice. Readers are encouraged to conduct their own research and consult with relevant experts before making any financial or investment decisions.

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A Robot-assisted real case-handling approach to improving students’ learning performances in vocational training

• Published: 14 May 2024

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• Chun-Chun Chang 1 &
• Gwo-Jen Hwang   ORCID: orcid.org/0000-0001-5155-276X 2 , 3  

In vocational education, cultivating students’ ability to deal with real cases is a crucial training objective. The BSFE (i.e., Brainstorming, Screening, Formation, Examination) model is a commonly adopted training procedure. Each stage is designed for guiding students to analyze and find solutions to handle real cases. However, as one teacher is generally responsible for several dozen students, it becomes challenging for the teacher to adequately address each student’s questions and individual needs. Therefore, this study proposed the robot teaching assistant-supported learning (RTAL) mode following the BSFE model to cope with this problem. This investigation assessed its efficacy through an experiment within an Acute Asthma Attack curriculum. The research involved 103 nursing students in their third year from two distinct classes at a vocational university. Fifty-three students from a class constituted the experimental group that implemented the RTAL approach, whereas the other class, comprising 50 students, was the control group utilizing the standard technology-supported learning (CTL) approach. Findings indicated that the experimental group surpassed the control group in various aspects, including learning outcomes, learning attitudes, problem-solving tedencies, critical thinking awareness, acceptance of technology, and satisfaction with the learning experience. The interview findings also revealed that the RTAL mode could cater to individualized learning needs, facilitate interaction, and serve as an auxiliary instructional tool.

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This study is supported in part by the National Science and Technology Council of Taiwan under contract numbers NSTC 112-2410-H-011-012-MY3 and MOST 111-2410-H-011 -007 -MY3. The study is also supported by the “Empower Vocational Education Research Center” of National Taiwan University of Science and Technology (NTUST) from the Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan.

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Department of Nursing, Chang Gung University of Science and Technology, Taoyuan City, Taiwan

Chun-Chun Chang

Graduate Institute of Educational Information and Measurement, National Taichung University of Education, Taichung City, Taiwan

Gwo-Jen Hwang

Graduate Institute of Digital Learning and Education, National Taiwan University of Science and Technology, Taipei City, Taiwan

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The authors contributed to the conceptualization and design of the study. Material preparation, data collection, analysis, project management and methodology were performed by Chun-Chun Chang. Methodology and supervision were performed Gwo-Jen Hwang.

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Chang, CC., Hwang, GJ. A Robot-assisted real case-handling approach to improving students’ learning performances in vocational training. Educ Inf Technol (2024). https://doi.org/10.1007/s10639-024-12778-w

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ORIGINAL RESEARCH article

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Research on Teaching Strategies and Skills in Different Educational Stages

Shaping Future-Ready Graduates with Mindset Shifts: Studying the Impact of Integrating Critical and Design Thinking in Design Innovation Education Provisionally Accepted

• 1 Singapore Institute of Technology, Singapore

The final, formatted version of the article will be published soon.

In an era marked by rapid change and complex global challenges, Institutes of Higher Learning (IHLs) are tasked with preparing students to navigate and address these evolving demands. This paper explores the critical role of Higher Education (HE) in equipping students with the necessary skills and mindsets to tackle real-world problems through innovative solutions. Integrating critical thinking and design thinking within a Design Innovation module is central to this exploration. The study is undergirded by a conceptual framework that blends critical, design, and futures thinking, focusing exclusively in this paper on applying critical thinking (CT) and design thinking (DT). The research investigates two primary questions: (1) How do students' DT and CT mindsets change after participation in a Design Innovation module? (2) Is CT a prerequisite for developing DT? This study aims to illuminate the shifts in students' mindsets from before to after the completion of the module, highlighting the importance of developing key dispositions for ethical and socially responsible problem-solving. Results show a statistically significant increase in CT and DT disposition scores from pre-to post-test, suggesting a shift to more positive CT and DT mindsets after going through the Design Innovation module. In addition, a significant moderation effect of pre-test CT mindset on the relationship between pre-test and post-test DT mindset scores was observed, implying that CT was a prerequisite for DT. The findings offer insights into the module's effectiveness in fostering future-ready graduates' thinking capabilities on innovating for real-world challenges and highlight the need for our future-ready students to achieve critical competence and creative confidence. Finally, we conclude the paper with recommendations for educators to integrate CT skill development intentionally and in tandem with DT skill development for a balanced approach to developing critical competence and creative confidence in interdisciplinary courses.

Keywords: Critical Thinking, design thinking, Design innovation, 21st-century skills and dispositions, interdisciplinary learning A. Tolerance for -Being comfortable with Ambiguity -Uncertainty

Received: 19 Dec 2023; Accepted: 15 May 2024.

Copyright: © 2024 Patel, Puah and Kok. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Dr. Nadya S. Patel, Singapore Institute of Technology, Singapore, Singapore

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Stormy Daniels Takes the Stand

The porn star testified for eight hours at donald trump’s hush-money trial. this is how it went..

This transcript was created using speech recognition software. While it has been reviewed by human transcribers, it may contain errors. Please review the episode audio before quoting from this transcript and email [email protected] with any questions.

It’s 6:41 AM. I’m feeling a little stressed because I’m running late. It’s the fourth week of Donald J. Trump’s criminal trial. It’s a white collar trial. Most of the witnesses we’ve heard from have been, I think, typical white collar witnesses in terms of their professions.

We’ve got a former publisher, a lawyer, accountants. The witness today, a little less typical, Stormy Daniels, porn star in a New York criminal courtroom in front of a jury more accustomed to the types of witnesses they’ve already seen. There’s a lot that could go wrong.

From “The New York Times,” I’m Michael Barbaro. This is “The Daily.”

Today, what happened when Stormy Daniels took the stand for eight hours in the first criminal trial of Donald J. Trump. As before, my colleague Jonah Bromwich was inside the courtroom.

[MUSIC PLAYING]

It’s Friday, May 10th.

So it’s now day 14 of this trial. And I think it’s worth having you briefly, and in broad strokes, catch listeners up on the biggest developments that have occurred since you were last on, which was the day that opening arguments were made by both the defense and the prosecution. So just give us that brief recap.

Sure. It’s all been the prosecution’s case so far. And prosecutors have a saying, which is that the evidence is coming in great. And I think for this prosecution, which is trying to show that Trump falsified business records to cover up a sex scandal, to ease his way into the White House in 2016, the evidence has been coming in pretty well. It’s come in well through David Pecker, former publisher of The National Enquirer, who testified that he entered into a secret plot with Trump and Michael Cohen, his fixer at the time, to suppress negative stories about Trump, the candidate.

It came in pretty well through Keith Davidson, who was a lawyer to Stormy Daniels in 2016 and negotiated the hush money payment. And we’ve seen all these little bits and pieces of evidence that tell the story that prosecutors want to tell. And the case makes sense so far. We can’t tell what the jury is thinking, as we always say.

But we can tell that there’s a narrative that’s coherent and that matches up with the prosecution’s opening statement. Then we come to Tuesday. And that day really marks the first time that the prosecution’s strategy seems a little bit risky because that’s the day that Stormy Daniels gets called to the witness stand.

OK, well, just explain why the prosecution putting Stormy Daniels on the stand would be so risky. And I guess it makes sense to answer that in the context of why the prosecution is calling her as a witness at all.

Well, you can see why it makes sense to have her. The hush money payment was to her. The cover-up of the hush money payment, in some ways, concerns her. And so she’s this character who’s very much at the center of this story. But according to prosecutors, she’s not at the center of the crime. The prosecution is telling a story, and they hope a compelling one. And arguably, that story starts with Stormy Daniels. It starts in 2006, when Stormy Daniels says that she and Trump had sex, which is something that Trump has always denied.

So if prosecutors were to not call Stormy Daniels to the stand, you would have this big hole in the case. It would be like, effect, effect, effect. But where is the cause? Where is the person who set off this chain reaction? But Stormy Daniels is a porn star. She’s there to testify about sex. Sex and pornography are things that the jurors were not asked about during jury selection. And those are subjects that bring up all kinds of different complex reactions in people.

And so, when the prosecutors bring Stormy Daniels to the courtroom, it’s very difficult to know how the jurors will take it, particularly given that she’s about to describe a sexual episode that she says she had with the former president. Will the jurors think that makes sense, as they sit here and try to decide a falsifying business records case, or will they ask themselves, why are we hearing this?

So the reason why this is the first time that the prosecution’s strategy is, for journalists like you, a little bit confusing, is because it’s the first time that the prosecution seems to be taking a genuine risk in what they’re putting before these jurors. Everything else has been kind of cut and dry and a little bit more mechanical. This is just a wild card.

This is like live ammunition, to some extent. Everything else is settled and controlled. And they know what’s going to happen. With Stormy Daniels, that’s not the case.

OK, so walk us through the testimony. When the prosecution brings her to the stand, what actually happens?

It starts, as every witness does, with what’s called direct examination, which is a fancy word for saying prosecutors question Stormy Daniels. And they have her tell her story. First, they have her tell the jury about her education and where she grew up and her professional experience. And because of Stormy Daniels’s biography, that quickly goes into stripping, and then goes into making adult films.

And I thought the prosecutor who questioned her, Susan Hoffinger, had this nice touch in talking about that, because not only did she ask Daniels about acting in adult films. But she asked her about writing and directing them, too, emphasizing the more professional aspects of that work and giving a little more credit to the witness, as if to say, well, you may think this or you may think that. But this is a person with dignity who took what she did seriously. Got it.

What’s your first impression of Daniels as a witness?

It’s very clear that she’s nervous. She’s speaking fast. She’s laughing to herself and making small jokes. But the tension in the room is so serious from the beginning, from the moment she enters, that those jokes aren’t landing. So it just feels, like, really heavy and still and almost oppressive in there. So Daniels talking quickly, seeming nervous, giving more answers than are being asked of her by the prosecution, even before we get to the sexual encounter that she’s about to describe, all of that presents a really discomfiting impression, I would say.

And how does this move towards the encounter that Daniels ultimately has?

It starts at a golf tournament in 2006, in Lake Tahoe, Nevada. Daniels meets Trump there. There are other celebrities there, too. They chatted very briefly. And then she received a dinner invitation from him. She thought it over, she says. And she goes to have dinner with Trump, not at a restaurant, by the way. But she’s invited to join him in the hotel suite.

So she gets to the hotel suite. And his bodyguard is there. And the hotel door is cracked open. And the bodyguard greets her and says she looks nice, this and that. And she goes in. And there’s Donald Trump, just as expected. But what’s not expected, she says, is that he’s not wearing what you would wear to a dinner with a stranger, but instead, she says, silk or satin pajamas. She asked him to change, she says. And he obliges.

He goes, and he puts on a dress shirt and dress pants. And they sit down at the hotel suite’s dining room table. And they have a kind of bizarre dinner. Trump is asking her very personal questions about pornography and safe sex. And she testifies that she teased him about vain and pompous he is. And then at some point, she goes to the bathroom. And she sees that he has got his toiletries in there, his Old Spice, his gold tweezers.

Very specific details.

Yeah, we’re getting a ton of detail in this scene. And the reason we’re getting those is because prosecutors are trying to elicit those details to establish that this is a credible person, that this thing did happen, despite what Donald Trump and his lawyers say. And the reason you can know it happened, prosecutors seem to be saying, is because, look at all these details she can still summon up.

She comes out of the bathroom. And she says that Donald Trump is on the hotel bed. And what stands out to me there is what she describes as a very intense physical reaction. She says that she blacked out. And she quickly clarifies, she doesn’t mean from drugs or alcohol. She means that, she says, that the intensity of this experience was such that, suddenly, she can’t remember every detail. The prosecution asks a question that cuts directly to the sex. Essentially, did you start having sex with him? And Daniels says that she did. And she continues to provide more details than even, I think, the prosecution wanted.

And I think we don’t want to go chapter and verse through this claimed sexual encounter. But I wonder what details stand out and which details feel important, given the prosecution’s strategy here.

All the details stand out because it’s a story about having had sex with a former president. And the more salacious and more private the details feel, the more you’re going to remember them. So we’ll remember that Stormy Daniels said what position they had sex in. We’ll remember that she said he didn’t use a condom. Whether that’s important to the prosecution’s case, now, that’s a much harder question to answer, as we’ve been saying.

But what I can tell you is, as she’s describing having had sex with Donald Trump, and Donald Trump is sitting right there, and Eric Trump, his son, is sitting behind him, seeming to turn a different color as he hears this embarrassment of his father being described to a courtroom full of reporters at this trial, it’s hard to even describe the energy in that room. It was like nothing I had ever experienced. And it was just Daniels’s testimony and, seemingly, the former President’s emotions. And you almost felt like you were trapped in there with both of them as this description was happening.

Well, I think it’s important to try to understand why the prosecution is getting these details, these salacious, carnal, pick your word, graphic details about sex with Donald Trump. What is the value, if other details are clearly making the point that she’s recollecting something?

Well, I think, at this point, we can only speculate. But one thing we can say is, this was uncomfortable. This felt bad. And remember, prosecutor’s story is not about the sex. It’s about trying to hide the sex. So if you’re trying to show a jury why it might be worthwhile to hide a story, it might be worth —

Providing lots of salacious details that a person would want to hide.

— exposing them to how bad that story feels and reminding them that if they had been voters and they had heard that story, and, in fact, they asked Daniels this very question, if you hadn’t accepted hush money, if you hadn’t signed that NDA, is this the story you would have told? And she said, yes. And so where I think they’re going with this, but we can’t really be sure yet, is that they’re going to tell the jurors, hey, that story, you can see why he wanted to cover that up, can’t you?

You mentioned the hush money payments. What testimony does Daniels offer about that? And how does it advance the prosecution’s case of business fraud related to the hush money payments?

So little evidence that it’s almost laughable. She says that she received the hush money. But we actually already heard another witness, her lawyer at the time, Keith Davidson, testify that he had received the hush money payment on her behalf. And she testified about feeling as if she had to sell this story because the election was fast approaching, almost as if her leverage was slipping away because she knew this would be bad for Trump.

That feels important. But just help me understand why it’s important.

Well, what the prosecution has been arguing is that Trump covered up this hush money payment in order to conceal a different crime. And that crime, they say, was to promote his election to the presidency by illegal means.

Right, we’ve talked about this in the past.

So when Daniels ties her side of the payment into the election, it just reminds the jurors maybe, oh, right, this is what they’re arguing.

So how does the prosecution end this very dramatic, and from everything you’re saying, very tense questioning of Stormy Daniels about this encounter?

Well, before they can even end, the defense lawyers go and they consult among themselves. And then, with the jury out of the room, one of them stands up. And he says that the defense is moving for a mistrial.

On what terms?

He says that the testimony offered by Daniels that morning is so prejudicial, so damning to Trump in the eyes of the jury, that the trial can no longer be fair. Like, how could these jurors have heard these details and still be fair when they render their verdict? And he says a memorable expression. He says, you can’t un-ring that bell, meaning they heard it. They can’t un-hear it. It’s over. Throw out this trial. It should be done.

Wow. And what is the response from the judge?

So the judge, Juan Merchan, he hears them out. And he really hears them out. But at the end of their arguments, he says, I do think she went a little too far. He says that. He said, there were things that were better left unsaid.

By Stormy Daniels?

By Stormy Daniels. And he acknowledges that she is a difficult witness. But, he says, the remedy for that is not a mistrial, is not stopping the whole thing right now. The remedy for that is cross-examination. If the defense feels that there are issues with her story, issues with her credibility, they can ask her whatever they want. They can try to win the jury back over. If they think this jury has been poisoned by this witness, well, this is their time to provide the antidote. The antidote is cross-examination. And soon enough, cross-examination starts. And it is exactly as intense and combative as we expected.

We’ll be right back.

So, Jonah, how would you characterize the defense’s overall strategy in this intense cross-examination of Stormy Daniels?

People know the word impeach from presidential impeachments. But it has a meaning in law, too. You impeach a witness, and, specifically, their credibility. And that’s what the defense is going for here. They are going to try to make Stormy Daniels look like a liar, a fraud, an extortionist, a money-grubbing opportunist who wanted to take advantage of Trump and sought to do so by any means necessary.

And what did that impeachment strategy look like in the courtroom?

The defense lawyer who questions Stormy Daniels is a woman named Susan Necheles. She’s defended Trump before. And she’s a bit of a cross-examination specialist. We even saw her during jury selection bring up these past details to confront jurors who had said nasty things about Trump on social media with. And she wants to do the same thing with Daniels. She wants to bring up old interviews and old tweets and things that Daniels has said in the past that don’t match what Daniels is saying from the stand.

What’s a specific example? And do they land?

Some of them land. And some of them don’t. One specific example is that Necheles confronts Daniels with this old tweet, where Daniels says that she’s going to dance down the street if Trump goes to jail. And what she’s trying to show there is that Daniels is out for revenge, that she hates Trump, and that she wants to see him go to jail. And that’s why she’s testifying against him.

And Daniels is very interesting during the cross-examination. It’s almost as if she’s a different person. She kind of squares her shoulders. And she sits up a little straighter. And she leans forward. Daniels is ready to fight. But it doesn’t quite land. The tweet actually says, I’ll dance down the street when he’s selected to go to jail.

And Daniels goes off on this digression about how she knows that people don’t get selected to go to jail. That’s not how it works. But she can’t really unseat this argument, that she’s a political enemy of Donald Trump. So that one kind of sticks, I would say. But there are other moves that Necheles tries to pull that don’t stick.

So unlike the prosecution, which typically used words like adult, adult film, Necheles seems to be taking every chance she can get to say porn, or pornography, or porn star, to make it sound base or dirty. And so when she starts to ask Daniels about actually being in pornography, writing, acting, and directing sex films, she tries to land a punch line, Necheles does. She says, so you have a lot of experience making phony stories about sex appear to be real, right?

As if to say, perhaps this story you have told about entering Trump’s suite in Lake Tahoe and having sex with him was made up.

Just another one of your fictional stories about sex. But Daniels comes back and says, the sex in the films, it’s very much real, just like what happened to me in that room. And so, when you have this kind of combat of a lawyer cross-examining very aggressively and the witness fighting back, you can feel the energy in the room shift as one lands a blow or the other does. But here, Daniels lands one back. And the other issue that I think Susan Necheles runs into is, she tries to draw out disparities from interviews that Daniels gave, particularly to N-TOUCH, very early on once the story was out.

It’s kind of like a tabloid magazine?

But some of the disparities don’t seem to be landing quite like Necheles would want. So she tries to do this complicated thing about where the bodyguard was in the room when Daniels walked into the room, as described in an interview in a magazine. But in that magazine interview, as it turns out, Daniels mentioned that Trump was wearing pajamas. And so, if I’m a juror, I don’t care where the bodyguard is. I’m thinking about, oh, yeah, I remember that Stormy Daniels said now in 2024 that Trump was wearing pajamas.

I’m curious if, as somebody in the room, you felt that the defense was effective in undermining Stormy Daniels’s credibility? Because what I took from the earlier part of our conversation was that Stormy Daniels is in this courtroom on behalf of the prosecution to tell a story that’s uncomfortable and has the kind of details that Donald Trump would be motivated to try to hide. And therefore, this defense strategy is to say, those details about what Trump might want to hide, you can’t trust them. So does this back and forth effectively hurt Stormy Daniels’s credibility, in your estimation?

I don’t think that Stormy Daniels came off as perfectly credible about everything she testified about. There are incidents that were unclear or confusing. There were things she talked about that I found hard to believe, when she, for instance, denied that she had attacked Trump in a tweet or talked about her motivations. But about what prosecutors need, that central story, the story of having had sex with him, we can’t know whether it happened.

But there weren’t that many disparities in these accounts over the years. In terms of things that would make me doubt the story that Daniels was telling, details that don’t add up, those weren’t present. And you don’t have to take my word for that, nor should you. But the judge is in the room. And he says something very, very similar.

What does he say? And why does he say it?

Well, he does it when the defense, again, at the end of the day on Thursday, calls for a mistrial.

With a similar argument as before?

Not only with a similar argument as before, but, like, almost the exact same argument. And I would say that I was astonished to see them do this. But I wasn’t because I’ve covered other trials where Trump is the client. And in those trials, the lawyers, again and again, called for a mistrial.

And what does Judge Marchan say in response to this second effort to seek a mistrial?

Let me say, to this one, he seems a little less patient. He says that after the first mistrial ruling, two days before, he went into his chambers. And he read every decision he had made about the case. He took this moment to reflect on the first decision. And he found that he had, in his own estimation, which is all he has, been fair and not allowed evidence that was prejudicial to Trump into this trial. It could continue. And so he said that again. And then he really almost turned on the defense. And he said that the things that the defense was objecting to were things that the defense had made happen.

He says that in their opening statement, the defense could have taken issue with many elements of the case, about whether there were falsified business records, about any of the other things that prosecutors are saying happened. But instead, he says, they focused their energy on denying that Trump ever had sex with Daniels.

And so that was essentially an invitation to the prosecution to call Stormy Daniels as a witness and have her say from the stand, yes, I had this sexual encounter. The upshot of it is that the judge not only takes the defense to task. But he also just says that he finds Stormy Daniels’s narrative credible. He doesn’t see it as having changed so much from year to year.

Interesting. So in thinking back to our original question here, Jonah, about the idea that putting Stormy Daniels on the stand was risky, I wonder if, by the end of this entire journey, you’re reevaluating that idea because it doesn’t sound like it ended up being super risky. It sounded like it ended up working reasonably well for the prosecution.

Well, let me just assert that it doesn’t really matter what I think. The jury is going to decide this. There’s 12 people. And we can’t know what they’re thinking. But my impression was that, while she was being questioned by the prosecution for the prosecution’s case, Stormy Daniels was a real liability. She was a difficult witness for them.

And the judge said as much. But when the defense cross-examined her, Stormy Daniels became a better witness, in part because their struggles to discredit her may have actually ended up making her story look more credible and stronger. And the reason that matters is because, remember, we said that prosecutors are trying to fill this hole in their case. Well, now, they have. The jury has met Stormy Daniels. They’ve heard her account. They’ve made of it what they will. And now, the sequence of events that prosecutors are trying to line up as they seek prison time for the former President really makes a lot of sense.

It starts with what Stormy Daniels says with sex in a hotel suite in 2006. It picks up years later, as Donald Trump is trying to win an election and, prosecutors say, suppressing negative stories, including Stormy Daniels’s very negative story. And the story that prosecutors are telling ends with Donald Trump orchestrating the falsification of business records to keep that story concealed.

Well, Jonah, thank you very much. We appreciate it.

Of course, thanks for having me.

The prosecution’s next major witness will be Michael Cohen, the former Trump fixer who arranged for the hush money payment to Stormy Daniels. Cohen is expected to take the stand on Monday.

Here’s what else you need to know today. On Thursday, Israeli Prime Minister Benjamin Netanyahu issued a defiant response to warnings from the United States that it would stop supplying weapons to Israel if Israel invades the Southern Gaza City of Rafah. So far, Israel has carried out a limited incursion into the city where a million civilians are sheltering, but has threatened a full invasion. In a statement, Netanyahu said, quote, “if we need to stand alone, we will stand alone.”

Meanwhile, high level ceasefire negotiations between Israel and Hamas have been put on hold in part because of anger over Israel’s incursion into Rafah.

A reminder, tomorrow, we’ll be sharing the latest episode of our colleague’s new show, “The Interview” This week on “The Interview,” Lulu Garcia-Navarro talks with radio host Charlamagne Tha God about his frustrations with how Americans talk about politics.

If me as a Black man, if I criticize Democrats, then I’m supporting MAGA. But if I criticize, you know, Donald Trump and Republicans, then I’m a Democratic shill. Why can’t I just be a person who deals in nuance?

Today’s episode was produced by Olivia Natt and Michael Simon Johnson. It was edited by Lexie Diao, with help from Paige Cowett, contains original music by Will Reid and Marion Lozano, and was engineered by Alyssa Moxley. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly.

That’s it for “The Daily.” I’m Michael Barbaro. See you on Monday.

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• May 13, 2024   •   27:46 How Biden Adopted Trump’s Trade War With China
• May 10, 2024   •   27:42 Stormy Daniels Takes the Stand
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• May 3, 2024   •   25:33 The Protesters and the President
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Hosted by Michael Barbaro

Featuring Jonah E. Bromwich

Produced by Olivia Natt and Michael Simon Johnson

Edited by Lexie Diao

With Paige Cowett

Original music by Will Reid and Marion Lozano

Engineered by Alyssa Moxley

Listen and follow The Daily Apple Podcasts | Spotify | Amazon Music | YouTube

This episode contains descriptions of an alleged sexual liaison.

What happened when Stormy Daniels took the stand for eight hours in the first criminal trial of former President Donald J. Trump?

Jonah Bromwich, one of the lead reporters covering the trial for The Times, was in the room.

On today’s episode

Jonah E. Bromwich , who covers criminal justice in New York for The New York Times.

Background reading

In a second day of cross-examination, Stormy Daniels resisted the implication she had tried to shake down Donald J. Trump by selling her story of a sexual liaison.

Here are six takeaways from Ms. Daniels’s earlier testimony.

There are a lot of ways to listen to The Daily. Here’s how.

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The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Mike Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, John Ketchum, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Dan Farrell, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Summer Thomad, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Renan Borelli, Maddy Masiello, Isabella Anderson and Nina Lassam.

Jonah E. Bromwich covers criminal justice in New York, with a focus on the Manhattan district attorney’s office and state criminal courts in Manhattan. More about Jonah E. Bromwich

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