What is the Critical Thinking Test?

Critical thinking practice test, take a free practice critical thinking test, practice critical thinking test.

Updated November 16, 2023

Edward Melett

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.

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 practice critical thinking test.

The test consists of three questions . 

After you have answered all the questions, you will be shown the correct answers and given full explanations.

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 .

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

Six friends are seated in a restaurant across a rectangular table. There are three chairs on each side. Adam and Dorky do not have anyone sitting to their right and Clyde and Benjamin do not have anyone sitting to their left. Adam and Benjamin are not sitting on the same side of the table.

If Ethan is not sitting next to Dorky, who is seated immediately to the left of Felix?

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15 Free Psychometric Test Questions and Answers

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  • Logic Reasoning Practice Questions with Answer key

Logical reasoning questions are designed to assess your ability to analyze, evaluate, and draw conclusions based on given information. There are many types of questions, each focusing on different aspects of critical thinking. Here are some common types of logical reasoning questions:

Verbal Reasoning       Problem Solving or Word Problems     Folding     Analogies

Image Analogies (Matching)     Analytical Reasoning   Verbal Classification

Sentence Logic     Abstract reasoning and Pattern Recognition

Verbal Reasoning

Verbal reasoning questions test your ability to understand and analyze written information.

Tom and Tim are brothers. They look exactly the same. They also have the same birthdays.

a. Tom is older than Tim b. Tim is more handsome than Tom c. Tom and Tim are twins d. Tom and Tim are best friends

1. C The only certain thing is they are twins.

Verbal Reasoning Practice

Tests with Verbal Reasoning Questions

Deputy Sheriff   Corrections Canada BC Police   RCMP

Abstract Reasoning & Pattern Recognition Questions

Abstract reasoning and pattern recognition.

Abstract reasoning and Pattern Recognition questions test your ability to identify patterns and relationships. Abstract reasoning and pattern recognition are cognitive skills that enable you to identify relationships, make connections, and solve problems that involve complex or abstract information. These skills are crucial for tasks that require higher-order thinking and adaptability to novel situations.

Example Question:

problem solving reasoning questions

1. B Each figure is created by adding the mirror image of the previous figure.

Abstract Reasoning and Pattern Recognition Practice

Tests with Abstract Reasoning and Pattern Recognition 

RCMP     TACHS

Problem Solving Questions

Problem solving or word problems..

   Word problems give background information, in plain English, on a real-world problem, with one or more variables missing.   You are required to translate into mathematical notation and solve for the missing information.

Problem-solving is the process of identifying, analyzing, and resolving problems in a systematic and logical manner. Word problems, are mathematical problems that in everyday language and use real-world scenarios. Some information is given, and one or more pieces of information, or variables, are missing.  You must understand the given information, and the relationship to the missing variables, identify the mathematical operations necessary to solve the problem, and then carry out those operations to arrive at the correct answer.

1. Employees of a discount appliance store receive an additional 20% off the lowest price on any item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher originally cost $450?

a. $280.90 b. $287.00 c. $292.50 d. $306.00

1. D The cost of the dishwasher = $450 15% discount amount = 450•15/100 = $67.5 The discounted price = 450 – 67.5 = $382.5 20% additional discount amount on lowest price = 382.5•20/100 = $76.5 So, the final discounted price = 382.5 – 76.5 = $306.0049

Problem Solving Practice

How to Solve Word Problems

Types of Word Problems

Most Common Word Problem Mistakes on a Test

Spatial Reasoning Visual Acuity Questions

Spatial reasoning questions.

test your ability to visualize and manipulate objects in two or three dimensions.  These questions require you to mentally visualize objects and their relationships in space, as well as to understand how they move and interact with each other.

Visual acuity is the accurately perception of different visual elements, such as shapes, colors, and patterns.

Example question:

problem solving reasoning questions

Spatial Ability Practice

Spatial Relations Practice (BOOK)

Spatial Relations II – Folding

Spatial Relations II – Folding questions are a type of visual-spatial reasoning question used in cognitive and intelligence tests, and pre-employment test such as the Canada Post GAT , CFAT , CBSA and the CCAT tests . These questions require individuals to mentally manipulate a two-dimensional object by folding it along specified lines to create a three-dimensional object, and then to identify the resulting object or how it would appear if unfolded.

Folding Example:

When the two longest sides touch what will the shape be?

problem solving reasoning questions

Folding Practice and Tutorial

Spatial Relations Practice (Book)

Analogies on a standardized test, such as IQ tests or aptitude tests, assess a test-taker’s verbal reasoning ability. An analogy question consists of two pairs of related words. The test-taker is then asked to identify a third pair of words that has the same or a similar relationship.

1.  Nest : Bird 

a. Cave : bear b. flower : petal c. window : house d. dog : basket

This is a Functional relationship.   A Bird lives in a nest, the way way a bear lives in a cave.

Analogy Practice Questions

Analogy Tutorial

Analogy Quiz

Analogies – I Images

An analogy is a comparison between 2 things.    You are presented with an object and asked to choose an object that is similar or is not similar.  Also called Matching.

In the following questions, select the choice that does not belong with the other three.

problem solving reasoning questions

1. C All signs are directional road signs except choice C.

Image Analogy (Matching) Practice

Analytical Reasoning

Analytical reasoning questions are included in standardized tests, such as IQ, aptitude, and entrance exams for graduate or professional programs. Analytical reasoning questions test a person’s ability to think logically and analyze complex information.

Analytical reasoning questions typically present a scenario, such as a a group of facts and rules, a diagram, chart, or passage of text. The test-taker is asked to use this information to answer a series of questions that requires drawing logical conclusions, or deductions.  The test-taker must determine, give a set of facts and rules what could or must be true.

1. Use your knowledge of the real relations between the existing nouns to determine the best response.

A CRUX resembles LILO but is closer to the Sun

A TIGO resembles Jupiter but is farther from the Sun

A LILO resembles Earth but is closer to the Sun

Which of the following is the best response?

a. LILO is farther from the Sun than Jupiter

b. CRUX is closer to the Sun than Jupiter

c. Jupiter is closer to the Sun than LILO

d. LILO is farther from the Sun than TIGO

1. B Based on the relations outlined in the first & third statements, we know that a CRUX is closer to the Sun than a LILO, which is closer than Earth. We also know that Earth is closer than Jupiter from the knowledge we have of these existing nouns, and, from the second statement, we know that Jupiter is closer than a TIGO. From closest to farthest, the order of the words is: CRUX, LILO, Earth, Jupiter, TIGO. Therefore, t choice 2 is the correct answer.

[CRUX<LILO<Earth<Jupiter<TIGO in terms of distance from the Sun] 

Analytical Reasoning Practice

Verbal Classification

Verbal classification.

Verbal classification are common on IQ or aptitude tests, that assess a person’s ability to identify relationships between words and concepts.

The test-taker is given a list of words and asked to identify the word does not belong, based on the relationships or patterns of the given words.

1. Which word does not belong?

a. Jet b. Float plane c. Kite d. Biplane

1. C A kite is not a type of plane.

Verbal Classification Practice

Sentence Logic

Sentence logic.

Sentence logic questions are found in standardized tests, such as aptitude or entrance tests for graduate or professional programs, that assess a person’s ability to understand and apply logical reasoning.

The test-taker is presented with a set of sentences or paragraphs in the form of syllogisms:  2 sentences, or premises are given, and students are asked if the third sentence is true or false.

1.  The Silver fish can swim faster than the black fish. The gold fish can swim faster than the black fish. The gold fish can swim faster than the silver fish. If the first 2 statements are true, then the third statement is:

True False Uncertain

1. Uncertain

We don’t have enough information here to make a decision. Perhaps the gold fish can swim faster than the black fish AND the silver fish – we don’t know.

Sentence Logic Practice

Logic Tutorial

problem solving reasoning questions

Logical Reasoning Questions and Answers

Logical reasoning interview questions and answers.

Here you can find Logical Reasoning interview questions and answers for your placement interviews and entrance exam preparation.

Why should I learn to solve Logical Reasoning questions?

Learn and practise solving Logical Reasoning questions to enhance your skills so that you can clear interviews, competitive examinations, and various entrance tests (CAT, GATE, GRE, MAT, bank exams, railway exams, etc.) with full confidence.

Where can I get Logical Reasoning questions and answers with explanations?

IndiaBIX provides you with numerous Logical Reasoning questions and answers with explanations. Fully solved problems with detailed answer descriptions and explanations are given and will be easy to understand.

Where can I get Logical Reasoning MCQ interview questions and answers (objective type, multiple choice)?

Here you can find multiple-choice-type Logical Reasoning questions and answers for your interviews and entrance examinations. Objective-type and true-or-false-type questions are also given here.

How do I download Logical Reasoning questions in PDF format?

You can download Logical Reasoning quiz questions and answers as PDF files or eBooks.

How do I solve Logical Reasoning quiz problems?

You can easily solve all kinds of quiz questions based on Logical Reasoning by practising the given exercises, including shortcuts and tricks.

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Analytical Reasoning Tests

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Analytical reasoning tests examine an individual’s ability to apply logic to solve problems. The questions vary depending on the type of analytical reasoning test you’re taking: from extracting key information from complex passages of text (verbal reasoning), to looking for patterns in a series of images (non-verbal reasoning), or using given information to draw conclusions or make predictions (inductive and deductive reasoning).

What is an analytical reasoning test?

An analytical reasoning test is a type of aptitude test that is often used by employers to assess a job candidate’s ability to think critically and solve complex problems.

As well as these skills, employers want to see evidence that you can keep calm under pressure and work quickly against the clock.

The test is nearly always timed, meaning you don’t have long to work through each question to find the correct answer.

Depending on which type of job you’re applying for, the test you take may be in the style of verbal reasoning , non-verbal reasoning , inductive reasoning or deductive reasoning . As such, it’s worth practicing as many different types of tests as you can to familiarise yourself with the questions.

The analytical reasoning test is widely used because it looks for skills that are sought after in almost every industry. It helps employers find candidates who will be quick to learn, adapt and solve problems.

Why do use analytical reasoning tests?

Employers use analytical reasoning tests to assess candidates’ ability to analyze complex information, make logical deductions, and solve problems effectively. These tests help employers evaluate candidates’ critical thinking skills, decision-making abilities, and aptitude for handling challenging situations. By administering analytical reasoning tests, employers can identify candidates who possess the cognitive abilities necessary for success in roles that require analytical thinking, such as management, finance, engineering, and data analysis. Additionally, these tests provide employers with valuable insights into candidates’ problem-solving approaches and their capacity to navigate intricate scenarios, aiding in the selection of the most suitable candidates for the job.

As applicants have to work harder and harder to make their CV stand out, an aptitude test like this is a good way of ensuring candidates possess the necessary skills.

It’s common for employers or recruiters to set the analytical reasoning test before the interview stage, so they can select candidates based on their test performance. The test therefore acts as a filter, ensuring employers get to meet the people they believe are most likely to excel.

Completing a good analytical reasoning test gives an indication that you’re a strong critical thinker who can rise to the challenge – an attractive proposition for any employer.

How do analytical reasoning tests work?

An employer will select the type of analytical reasoning test (verbal, non-verbal, inductive or deductive) based on the skills they want to examine.

Finding out exactly which type of test you’ll be taking is helpful so you can focus your preparation, but if you don’t know we recommend trying out all of the different mock tests to familiarise yourself with the individual question styles and formats.

When you take the test, you’ll normally have around one minute to answer each question – which is yet another reason to familiarise yourself with the kinds of questions you’re likely to be asked.

Here’s a brief overview of the four different test types:

  • Verbal reasoning – requires you to read through long passages of text and showcase your comprehension and analysis skills by answering a series of questions on what you’ve just read.
  • Non-verbal reasoning – presents you with images such as graphs, pictures and patterns, and requires you to use your logic and problem-solving skills to decipher the rule that connects the sequence.
  • Inductive reasoning – equips you with certain facts or information, and then asks you to make predictions or assumptions based on that evidence.
  • Deductive reasoning – will ask you to use the statements given to you to make further statements of fact.

After the test, your score will be calculated and compared to those of the other individuals who took the same test, or a normative group (which can help an employer see how well you fared compared to previous candidates).

Analytical test formats

Verbal Reasoning Tests

Verbal reasoning tests examine your ability to draw out key information from long, often complex passages of text, to form a conclusion. Very often this takes the form of questions to which you would select ‘true’, ‘false’ or ‘cannot say’ as the response.

No prior knowledge of the subject matter is required, but it is important to practice verbal reasoning tests as it can take a while to get used to the question format.

You will need to be able to distinguish between what’s fact and what’s merely being inferred when you’re reading through the passages of text. This shows an employer that you have the comprehension, logic and analytical skills they’re looking for.

Practising verbal reasoning tests before you take the one that really matters is vital if you want to showcase the best of your abilities to a potential employer. The more mock tests you take, the better you’ll get at sifting through the passages of text for evidence, quickly assimilating the information and confidently deciding what’s true, false or uncertain.

You’ll normally have around one minute to answer each question on the verbal reasoning test (although it’s always worth checking this is the case with your test when you begin). It’s important you don’t spend ages on a challenging problem, as you could end up not answering other questions that you might have easily been able to answer.

At the end, if you have time left you can always go back to anything you weren’t sure about and have another go.

The verbal reasoning test is most commonly used by employers or recruiters hiring for roles where strong communication skills are critical – which applies to most jobs, hence their popularity.

Non-Verbal Reasoning Tests

Non-verbal reasoning tests comprise graphs, tables and data, and the accompanying questions will assess how adept you are at drawing conclusions from limited information, finding connecting patterns and working quickly under considerable time pressure.

These types of analytical reasoning tests are often part of the application process for roles in industries such as finance, engineering and HR.

The best way you can prepare for a non-verbal reasoning test is to take as many mock tests as you can. After you’ve completed a test, it’s important to look back through your answers and identify your weaker areas, so you know where you need to direct your focus.

Not only will practising ensure you get quicker and better, it’ll also help you familiarise yourself with the different graphs, tables and images you’re likely to be confronted with on a non-verbal reasoning test.

As with the verbal reasoning test, you normally get around one minute to answer each question, so finding the right balance between speed and accuracy is really important – something that you’ll find a lot easier if you’ve put the practice time in beforehand.

A successful non-verbal reasoning test will prove to an employer that you have the critical thinking, reasoning and logical skills needed to cope with the demands of the job you’re applying for.

Inductive / Deductive Reasoning Tests

If you’re asked to take an inductive test or deductive test , you’re essentially being asked to show how well you can identify patterns and use your logic. Although the overall skills you’ll demonstrate are very similar, the two tests are slightly different.

Inductive reasoning test – you’ll need to identify relationships between statements, images or facts and figures, and use this analysis to show, logically, what should come next.

Deductive reasoning test – you’ll be given a statement of fact and you’ll need to use this information to deduce another factually correct statement.

These aptitude tests are most commonly used in the hiring of science, tech and IT roles, as the type of skills they seek to showcase – logical thinking, identifying patterns, problem solving and critical thinking – are all valuable in these industries.

So even if you have the type of brain that finds these kinds of problems easier than most, it’s always worth practising inductive/deductive reasoning tests beforehand to familiarise yourself with the specific style of question, and what’s required of you in a short amount of time.

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5 Free Example Analytical Reasoning Questions

Here are five example analytical questions to try out. Answers for all five are below the tests. If you need further practice, try out our full free tests.

Verbal Question 1

verbal reasoning question

Statement : A derivative could be used by an airline to secure the price of oil now, which it won’t use until six months time.

Verbal Question 2

verbal reasoning practice questions

Statement : More people taking early retirement is the major contributory factor to the public sector pension deficit.

Diagrammatic Question 1

diagrammatic reasoning question

Which is the next logical image in the sequence?

Numerical Question 1

numerical reasoning question

What was the ratio of the cost of a Google click in April compared to the cost of a Facebook and Yahoo click in February?

Abstract Question 1

abstract reasoning question

Which of the boxes comes next in the sequence?

Verbal Question 1 : True – “to secure the price of a commodity which is to be “bought” at a future date, but at a price that is set today.”

Verbal Question 2 : Cannot tell – the passage refers to both this fact, extended life expectancy, and that the value of pension fund assets has fallen.

Diagrammatic Question 1 : There is a central figure and four figures with one in each corner: (i) The central figure firstly increases in size over a series of three, then decreases in the same fashion; (ii) The central figure changes from white, to having a dotted outline, to black; and (iii) The four figures rotate around the four corners, moving two corners at a time. So the correct answer is F.

Numerical Question 1 : Step 1. Extract the relevant figures from the graph Cost of per click in April. Google 18 cents : Facebook + Yahoo (14 + 6 = 20 cents). Step 2. Divide 20 by 18 to calculate the ratio. 20 ÷18 = 1.11 Step 3. Present as a ratio 1 : 1.11

Abstract Question 1 : Arrow changes direction from pointing up, to pointing down, with each turn. 2. Triangle moves from top left corner in an anti-clockwise direction around the frame with each turn. So the answer is B.

Sample Analytical Reasoning Tests question Test your knowledge!

Question 1

Consider a set of figures where the size of shapes increases with each subsequent figure. If the sequence starts with a small triangle and each figure adds two centimeters to each side of the shape, what size would the fifth shape be?

When analyzing a series of processes in a diagram, you notice that there is a cyclical pattern. If a process starts with A, continues to B, followed by C, and then starts over, what would be the fourth step after starting over twice?

  • The process ends.

If a premise states that 'All managers can handle stress' and 'Susan is a manager', what conclusion can you draw?

  • Susan cannot handle stress.
  • Not all managers can handle stress.
  • Susan can handle stress.
  • The ability to handle stress is not important for managers.

You are given a dataset where the sales of a company have increased by 5% every month for the past 4 months. If the sales in the first month were $200,000, what should be the sales in the fifth month?

After reading the following passage, determine the main argument presented by the author. 'Many companies focus on short-term gains rather than long-term stability. This can lead to decisions that are profitable in the immediate future but may jeopardize the company's longevity. It is essential for businesses to balance immediate profits with sustainable growth.'

  • Short-term gains are more important than long-term stability.
  • Companies should consider long-term stability over short-term profits.
  • Decisions should balance immediate profits and sustainable growth.
  • Long-term stability is impossible to achieve for most companies.

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Analytical Reasoning Tests Tips

1 background research.

Get as much background information as possible on the test you’ll be taking from the employer or recruiter, so you know which areas to focus on.

2 Prepare with mock tests

Preparation is key – take mock tests in a quiet, distraction-free area and always make sure you go back through your answers at the end to identify any areas you need to work harder at.

3 Tips for test day

On the test day itself, make sure you have everything you need to complete the test. When you start, ensure you know roughly how long you’ve got to answer each question, as although you’ll always need to work quickly, it’s important to read the question thoroughly and ensure you’ve understood it before getting started.

4 Stay positive

Try and remain positive. The tests are designed to be challenging, since employers want to push you. If you’ve put the time and effort into practising aptitude tests, you should feel confident you’ve given yourself the best chance possible to succeed.

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Analytical Reasoning Tests FAQs

What is this test used for.

Analytical reasoning tests are a go-to tool for employers looking to gauge a candidate’s problem-solving prowess. Organizations across a myriad of industries use these assessments to get a handle on the analytical skills that are crucial in the modern workplace.

What do these tests involve?

Dive into questions that challenge your problem-solving abilities across verbal, non-verbal, inductive, and deductive reasoning areas. Whether it’s deciphering complex texts, spotting trends in images, or making predictions, these tests are your all-in-one gym to flex those analytical muscles.

What do these tests measure?

Our tests aren’t just a bunch of random questions; they are refined and updated using cutting-edge tech. They’re designed to measure your logical and analytical acumen, ensuring you’re tested against the latest industry benchmarks for analytical reasoning.

Where can I practice these tests?

Ready to put your analytical skills to the test? Practice Aptitude Tests is your one-stop shop for simulating real-world analytical reasoning exams. Here, you’ll find a treasure trove of practice material to get you test-ready!

Which employers use these tests?

Analytical reasoning tests aren’t just popular; they’re a staple in the hiring toolkit for a vast array of organizations looking to identify top talent who can navigate complex problem-solving tasks with ease.

Reviews of our Analytical Reasoning tests

What our customers say about our Analytical Reasoning tests

Bob Gautier

United States of America

October 23, 2023

I really do not think negatively in any way about this test. It dies what it’s supposed to do, and designed to do what it does.

Andrew Smith

United Kingdom

October 05, 2023

A good range of alternating patterns, some repeat themselves on several questions, while others are one-offs.

Caramel Teoh

The seqence

I like how convenient it was to answer to question. I dislike that all the question is almost all the same

Juan Garcera

August 06, 2023

Interesting

It is a good first immersion on the complexity of analytical reasoning and a good first step to get into more demanding exercises.

Stephanie Scalzo

July 25, 2023

Find patterns, but attack each question individually

I have not had the opportunity to take a test like this in years! It was really cool to use my brain in this kind of way again and to work through each individual problem while also finding patterns throughout the test.

MemeLord 29

July 13, 2023

Understanding the sequences

I liked the fact you had to use logical thinking and process of elimination sometimes, to figure the answer

Simulation Aeronautics

July 09, 2023

Attention to detail

The shapes in the pattern have changes which require sharp attention to detail to select the next sequence.

Marco Cavallari

June 03, 2023

My 1st ever psychometric test

It was quite challenging at first, but after a while it became more and more easier to find patterns.

Elizabeth M.Calinawan

Philippines

May 31, 2023

The refreshing abstract reasoning

i like the test very much. Refreshing the next sequence, need enough time to think it over but with the time limit. Yeah, very interesting this test too. Well, when.this test refer to a real life of course anticipation in the area may prevail have a swift solution in every conce

khadijah Ansari

May 16, 2023

My brain had a hard time focusing and differentiating between them, trying to recognise a pattern was difficult.

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problem solving reasoning questions

Mathematical Reasoning & Problem Solving

In this lesson, we’ll discuss mathematical reasoning and methods of problem solving with an eye toward helping your students make the best use of their reasoning skills when it comes to tackling complex problems.

Previously Covered:

  • Over the course of the previous lesson, we reviewed some basics about chance and probability, as well as some basics about sampling, surveys, etc. We also covered some ideas about data sets, how they’re represented, and how to interpret the results.

Approaches to Problem Solving

When solving a mathematical problem, it is very common for a student to feel overwhelmed by the information or lack a clear idea about how to get started.

To help the students with their problem-solving “problem,” let’s look at some examples of mathematical problems and some general methods for solving problems:

Identify the following four-digit number when presented with the following information:

  • One of the four digits is a 1.
  • The digit in the hundreds place is three times the digit in the thousands place.
  • The digit in the ones place is four times the digit in the ten’s place.
  • The sum of all four digits is 13.
  • The digit 2 is in the thousands place.

Help your students identify and prioritize the information presented.

In this particular example, we want to look for concrete information. Clue #1 tells us that one digit is a 1, but we’re not sure of its location, so we see if we can find a clue with more concrete information.

We can see that clue #5 gives us that kind of information and is the only clue that does, so we start from there.

Because this clue tells us that the thousands place digit is 2, we search for clues relevant to this clue. Clue #2 tells us that the digit in the hundreds place is three times that of the thousands place digit, so it is 6.

So now we need to find the tens and ones place digits, and see that clue #3 tells us that the digit in the ones place is four times the digit in the tens place. But we remember that clue #1 tells us that there’s a one somewhere, and since one is not four times any digit, we see that the one must be in the tens place, which leads us to the conclusion that the digit in the ones place is four. So then we conclude that our number is:

If you were following closely, you would notice that clue #4 was never used. It is a nice way to check our answer, since the digits of 2614 do indeed add up to be thirteen, but we did not need this clue to solve the problem.

Recall that the clues’ relevance were identified and prioritized as follows:

  • clue #3 and clue #1

By identifying and prioritizing information, we were able to make the information given in the problem seem less overwhelming. We ordered the clues by relevance, with the most relevant clue providing us with a starting point to solve the problem. This method also utilized the more general method of breaking a problem into smaller and simpler parts to make it easier to solve.

Now let’s look at another mathematical problem and another general problem-solving method to help us solve it:

Two trees with heights of 20 m and 30 m respectively have ropes running from the top of each tree to the bottom of the other tree. The trees are 40 meters apart. We’ll assume that the ropes are pulled tight enough that we can ignore any bending or drooping. How high above the ground do the ropes intersect?

Let’s solve this problem by representing it in a visual way , in this case, a diagram:

You can see that we have a much simpler problem on our hands after drawing the diagram. A, B, C, D, E, and F are vertices of the triangles in the diagram. Now also notice that:

b = the base of triangle EFA

h = the height of triangle EFA and the height above the ground at which the ropes intersect

If we had not drawn this diagram, it would have been very hard to solve this problem, since we need the triangles and their properties to solve for h. Also, this diagram allows us to see that triangle BCA is similar to triangle EFC, and triangle DCA is similar to triangle EFA. Solving for h shows that the ropes intersect twelve meters above the ground.

Students frequently complain that mathematics is too difficult for them, because it is too abstract and unapproachable. Explaining mathematical reasoning and problem solving by using a variety of methods , such as words, numbers, symbols, charts, graphs, tables, diagrams, and concrete models can help students understand the problem better by making it more concrete and approachable.

Let’s try another one.

Given a pickle jar filled with marbles, about how many marbles does the jar contain?

Problems like this one require the student to make and use estimations . In this case, an estimation is all that is required, although, in more complex problems, estimates may help the student arrive at the final answer.

How would a student do this? A good estimation can be found by counting how many marbles are on the base of the jar and multiplying that by the number of marbles that make up the height of the marbles in the jar.

Now to make sure that we understand when and how to use these methods, let’s solve a problem on our own:

How many more faces does a cube have than a square pyramid?

Reveal Answer

The answer is B. To see how many more faces a cube has than a square pyramid, it is best to draw a diagram of a square pyramid and a cube:

From the diagrams above, we can see that the square pyramid has five faces and the cube has six. Therefore, the cube has one more face, so the answer is B.

Before we start having the same problem our model student in the beginning did—that is, being overwhelmed with too much information—let’s have a quick review of all the problem-solving methods we’ve discussed so far:

  • Sort and prioritize relevant and irrelevant information.
  • Represent a problem in different ways, such as words, symbols, concrete models, and diagrams.
  • Generate and use estimations to find solutions to mathematical problems.

Mathematical Mistakes

Along with learning methods and tools for solving mathematical problems, it is important to recognize and avoid ways to make mathematical errors. This section will review some common errors.

Circular Arguments

These involve drawing a conclusion from a premise that is itself dependent on the conclusion. In other words, you are not actually proving anything. Circular reasoning often looks like deductive reasoning, but a quick examination will reveal that it’s far from it. Consider the following argument:

  • Premise: Only an untrustworthy man would become an insurance salesman; the fact that insurance salesmen cannot be trusted is proof of this.
  • Conclusion: Therefore, insurance salesmen cannot be trusted.

While this may be a simplistic example, you can see that there’s no logical procession in a circular argument.

Assuming the Truth of the Converse

Simply put: The fact that A implies B doesn’t not necessarily mean that B implies A. For example, “All dogs are mammals; therefore, all mammals are dogs.”

Assuming the Truth of the Inverse

Watch out for this one. You cannot automatically assume the inverse of a given statement is true. Consider the following true statement:

If you grew up in Minnesota , you’ve seen snow.

Now, notice that the inverse of this statement is not necessarily true:

If you didn’t grow up in Minnesota , you’ve never seen snow.

Faulty Generalizations

This mistake (also known as inductive fallacy) can take many forms, the most common being assuming a general rule based on a specific instance: (“Bridge is a hard game; therefore, all card games are difficult.”) Be aware of more subtle forms of faulty generalizations.

Faulty Analogies

It’s a mistake to assume that because two things are alike in one respect that they are necessarily alike in other ways too. Consider the faulty analogy below:

People who absolutely have to have a cup of coffee in the morning to get going are as bad as alcoholics who can’t cope without drinking.

False (or tenuous) analogies are often used in persuasive arguments.

Now that we’ve gone over some common mathematical mistakes, let’s look at some correct and effective ways to use mathematical reasoning.

Let’s look at basic logic, its operations, some fundamental laws, and the rules of logic that help us prove statements and deduce the truth. First off, there are two different styles of proofs: direct and indirect .

Whether it’s a direct or indirect proof, the engine that drives the proof is the if-then structure of a logical statement. In formal logic, you’ll see the format using the letters p and q, representing statements, as in:

If p, then q

An arrow is used to indicate that q is derived from p, like this:

This would be the general form of many types of logical statements that would be similar to: “if Joe has 5 cents, then Joe has a nickel or Joe has 5 pennies “. Basically, a proof is a flow of implications starting with the statement p and ending with the statement q. The stepping stones we use to link these statements in a logical proof on the way are called axioms or postulates , which are accepted logical tools.

A direct proof will attempt to lay out the shortest number of steps between p and q.

The goal of an indirect proof is exactly the same—it wants to show that q follows from p; however, it goes about it in a different manner. An indirect proof also goes by the names “proof by contradiction” or reductio ad absurdum . This type of proof assumes that the opposite of what you want to prove is true, and then shows that this is untenable or absurd, so, in fact, your original statement must be true.

Let’s see how this works using the isosceles triangle below. The indirect proof assumption is in bold.

Given: Triangle ABC is isosceles with B marking the vertex

Prove: Angles A and C are congruent.

Now, let’s work through this, matching our statements with our reasons.

  • Triangle ABC is isosceles . . . . . . . . . . . . Given
  • Angle A is the vertex . . . . . . . . . . . . . . . . Given
  • Angles A and C are not congruent . . Indirect proof assumption
  • Line AB is equal to line BC . . . . . . . . . . . Legs of an isosceles triangle are congruent
  • Angles A and C are congruent . . . . . . . . The angles opposite congruent sides of a triangle are congruent
  • Contradiction . . . . . . . . . . . . . . . . . . . . . . Angles can’t be congruent and incongruent
  • Angles A and C are indeed congruent . . . The indirect proof assumption (step 3) is wrong
  • Therefore, if angles A and C are not incongruent, they are congruent.

“Always, Sometimes, and Never”

Some math problems work on the mechanics that statements are “always”, “sometimes” and “never” true.

Example: x < x 2 for all real numbers x

We may be tempted to say that this statement is “always” true, because by choosing different values of x, like -2 and 3, we see that:

Example: For all primes x ≥ 3, x is odd.

This statement is “always” true. The only prime that is not odd is two. If we had a prime x ≥ 3 that is not odd, it would be divisible by two, which would make x not prime.

  • Know and be able to identify common mathematical errors, such as circular arguments, assuming the truth of the converse, assuming the truth of the inverse, making faulty generalizations, and faulty use of analogical reasoning.
  • Be familiar with direct proofs and indirect proofs (proof by contradiction).
  • Be able to work with problems to identify “always,” “sometimes,” and “never” statements.

Logical Reasoning

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Logical reasoning topics assess a candidate's deductive and inductive reasoning abilities. Mastering them involves understanding concepts, formulas, tips, and tricks. Additionally, practicing questions and answers is vital for achieving high scores in placement exams, where they carry significant weightage.

Logical Reasoning Topics

Order of Importance Order of Preparation Easy to Hard Hard to Easy

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Is the logical reasoning section difficult?

A resounding NO! In reality, most people find logical reasoning questions and answers to be quite straightforward and intriguing to solve.

How many topics are there in logical reasoning?

There are typically around 10-20 common logical reasoning topics that are commonly asked in most placement exams. Here are the common verbal ability topics:

  • Making Judgments
  • Logical Problems
  • Analyzing Arguments
  • Statement and Assumption
  • Course of Action
  • Statement and Conclusion
  • Theme Detection
  • Cause and Effect
  • Statement and Argument
  • Order and Ranking
  • Odd Man Out
  • Series Completion
  • Letter and Symbol Series
  • Number Series

How to prepare for logical reasoning for placements?

To prepare for logical reasoning in placements, we recommend diving right into problem-solving to save time. This approach helps you develop your critical thinking skills.

Once you have attempted solving problems across various subtopics, you can seek out effective shortcuts to learn the quickest ways to solve questions.

For detailed guidance on preparing for logical reasoning, check out our blog post on how to prepare for logical reasoning for placements .

How much time does it take to learn logical reasoning for placements?

The time it takes to learn logical reasoning for placements varies depending on each individual's capacity for creative thinking and problem-solving.

On average, gaining a fundamental understanding of each subtopic can take approximately 1-2 hours with clear learning direction and available resources.

What are some of the best books to learn logical reasoning?

There is no such thing as the perfect book for logical reasoning. Instead of focusing on a single book, it is more important to understand and practice logical reasoning questions.

At Placement Preparation, we provide the best available information to help you in learning logical reasoning effectively.

For more information, refer to our blog post on the best books to learn logical reasoning .

Which is the best website to learn logical reasoning?

Placement Preparation is the best website to learn logical reasoning. Our website is dedicated to providing students with the most valuable and useful information for learning logical reasoning.

We strive to continuously update and improve our content to make it the best resource for logical reasoning learning.

For more information, refer to our blog post on the best websites to learn logical reasoning .

Which is the best youtube channel to learn logical reasoning?

There is no such thing as the best YouTube channel to learn logical reasoning.

We encourage you to follow individuals and channels that promote understanding the underlying principles and reasoning behind formulas, rather than simply memorizing and applying them blindly.

How do you benefit from practicing logical reasoning questions?

Practicing logical reasoning questions benefits you by improving critical thinking, analytical skills, and problem-solving abilities.

How many questions should I practice for each logical reasoning topic?

The number of questions you should practice for each logical reasoning topic may vary depending on your level of proficiency and the complexity of the topic.

It is generally recommended to start with a sufficient number of practice questions to grasp the basic concepts and techniques. As you become more comfortable, gradually increase the number of questions to challenge yourself.

What is the right way to practice logical reasoning questions?

The right way to practice logical reasoning questions involves understanding concepts, practicing a variety of questions, analyzing patterns, reviewing solutions, and seeking clarification when needed. Consistency and regular practice are important.

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Practice Logical Reasoning Test Example Questions – 2024

Job Aptitude Tests Preparation

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One of the most popular, and perhaps most dreaded, type of psychometric test is the logical reasoning test. These screening questions won’t ask you for formulas or equations. You’ll have to rely solely on your own ingenuity to solve these problems.

You’ll need a great deal of concentration to succeed on a logic test. Logic tests are really designed to assess your intelligence. Similar to I.Q. tests in design, these aptitude assessments test your problem-solving skills, your critical thinking skills, and your creativity.

Below, we’ll explain a little bit more about the logic test questions you can expect on logic pre-employment exams and how you should approach them. We’ll also discuss some of our best tips for logic tests, so make sure to take notes! When you’re done, click over to the second tab and try your hand at our logical reasoning sample questions.

What Is a Logical Reasoning Test?

A logical reasoning test, as opposed to a numerical or verbal reasoning test , requires solely your reasoning ability. While you will have to know how to read, you won’t need to know any grammar, and you certainly won’t need to know how to multiply numbers.

Based on deductive and inductive reasoning, logical thinking questions will take one of two forms. Either you’ll be presented with a series of shapes and asked about the patterns they make, or you’ll be given a series of statements and asked to state what you know to be certain. We’ll go through both of these types of questions.

Why Do I Need to Take Logical Reasoning Tests?

Employers want to know, first and foremost, that you know how to analyze information and learn new skills quickly. These so-called “soft skills” are really far more important to a company than you might imagine, and they’re nearly impossible to really measure in an interview.

Logical questions help employers to see how well applicants recognize patterns, overcome adversity, and concentrate for extended periods of time. The skills you’ll need to pass a logical reasoning test are the same ones that will help you anticipate pitfalls, develop winning strategies, and start new initiatives.

Logical aptitude tests are designed, very simply, to test for intelligence. In fact, you’ll probably see a lot of the same questions on an I.Q. test. As it turns out, intelligence and success are very closely linked. The more intelligent someone is, the more quickly he learns and masters new skills, the better he remembers information told to him, and the more easily he overcomes problems.

How to Answer Logical Reasoning Questions:

Every logical reasoning question is different, and while you should be able to recognize patterns after a while, there are no shortcuts or one-size-fits-all responses. Here we have a few principles you should keep in mind. However, if you find that you’re still struggling with logic, then make sure to check out the free logic examples we have printed in our questions tab.

  • Identify a Major Pattern: Whenever dealing with diagrams, you’ll want to focus on patterns. The series or matrix will be assembled of various sequences, and it’s your job to figure out what they are. Once you’ve identified a major pattern, you’ll want to see if you can also identify a minor pattern. Typically, series and matrices use at least two different patterns.

For example, if Jenny’s coat is both long and blue, we can logically assume that any red or green coats we may find do not belong to Jenny. On the other hand, if Jenny’s coat is either long or blue, we have a different set of criteria.

Logic also makes use of if–>then statements. For example, “If Jenny buys a new coat, she’ll buy one that is long and blue.” In that case, we know that Jenny can only buy a long, blue coat if, in fact, she buys a new coat. If her brother buys a coat for her, she won’t have bought a long, blue coat. These facts may seem redundant if you’ve never studied logic before, but they become quite significant when programming computers, for instance.

Diagrammatic Abstract Reasoning

This non-verbal form of logical reasoning usually involves series or matrices made up of shapes or figures arranged in a certain pattern.

To solve these questions, you’re going to use inductive reasoning. Your goal as the job-seeker is to identify the pattern and complete the task. Here are the four different kinds of tasks you can expect on non-verbal logic test questions.

  • Series In a series question, you’ll be shown 4-6 pictures and asked to choose the next figure in the series from several choices. You might also find that one of the figures in the middle of the series has been left out, and you’ll have to choose which picture best completes the pattern.
  • Matrices Matrices are very similar to series except they extend in two directions. While a series only goes from left to right, a matrix has patterns both horizontally and vertically. Not only will you have to make sure that the figure you choose completes the pattern in its row, but you’ll also have to check to see whether it agrees with the figures above and below it.
  • Odd One Out Sometimes you’ll be given a set of figures and asked to identify the outlier. While the figures won’t be lined up in a series, they will have something in common. It will be your job determine which characteristics are relevant and to group the pictures based on these similarities.
  • A/B Groups In A/B grouping questions, you’ll be given two groups of figures and one figure on its own. You’ll have to decide why the figures were grouped the way they were. You’ll then have to place the single figure in one of the two groups.

Verbal Logical Reasoning

While diagrammatic questions require inductive reasoning, verbal questions call for deductive reasoning. On a verbal question, you’ll be given a series of statements, premises, said to be true, and you’ll have to determine whether the conclusion necessarily follows from those statements.

  • All men are mortal.
  • Socrates is a man.
  • Therefore, Socrates is mortal
  • If it rains, the school will cancel the picnic.
  • If the school cancels the picnic, the children will watch a film instead.
  • Therefore, if it rains, the children will watch a film.
  • Either I will go swimming or hiking.
  • I will go swimming.
  • I will not go hiking.
  • Order Other deductive questions will ask you to put a set of people or items in order based on certain descriptions. For instance, they might tell you that “Sam is not last,” or that “Jaimie is before Paul,” but it will be up to you to figure out exactly where they are in line.

Logical Reasoning Test Tips:

Make sure you read our top tips for logical aptitude tests before heading out to the assessment center.

  • Write Everything Down: Logic questions are particularly tricky. Instead of trying to keep everything straight in your head, try to write down the details on a piece of paper. Diagrams can be especially helpful when recording important facts.

For example, if the grass is wet, we can assume it probably rained. Logically, though, we can’t state for certain that it rained if we have no proof. It could have been the gardener who left the sprinklers on overnight.

  • Focus on Truth Values: Make sure you know the difference between words like some, many, and all or words like sometimes, always, and never. These qualifying words can completely change the truth value of a statement.
  • Pay Attention to All Details: When completing diagrammatic tests, be very careful to pay attention to all relevant details. A pattern may be based on multiple dots and lines, and if you rush, you’ll miss subtle aspects of the pattern.

Final Thoughts on Logical Questioning:

While most of us study science and history in school, very few of us ever study formal logic. In fact, unless you went to graduate school for law, engineering, philosophy, or abstract mathematics, logic as a concept in and of itself is probably pretty foreign to you.

If this is the case, then don’t fret. Logic is, not coincidentally, fairly logical. As long as you’re familiar with some of the basic fundamentals, you shouldn’t have too much trouble. Click over to the second tab to prepare with some of our online practice questions. Then read the answer explanations to see whether or not your reasoning was on track.

Free Logical Reasoning Practice Test

Practice4Me’s experts designed an example test for your needs to get you familiarized with various question types and to improve your chances of scoring high. This free test is a printable PDF file that includes questions and answers.

Download our free logical reasoning practice test PDF here .

Free Example Questions to Practice

Logical Reasoning Example Question 1

Questions 4 and 5 deal with the following information:

Given the following premises, state whether the conclusions are true, false, or unknown:

All athletes are coaches, but not all coaches are athletes. All coaches live in Chicago. No students are athletes, but all students are coaches. Some teachers are both athletes and students. Some parents are teachers, but no parents are students or athletes.

Explained Answers:

  • B: Notice how the middle shape alternates between the three dots and the stripes. The figures on either side are in a three-way rotation with a circle, a bow, and a diamond.
  • C: Picture C is the odd picture out because it’s the only one in which the bars don’t dip down below the line.
  • C: Deanna—the order is: Clayton, Billy, Deanna, Annie, Elise

Free Logical Reasoning Test Practice Answer 4

  • B: All students are coaches, but as you can see in the picture, there may be many coaches who are not students. So, the answer is false.

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Fluency, Reasoning and Problem Solving: What This Looks Like In Every Math Lesson

Neil Almond

Fluency, reasoning and problem solving are central strands of mathematical competency, as recognized by the National Council of Teachers of Mathematics (NCTM) and the National Research Council’s report ‘Adding It Up’.

They are key components to the Standards of Mathematical Practice, standards that are interwoven into every mathematics lesson. Here we look at how these three approaches or elements of math can be interwoven in a child’s math education through elementary and middle school.

We look at what fluency, reasoning and problem solving are, how to teach them, and how to know how a child is progressing in each – as well as what to do when they’re not, and what to avoid.

The hope is that this blog will help elementary and middle school teachers think carefully about their practice and the pedagogical choices they make around the teaching of what the common core refers to as ‘mathematical practices’, and reasoning and problem solving in particular.

Before we can think about what this would look like in Common Core math examples and other state-specific math frameworks, we need to understand the background to these terms.

What is fluency in math?

What is reasoning in math, what is problem solving in math, mathematical problem solving is a learned skill, performance vs learning: what to avoid when teaching fluency, reasoning, and problem solving.

  • What IS ‘performance vs learning’?
  • Teaching to “cover the curriculum” hinders development of strong problem solving skills.
  • Fluency and reasoning – Best practice in a lesson, a unit, and a semester

Best practice for problem solving in a lesson, a unit, and a semester 

Fluency, reasoning and problem solving should not be taught by rote .

The Ultimate Guide to Problem Solving Techniques

The Ultimate Guide to Problem Solving Techniques

Develop problem solving skills in the classroom with this free, downloadable worksheet

Fluency in math is a fairly broad concept. The basics of mathematical fluency – as defined by the Common Core State Standards for math – involve knowing key mathematical skills and being able to carry them out flexibly, accurately and efficiently.

But true fluency in math (at least up to middle school) means being able to apply the same skill to multiple contexts, and being able to choose the most appropriate method for a particular task.

Fluency in math lessons means we teach the content using a range of representations, to ensure that all students understand and have sufficient time to practice what is taught.

Read more: How the best schools develop math fluency

Reasoning in math is the process of applying logical thinking to a situation to derive the correct math strategy for problem solving  for a question, and using this method to develop and describe a solution.

Put more simply, mathematical reasoning is the bridge between fluency and problem solving. It allows students to use the former to accurately carry out the latter.

Read more: Developing math reasoning: the mathematical skills required and how to teach them .

It’s sometimes easier to start off with what problem solving is not. Problem solving is not necessarily just about answering word problems in math. If a child already has a readily available method to solve this sort of problem, problem solving has not occurred. Problem solving in math is finding a way to apply knowledge and skills you have to answer unfamiliar types of problems.

Read more: Math problem solving: strategies and resources for primary school teachers .

We are all problem solvers

First off, problem solving should not be seen as something that some students can do and some cannot. Every single person is born with an innate level of problem-solving ability.

Early on as a species on this planet, we solved problems like recognizing faces we know, protecting ourselves against other species, and as babies the problem of getting food (by crying relentlessly until we were fed).

All these scenarios are a form of what the evolutionary psychologist David Geary (1995) calls biologically primary knowledge. We have been solving these problems for millennia and they are so ingrained in our DNA that we learn them without any specific instruction.

image of baby crying used to illustrate ingrained problem solving skills.

Why then, if we have this innate ability, does actually teaching problem solving seem so hard?

As you might have guessed, the domain of mathematics is far from innate. Math doesn’t just happen to us; we need to learn it. It needs to be passed down from experts that have the knowledge to novices who do not.

This is what Geary calls biologically secondary knowledge. Solving problems (within the domain of math) is a mixture of both primary and secondary knowledge.

The issue is that problem solving in domains that are classified as biologically secondary knowledge (like math) can only be improved by practicing elements of that domain.

So there is no generic problem-solving skill that can be taught in isolation and transferred to other areas.

This will have important ramifications for pedagogical choices, which I will go into more detail about later on in this blog.

The educationalist Dylan Wiliam had this to say on the matter: ‘for…problem solving, the idea that students can learn these skills in one context and apply them in another is essentially wrong.’ (Wiliam, 2018) So what is the best method of teaching problem solving to elementary and middle school math students?

The answer is that we teach them plenty of domain specific biological secondary knowledge – in this case, math. Our ability to successfully problem solve requires us to have a deep understanding of content and fluency of facts and mathematical procedures.

Here is what cognitive psychologist Daniel Willingham (2010) has to say:

‘Data from the last thirty years leads to a conclusion that is not scientifically challengeable: thinking well requires knowing facts, and that’s true not simply because you need something to think about.

The very processes that teachers care about most—critical thinking processes such as reasoning and problem solving—are intimately intertwined with factual knowledge that is stored in long-term memory (not just found in the environment).’

Colin Foster (2019), a reader in Mathematics Education in the Mathematics Education Center at Loughborough University, UK, says, ‘I think of fluency and mathematical reasoning, not as ends in themselves, but as means to support students in the most important goal of all: solving problems.’

In that paper he produces this pyramid:

pyramid diagram showing the link between fluency, reasoning and problem solving

This is important for two reasons:

1)    It splits up reasoning skills and problem solving into two different entities

2)    It demonstrates that fluency is not something to be rushed through to get to the ‘problem solving’ stage but is rather the foundation of problem solving.

In my own work I adapt this model and turn it into a cone shape, as education seems to have a problem with pyramids and gross misinterpretation of them (think Bloom’s taxonomy).

conical diagram showing the link between fluency, reasoning skills and problem solving

Notice how we need plenty of fluency of facts, concepts, procedures and mathematical language.

Having this fluency will help with improving logical reasoning skills, which will then lend themselves to solving mathematical problems – but only if it is truly learnt and there is systematic retrieval of this information carefully planned across the curriculum.

I mean to make no sweeping generalization here; this was my experience both at university when training and from working in schools.

At some point, schools become obsessed with the ridiculous notion of moving students through content at an accelerated rate. I have heard it used in all manner of educational contexts while training and being a teacher. ‘You will need to show ‘accelerated progress in math’ in this lesson,’ ‘School officials will be looking for ‘accelerated progress’ etc.

I have no doubt that all of this came from a good place and from those wanting the best possible outcomes – but it is misguided.

I remember being told that we needed to get students onto the problem solving questions as soon as possible to demonstrate this mystical ‘accelerated progress’.

This makes sense; you have a group of students and you have taken them from not knowing something to working out pretty sophisticated 2-step or multi-step word problems within an hour. How is that not ‘accelerated progress?’

This was a frequent feature of my lessons up until last academic year: teach a mathematical procedure; get the students to do about 10 of them in their books; mark these and if the majority were correct, model some reasoning/problem solving questions from the same content as the fluency content; give the students some reasoning and word problem questions and that was it.

I wondered if I was the only one who had been taught this while at university so I did a quick poll on Twitter and found that was not the case.

twitter poll regarding teaching of problem solving techniques in primary school

I know these numbers won’t be big enough for a representative sample but it still shows that others are familiar with this approach.

The issue with the lesson framework I mentioned above is that it does not take into account ‘performance vs learning.’

What IS ‘performance vs learning’?

The premise is that performance in a lesson is not a good proxy for learning.

Yes, those students were performing well after I had modeled a mathematical procedure for them, and managed to get questions correct.

But if problem solving depends on a deep knowledge of mathematics, this approach to lesson structure is going to be very ineffective.

As mentioned earlier, the reasoning and problem solving questions were based on the same math content as the fluency exercises, making it more likely that students would solve problems correctly whether they fully understood them or not.

Chances are that all they’d need to do is find the numbers in the questions and use the same method they used in the fluency section to get their answers (a process referred to as “number plucking”) – not exactly high level problem solving skills.

Teaching to “cover the curriculum” hinders development of strong problem solving skills.

This is one of my worries with ‘math mastery schemes’ that block content so that, in some circumstances, it is not looked at again until the following year (and with new objectives).

The pressure for teachers to ‘get through the curriculum’ results in many opportunities to revisit content being missed in the classroom.

Students are unintentionally forced to skip ahead in the fluency, reasoning, problem solving chain without proper consolidation of the earlier processes.

As David Didau (2019) puts it, ‘When novices face a problem for which they do not have a conveniently stored solution, they have to rely on the costlier means-end analysis.

This is likely to lead to cognitive overload because it involves trying to work through and hold in mind multiple possible solutions.

It’s a bit like trying to juggle five objects at once without previous practice. Solving problems is an inefficient way to get better at problem solving.’

Fluency and reasoning – Best practice in a lesson, a unit, and a semester

By now I hope you have realized that when it comes to problem solving, fluency is king. As such we should look to mastery math based teaching to ensure that the fluency that students need is there.

The answer to what fluency looks like will obviously depend on many factors, including the content being taught and the grade you find yourself teaching.

But we should not consider rushing them on to problem solving or logical reasoning in the early stages of this new content as it has not been learnt, only performed.

I would say that in the early stages of learning, content that requires the end goal of being fluent should take up the majority of lesson time – approximately 60%. The rest of the time should be spent rehearsing and retrieving other knowledge that is at risk of being forgotten about.

This blog on mental math strategies students should learn at each grade level is a good place to start when thinking about the core aspects of fluency that students should achieve.

Little and often is a good mantra when we think about fluency, particularly when revisiting the key mathematical skills of number bond fluency or multiplication fluency. So when it comes to what fluency could look like throughout the day, consider all the opportunities to get students practicing.

They could chant multiplication facts when transitioning. If a lesson in another subject has finished earlier than expected, use that time to quiz students on number bonds. Have fluency exercises as part of the morning work.

Read more: How to teach multiplication for instant recall

What about best practice over a longer period?

Thinking about what fluency could look like across a unit of work would again depend on the unit itself.

Look at this unit below from a popular scheme of work.

example scheme of work

They recommend 20 days to cover 9 objectives. One of these specifically mentions problem solving so I will forget about that one at the moment – so that gives 8 objectives.

I would recommend that the fluency of this unit look something like this:

example first lesson of a unit of work targeted towards fluency

This type of structure is heavily borrowed from Mark McCourt’s phased learning idea from his book ‘Teaching for Mastery.’

This should not be seen as something set in stone; it would greatly depend on the needs of the class in front of you. But it gives an idea of what fluency could look like across a unit of lessons – though not necessarily all math lessons.

When we think about a semester, we can draw on similar ideas to the one above except that your lessons could also pull on content from previous units from that semester.

So lesson one may focus 60% on the new unit and 40% on what was learnt in the previous unit.

The structure could then follow a similar pattern to the one above.

When an adult first learns something new, we cannot solve a problem with it straight away. We need to become familiar with the idea and practice before we can make connections, reason and problem solve with it.

The same is true for students. Indeed, it could take up to two years ‘between the mathematics a student can use in imitative exercises and that they have sufficiently absorbed and connected to use autonomously in non-routine problem solving.’ (Burkhardt, 2017).

Practice with facts that are secure

So when we plan for reasoning and problem solving, we need to be looking at content from 2 years ago to base these questions on.

You could get students in 3rd grade to solve complicated place value problems with the numbers they should know from 1st or 2nd grade. This would lessen the cognitive load , freeing up valuable working memory so they can actually focus on solving the problems using content they are familiar with.

Increase complexity gradually

Once they practice solving these types of problems, they can draw on this knowledge later when solving problems with more difficult numbers.

This is what Mark McCourt calls the ‘Behave’ phase. In his book he writes:

‘Many teachers find it an uncomfortable – perhaps even illogical – process to plan the ‘Behave’ phase as one that relates to much earlier learning rather than the new idea, but it is crucial to do so if we want to bring about optimal gains in learning, understanding and long term recall.’  (Mark McCourt, 2019)

This just shows the fallacy of ‘accelerated progress’; in the space of 20 minutes some teachers are taught to move students from fluency through to non-routine problem solving, or we are somehow not catering to the needs of the child.

When considering what problem solving lessons could look like, here’s an example structure based on the objectives above.

example lesson of a unit using fluency and reasoning to embed problem solving

It is important to reiterate that this is not something that should be set in stone. Key to getting the most out of this teaching for mastery approach is ensuring your students (across abilities) are interested and engaged in their work.

Depending on the previous attainment and abilities of the children in your class, you may find that a few have come across some of the mathematical ideas you have been teaching, and so they are able to problem solve effectively with these ideas.

Equally likely is encountering students on the opposite side of the spectrum, who may not have fully grasped the concept of place value and will need to go further back than 2 years and solve even simpler problems.

In order to have the greatest impact on class performance, you will have to account for these varying experiences in your lessons.

Read more: 

  • Math Mastery Toolkit : A Practical Guide To Mastery Teaching And Learning
  • Problem Solving and Reasoning Questions and Answers
  • Get to Grips with Math Problem Solving For Elementary Students
  • Mixed Ability Teaching for Mastery: Classroom How To
  • 21 Math Challenges To Really Stretch Your More Able Students
  • Why You Should Be Incorporating Stem Sentences Into Your Elementary Math Teaching

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

The content in this article was originally written by primary school lead teacher Neil Almond and has since been revised and adapted for US schools by elementary math teacher Jaclyn Wassell.

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Ultimate Guide to Metacognition [FREE]

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Logical Problems in Logical Reasoning

Logical Problems in Reasoning: Logical Problems are like captivating puzzles and challenges that test your thinking skills. These Logical problems questions present complex scenarios where you need to find patterns, make logical connections, and come up with precise solutions. Logical Problems come in various forms, from math puzzles that require number skills to creative challenges where you need to think outside the box. They are a great way to improve your critical thinking, boost your brainpower, get better at solving real-life problems and become more efficient at resolving real-life problems through the application of logical reasoning .

In this article, we will provide you with a variety of logical problems and answers. We will also discuss some common strategies for solving logical problems and its explanation as well for better understanding.

Logical Problems with Answers – Solved Examples

Solved Example 1:

Tanya is older than Eric.

Cliff is older than Tanya.

Eric is older than Cliff.

If the first two statements are true, the third statement is

c. uncertain

Answer: b. false

Explanation: If Tanya is older than Eric, and Cliff is older than Tanya, it implies that Eric is younger than Cliff, contradicting the third statement. Therefore, the third statement is false.

Solved Example 2:

In a row of cars, Tina’s car is red.

John’s car is behind Tina’s car.

Katie’s car is in front of John’s car.

Answer: a. true

Explanation: If Tina’s car is red, and John’s car is behind Tina’s car, it implies that Katie’s car must be in front of both Tina’s and John’s cars for the statements to be true. Therefore, the third statement is true.

Solved Example 3:

All apples in the basket are green.

Some fruits in the basket are apples.

Therefore, some fruits in the basket are green.

Explanation: If all apples in the basket are green, and some fruits in the basket are apples, it logically follows that some fruits in the basket are green. Therefore, the third statement is true.

Solved Example 4:

All students in the class passed the math exam.

Some students in the class failed the science exam.

Therefore, some students in the class failed at least one exam.

Explanation: If all students in the class passed the math exam, and some students in the class failed the science exam, it logically follows that some students in the class failed at least one exam. Therefore, the third statement is true.

Solved Example 5:

John is taller than Alice.

Alice is taller than Bob.

Therefore, John is taller than Bob.

Explanation: If John is taller than Alice, and Alice is taller than Bob, it logically follows that John is taller than Bob. Therefore, the third statement is true.

Solved Example 6:

All triangles have three sides.

This shape has three sides.

Therefore, this shape is a triangle.

Explanation: If all triangles have three sides, and this shape has three sides, it logically follows that this shape is a triangle. Therefore, the third statement is true.

Solved Example 7:

All dogs are mammals.

Some animals in the zoo are dogs.

Therefore, some animals in the zoo are mammals.

Explanation: If all dogs are mammals, and some animals in the zoo are dogs, it logically follows that some animals in the zoo are mammals. Therefore, the third statement is true.

Solved Example 8:

All birds have feathers.

This animal has feathers.

Therefore, this animal is a bird.

Explanation: If all birds have feathers, and this animal has feathers, it logically follows that this animal is a bird. Therefore, the third statement is true.

Solved Example 9:

Some fruits are sweet.

All apples are fruits.

Therefore, some apples are sweet.

Explanation: If some fruits are sweet, and all apples are fruits, it logically follows that some apples are sweet. Therefore, the third statement is true.

Solved Example 10:

All cars have wheels.

Some vehicles have wheels.

Therefore, some vehicles are cars.

Answer: c. uncertain

Explanation: While all cars have wheels, and some vehicles have wheels, it does not necessarily mean that some vehicles are cars. The term “vehicles” is more inclusive and can refer to various types of vehicles, not just cars. Therefore, the third statement is uncertain.

Related Resource :

  • Essential Part – Logical Reasoning​​
  • ​ Artificial Language – Logical Reasoning​
  • ​Matching Definitions – Logical Reasoning

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Reasoning and Problem Solving Questions Collection - KS1 and KS2

Reasoning and Problem Solving Questions Collection - KS1 and KS2

Subject: Mathematics

Age range: 5-7

Resource type: Worksheet/Activity

White Rose Education's Shop

Last updated

10 March 2023

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problem solving reasoning questions

These booklets each contain over 40 reasoning and problem solving questions suitable for KS1, KS2 and KS3 classes. These are the questions that we have been putting out each day in March 2016 on Twitter in the run up to SATS.

The answers are provided with some simple notes at the back of the booklet and for some problems supplementary questions and variation has been provided.

As always we welcome any feedback on the work we are doing and the materials that we are releasing. Thank you for taking an interest in our work. The White Rose Maths Hub Team

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We are pleased to let you know that your resource Reasoning and Problem Solving Questions Collection - KS1 and KS2, has been hand-picked by the Tes resources content team to be featured in https://www.tes.com/teaching-resources/blog/fluency-reasoning-and-problem-solving-primary-maths in April 2024 on https://www.tes.com/teaching-resources/blog. Congratulations on your resource being chosen and thank you for your ongoing contributions to the Tes Resources marketplace.

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A very good and engaging way to teach mastery of maths. Thank you for sharing

thank you for sharing, this is really good

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15 Common Problem-Solving Interview Questions

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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

problem solving reasoning questions

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:

Get Our Job Interview Questions & Answers Cheat Sheet!

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 .

CLICK HERE TO GET THE JOB INTERVIEW QUESTIONS CHEAT SHEET

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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problem solving reasoning questions

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15 Logical Thinking Interview Questions and Answers

Prepare for the types of questions you are likely to be asked when interviewing for a position where Logical Thinking skills will be used.

problem solving reasoning questions

Logical thinking is the ability to see the relationships between ideas and to understand complex systems. It’s a critical skill for anyone who wants to be successful in today’s fast-paced, ever-changing world.

Whether you’re applying for a job in business, technology, or another field, you can expect to be asked interview questions that test your logical thinking skills. Employers want to know if you can think critically and solve problems effectively.

To help you prepare, we’ve compiled a list of sample logical thinking interview questions and answers. By reviewing these questions and practicing your responses, you’ll be better prepared to impress employers with your logical thinking skills.

  • What is logical thinking?
  • Can you explain what a logic puzzle is?
  • What are the advantages of logical thinking in business?
  • How can you use logical thinking to make better decisions?
  • Why do some people find it so difficult to think logically?
  • How can you improve your ability to think logically?
  • What types of problems can be solved using logical reasoning?
  • What’s the difference between inductive and deductive reasoning?
  • Are there any situations where it wouldn’t be appropriate for me to apply logic to solve a problem?
  • When should I not use logic to solve problems?
  • Do all illogical arguments lead to false conclusions?
  • How does logical thinking differ from analytical thinking?
  • Is critical thinking useful for solving every type of problem?
  • How can critical thinking help with decision making?
  • How can we develop our critical thinking skills?

1. What is logical thinking?

This question is a great way to show your interviewer that you understand the importance of logical thinking and how it can be used in many different situations. When answering this question, try to explain what logical thinking is and give an example of when you have applied it to a situation or problem.

Example: “Logical thinking is the process of analyzing information and making decisions based on facts rather than emotions. I use logical thinking every day at work when I am trying to solve problems or find solutions to issues my team members are having with their projects. For example, recently one of my coworkers was having trouble finding data for a project they were working on. Instead of telling them to look harder for the data, I asked questions about where they had already looked and then helped them narrow down their search.”

2. Can you explain what a logic puzzle is?

Interviewers may ask this question to assess your knowledge of logic puzzles and how you would solve one. They want to know that you can apply the skills you learned in school to real-world situations. In your answer, explain what a logic puzzle is and give an example of one.

Example: “A logic puzzle is a problem that requires critical thinking to solve. It’s usually presented as a picture or story with missing pieces. You have to figure out which piece goes where by using deductive reasoning. For instance, if I was looking at a picture of a man on a boat who lost his hat, I might think about other times I’ve seen people lose their hats while they were on boats. Then, I’d realize that he must be fishing.”

3. What are the advantages of logical thinking in business?

This question is a great way to show your interviewer that you understand the importance of logical thinking in business. Use examples from your own experience or refer to research studies to explain how logical thinking can benefit businesses and organizations.

Example: “Logical thinking is an essential skill for any professional because it helps us make better decisions, solve problems more efficiently and communicate clearly with others. In my last role as a marketing manager, I used logical thinking skills to create effective marketing campaigns for our company’s products. This helped me develop strategies that increased sales by 20% over the previous year.”

4. How can you use logical thinking to make better decisions?

This question can help the interviewer understand how you use your critical thinking skills to make important decisions. Use examples from past experiences where you used logical thinking to solve problems or make a decision that benefited your team or organization.

Example: “In my last role, I was tasked with creating a new marketing campaign for our company’s website. After researching different types of campaigns and analyzing data about our target audience, I decided on an email marketing strategy because it would be more cost-effective than other strategies we were considering. This helped us save money while still reaching our target market.”

5. Why do some people find it so difficult to think logically?

This question can help you show the interviewer that you understand why logical thinking is important and how it can be beneficial to people. You can answer this question by explaining what causes someone to think illogically, such as stress or emotions, and how these things can affect a person’s ability to make good decisions.

Example: “Some people find it difficult to think logically because they are too stressed or emotional to focus on making rational decisions. When we’re under pressure, our minds become clouded with negative thoughts and feelings, which makes it hard for us to concentrate on solving problems. This can lead to poor decision-making, like choosing an option that seems best in the moment but may not be the most effective long-term solution.”

6. How can you improve your ability to think logically?

Employers may ask this question to see if you can improve your logical thinking skills. They want to know that you are willing to learn and grow as a professional. In your answer, explain how you have already done this in the past or what steps you would take to do so.

Example: “I think it’s important to keep my mind active by learning new things. I try to read at least one book per month on topics that interest me. This helps me stay up-to-date on current events and also gives me more knowledge about different subjects. Another way I’ve improved my ability to think logically is through meditation. Studies show that meditating regularly can help people focus their thoughts and make better decisions.”

7. What types of problems can be solved using logical reasoning?

This question can help the interviewer understand your ability to apply logical reasoning in a variety of situations. Use examples from previous work or school experiences that highlight your ability to use logic and problem-solving skills effectively.

Example: “There are many types of problems that can be solved using logical reasoning, including math problems, word problems, puzzles and riddles. In my last job as an accountant, I helped solve several math problems by applying basic mathematical principles and formulas. For example, when calculating payroll taxes for employees, I used basic algebraic equations to determine how much money each employee should receive after taxes were deducted.”

8. What’s the difference between inductive and deductive reasoning?

This question tests your ability to apply logic in a variety of situations. Your answer should show the interviewer that you can use inductive and deductive reasoning to solve problems, make decisions and analyze data.

Example: “Inductive and deductive reasoning are two different approaches to solving problems or making conclusions based on available information. Induction is when I take specific observations and generalize them into broader principles. For example, if I notice that every time I eat ice cream it makes me feel sick, I can conclude that ice cream will probably make me feel sick again in the future. Deduction is when I start with broad principles and apply them to specific cases. If I know that all dogs have four legs, I can deduce that any dog I see will also have four legs.”

9. Are there any situations where it wouldn’t be appropriate for me to apply logic to solve a problem?

This question can help the interviewer understand your thought process and how you apply logic to solve problems. It can also show them that you know when it’s appropriate to use logical thinking skills and when it might not be.

Example: “There are times where I would need to rely on my intuition or gut feeling to make a decision, but only if there is no other way to logically decide what to do. For example, if I’m in a situation where I have to choose between two things, like which restaurant to go to for lunch, then I would use logic to decide which one to go to. However, if I was trying to decide whether or not to break up with my significant other, I would probably rely more on my gut feeling because there isn’t really any way to logically decide.”

10. When should I not use logic to solve problems?

This question is a great way to test your critical thinking skills. It also shows the interviewer that you understand when logic isn’t appropriate for certain situations. In your answer, explain why it’s important to know when not to use logic and how you would handle those situations.

Example: “I think it’s important to know when logic should be used and when it shouldn’t. For example, if I’m working with someone who has different opinions than me, I wouldn’t want to argue with them about their ideas. Instead, I would try to find common ground where we can both agree on something and then work from there. This helps build relationships and allows us to come up with better solutions.”

11. Do all illogical arguments lead to false conclusions?

This question is a continuation of the previous one, and it tests your ability to apply logical thinking skills in real-world situations. Your answer should show that you can use critical thinking to analyze arguments and determine whether they are valid or not.

Example: “No, all illogical arguments do not lead to false conclusions. For example, if someone says ‘All dogs have four legs’ this statement is logically true because there are no dogs without four legs. However, this argument is still illogical because it does not make sense to say ‘all dogs.’ It would be more appropriate to say ‘some dogs have four legs,’ which is also logically true.”

12. How does logical thinking differ from analytical thinking?

This question can help the interviewer understand your knowledge of logical thinking and how it differs from other types of critical thinking. Use examples from past experiences to show that you know the difference between these two skills and how they apply in different situations.

Example: “Logical thinking is a process where you use facts, data and information to make decisions or solve problems. It’s important to be able to think logically when making decisions because it helps you find solutions that are based on evidence rather than assumptions. Analytical thinking is similar to logical thinking but focuses more on analyzing data and information to reach conclusions. I’ve used both logical and analytical thinking in my previous role as an accountant to ensure all financial reports were accurate.”

13. Is critical thinking useful for solving every type of problem?

Critical thinking is a skill that can be used to solve many different types of problems. Employers may ask this question to see if you understand the limitations of critical thinking and how it can help you in your future role. In your answer, explain why critical thinking is useful for solving some problems but not others.

Example: “Critical thinking is an important skill because it helps us analyze information more effectively. However, I do believe there are times when critical thinking isn’t as helpful. For example, if someone has a phobia or anxiety disorder, using critical thinking skills might make them feel worse. Instead, I would use other problem-solving techniques like brainstorming or trial and error.”

14. How can critical thinking help with decision making?

Critical thinking is a skill that helps you make better decisions. Employers ask this question to see if you can apply critical thinking skills to your work and help the company achieve its goals. In your answer, explain how critical thinking helped you in your previous roles.

Example: “Critical thinking helps me with decision making because it allows me to analyze information and come up with solutions. I use critical thinking when I’m trying to solve problems or find answers to questions. For example, at my last job, we were having issues with our website’s search function. I used critical thinking to troubleshoot the problem by looking for common issues with websites’ search functions. After some research, I found out that the issue was due to the coding of the website. We fixed the coding and then tested the search function again.”

15. How can we develop our critical thinking skills?

Critical thinking is a skill that can be developed through practice. Employers may ask this question to see if you have any strategies for improving your critical thinking skills. In your answer, explain how you would encourage others to develop their critical thinking skills as well.

Example: “I think the best way to improve our critical thinking skills is by practicing them regularly. I try to read and research different topics on my own time so that I’m always learning new things. I also find it helpful to discuss ideas with other people. Hearing someone else’s perspective often helps me understand an issue more clearly. Finally, I find that writing down my thoughts in a journal or blog has helped me become a better writer.”

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What Is A Fluid Intelligence Test

What Is A Fluid Intelligence Test

Ever wondered how some people can effortlessly solve complex puzzles, recognize patterns like a pro, or adapt quickly to new situations? The secret weapon might just be their fluid intelligence. In this article, we’ll explore what a fluid intelligence test is, why it matters, and how it can benefit students, professionals, and researchers alike. Get ready to unlock the mysteries of your cognitive abilities and enhance your problem-solving skills.

Understanding Fluid Intelligence

Fluid intelligence is your brain's ability to think on its feet. Unlike crystallized intelligence, which relies on knowledge and experience, fluid intelligence is all about reasoning, abstract thinking, and solving new problems. Imagine being thrown into an escape room without any prior knowledge—you'd need fluid intelligence to find your way out.

Key Characteristics of Fluid Intelligence

  • Abstract Reasoning

Fluid intelligence allows you to understand complex concepts without relying on past experiences. For instance, in a fluid intelligence test, you might be asked to identify the next shape in a sequence, which requires you to think abstractly.

  • Pattern Recognition

Your ability to spot patterns and relationships among different elements is a hallmark of fluid intelligence. This skill is especially useful in fields like data analysis and coding, where recognizing trends can make or break a project.

  • Problem-Solving Skills

Fluid intelligence enables you to tackle new challenges head-on. Whether you're solving a Rubik's cube or a real-world problem at work, this type of intelligence helps you find innovative solutions quickly.

What Is A Fluid Intelligence Test?

A fluid intelligence test is designed to measure these very abilities. These tests often include tasks that require abstract reasoning, pattern recognition, and logical thinking. You might be asked to solve puzzles, identify the next item in a sequence, or complete complex visual patterns.

Types of Fluid Intelligence Tests

  • Raven's Progressive Matrices

One of the most well-known fluid intelligence tests, Raven's Progressive Matrices, involves identifying the missing piece in a series of patterns. It's a staple in many cognitive assessments and is widely used in both educational and professional settings.

  • Cattell Culture Fair Intelligence Test

Designed to minimize cultural and language biases, this test focuses on non-verbal tasks like pattern recognition and problem-solving. It's perfect for measuring pure cognitive abilities without the influence of external factors.

  • Abstract Reasoning Tests

These tests are often used in recruitment processes to identify candidates with strong problem-solving skills. Tasks may include identifying the next shape in a sequence or completing a complex puzzle under time constraints.

The Importance of Fluid Intelligence Tests

Fluid intelligence tests are valuable tools in various settings, from schools to workplaces. They provide a reliable measure of cognitive abilities that are crucial for problem-solving and learning new information.

Educational Assessments

For students, fluid intelligence tests can identify strengths and weaknesses in cognitive abilities, helping educators tailor their teaching methods. These tests can also be used to identify gifted students who might benefit from advanced learning programs.

Recruitment Processes

In the professional world, employers use fluid intelligence tests to identify candidates with strong problem-solving skills. These tests can be a game-changer in fields that require quick thinking and adaptability, such as technology, finance, and consulting.

Research and Development

Researchers use fluid intelligence tests to study cognitive development and the impact of various factors on cognitive abilities. These tests provide valuable data that can lead to breakthroughs in understanding human intelligence.

How to Prepare for a Fluid Intelligence Test

While fluid intelligence is largely innate, you can still prepare for these tests to maximize your performance. Here are some tips to get you started:

Practice Abstract Reasoning

Engage in activities that require abstract reasoning, such as puzzles, logic games, and brainteasers. The more you practice, the better you'll become at recognizing patterns and solving complex problems.

Improve Your Pattern Recognition Skills

Spend time on exercises that enhance your pattern recognition abilities. This could include anything from playing chess to analyzing data sets. The goal is to train your brain to spot relationships between different elements quickly.

Stay Mentally Sharp

Maintain a healthy lifestyle to keep your brain in top shape. Regular exercise, a balanced diet, and adequate sleep can all contribute to optimal cognitive functioning. Consider incorporating mindfulness practices like meditation to reduce stress and improve focus.

Benefits of Taking Fluid Intelligence Tests

Taking fluid intelligence tests offers a range of benefits, from personal growth to professional development. Here’s how these tests can make a difference in your life:

Enhanced Problem-Solving Skills

By regularly engaging in tasks that challenge your fluid intelligence, you'll become more adept at solving problems. This skill is invaluable in both personal and professional contexts.

Increased Self-Awareness

Fluid intelligence tests provide insights into your cognitive strengths and weaknesses. Understanding these aspects of your intelligence can help you make informed decisions about your education and career.

Competitive Advantage

In the job market, strong fluid intelligence can set you apart from other candidates. Employers value problem-solving skills and the ability to adapt to new situations, making fluid intelligence a key differentiator.

The Future of Fluid Intelligence Testing

The field of fluid intelligence testing is constantly evolving, with new methods and technologies emerging to provide more accurate assessments. Here’s a glimpse into what the future holds:

Advances in Technology

Artificial intelligence and machine learning are revolutionizing the way fluid intelligence tests are administered and analyzed. These technologies can provide more personalized and adaptive testing experiences.

Broader Applications

As our understanding of fluid intelligence grows, so does its application in various fields. Expect to see more industries adopting fluid intelligence tests to assess cognitive abilities and improve performance.

Continuous Research

Ongoing research continues to shed light on the factors that influence fluid intelligence. This research will lead to more effective training programs and interventions to enhance cognitive abilities.

Fluid intelligence tests are powerful tools that can unlock your cognitive potential. Whether you're a student, professional, or researcher, understanding your fluid intelligence can provide valuable insights and enhance your problem-solving skills. By preparing effectively and staying mentally sharp, you can maximize your performance on these tests and reap the benefits in various aspects of your life.

Ready to discover your cognitive edge? Start incorporating fluid intelligence tests into your routine and watch your problem-solving skills soar. For more insights and resources, explore our additional articles and guides.

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What IQ Test Does The Military Use?

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COMMENTS

  1. Practice Reasoning Tests

    It is designed to assess problem-solving and reasoning skills in the following areas: Non-verbal; Verbal; 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 ...

  2. Problem Solving Reasoning

    Problem Solving Reasoning is a logical reasoning part where candidates will be given various questions and they need to perform various operations such as addition, division, greater than, lesser than, etc are interchanged or substituted to find the correct answer. Almost all the government examinations ask questions on the problem solving reasoning section.

  3. Critical Thinking Test: Free Practice Questions

    PRT Critical Thinking Test: question 1 of 3. Six friends are seated in a restaurant across a rectangular table. There are three chairs on each side. Adam and Dorky do not have anyone sitting to their right and Clyde and Benjamin do not have anyone sitting to their left. Adam and Benjamin are not sitting on the same side of the table.

  4. Logical Problems

    Practice logical problems with three statements and find out if the third statement is true, false, or uncertain. See fully solved examples with detailed explanations for placement interviews and competitive exams.

  5. Logic Reasoning Practice Questions with Answer key

    Logical reasoning questions are designed to assess your ability to analyze, evaluate, and draw conclusions based on given information. There are many types of questions, each focusing on different aspects of critical thinking. ... Problem-solving is the process of identifying, analyzing, and resolving problems in a systematic and logical manner ...

  6. Logical Reasoning Test: 100s Of Free Practice Questions (2024)

    A logical reasoning test is an assessment that measures your ability to interpret information, apply logic to solve problems and draw relevant conclusions. It is typically non-verbal and in a multiple-choice format, and requires the use of rules and deduction to reach answers, rather than prior knowledge.

  7. Logical Reasoning Questions and Answers

    Learn and practise solving Logical Reasoning questions to enhance your skills so that you can clear interviews, competitive examinations, and various entrance tests (CAT, GATE, GRE, MAT, bank exams, railway exams, etc.) with full confidence. ... Fully solved problems with detailed answer descriptions and explanations are given and will be easy ...

  8. Analytical Reasoning Tests: Free Online Questions & Tips

    5 Free Example Analytical Reasoning Questions. Here are five example analytical questions to try out. Answers for all five are below the tests. If you need further practice, try out our full free tests. ... Dive into questions that challenge your problem-solving abilities across verbal, non-verbal, inductive, and deductive reasoning areas ...

  9. PDF KS2 Reasoning & Problem Solving Questions

    This booklet contains over 40 reasoning and problem solving questions suitable for KS2 and KS3 classes. These are the questions that we have been putting out each day in March 2016 on Twitter in the run up to SATS. The answers are provided with some simple notes at the back of the booklet and for some questions ...

  10. Mathematical Reasoning & Problem Solving

    Explaining mathematical reasoning and problem solving by using a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and concrete models can help students understand the problem better by making it more concrete and approachable. Let's try another one.

  11. 90 Most Asked Aptitude and Reasoning Questions in Interviews

    To enhance our problem-solving skills and sharpen our minds, a set of topics has been created. It includes two questions along with solutions to give us an idea of topics and types of questions that are usually asked. This article presents every topic and the commonly asked questions under it. ... Analogy Reasoning. Question 1: ...

  12. Logical Reasoning Questions and Answers

    Learn about logical reasoning, a key component of many competitive exams, and practice various types of questions with solutions. Find topics, books, FAQs and tips for verbal and non-verbal reasoning.

  13. Analytical Reasoning Questions: Concepts, Syllabus Topics, Examples

    Analytical Reasoning Questions solving Tips. Solving Analytical Reasonging problems not only make you good at solving questions for exams but also it teaches you how to think critically in daily life. Here's the 5 tips that will help you in solving the analytical reasoning questions in efficient way. 1. Understand the Question

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    1. All-in-One Solution. Our platform provides a comprehensive collection of logical reasoning questions, allowing you to enhance your problem-solving skills. You can practice the latest logical reasoning questions for various topics, along with definitions, concepts, real-time applications, and formulas. 2.

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    Free Example Questions. One of the most popular, and perhaps most dreaded, type of psychometric test is the logical reasoning test. These screening questions won't ask you for formulas or equations. You'll have to rely solely on your own ingenuity to solve these problems. You'll need a great deal of concentration to succeed on a logic test.

  16. Fluency, Reasoning & Problem Solving: What They REALLY Are

    This was a frequent feature of my lessons up until last academic year: teach a mathematical procedure; get the students to do about 10 of them in their books; mark these and if the majority were correct, model some reasoning/problem solving questions from the same content as the fluency content; give the students some reasoning and word problem ...

  17. Problem Solving MCQ [Free PDF]

    Problem Solving Question 1: Arrange the stages of the problem-solving process in the correct order: A. Identifying the problem. B. Generating potential solutions. C. Implementing the chosen solution. D. Evaluating the outcomes. E. Analyzing the available information.

  18. Reasoning

    It helps candidates in improving their decision-making skills, problem-solving skills and setting goals. Five Steps to Solve Reasoning-Based Questions. The following steps are required to solve the Logical Reasoning questions: Read the information thoroughly as a thorough reading of information makes a better understanding.

  19. 6.6: Strategies for Teaching Mathematical Reasoning

    Mathematical reasoning is a fundamental skill that allows students to understand and make sense of mathematical concepts. It involves critical thinking, problem-solving, and the ability to justify and explain one's thinking. There are various strategies that elementary school teachers can use to foster mathematical reasoning in their students.

  20. Logical Problems in Logical Reasoning

    Logic Games Questions and Answers: In logical reasoning, "Logical Games" are like fun mental workouts filled with puzzles and brain-teasers. These games are meant to make you think, be creative, and get better at solving problems while having a good time. Logical Games include a variety of mind-challenging activities, from classic board games like

  21. Reasoning and Problem Solving Questions Collection

    pptx, 2.35 MB. pdf, 3.51 MB. These booklets each contain over 40 reasoning and problem solving questions suitable for KS1, KS2 and KS3 classes. These are the questions that we have been putting out each day in March 2016 on Twitter in the run up to SATS. The answers are provided with some simple notes at the back of the booklet and for some ...

  22. 15 Common Problem-Solving Interview Questions

    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.

  23. Top 20 Problem Solving Interview Questions (Example Answers Included)

    MIKE'S TIP: When you're answering this question, quantify the details. This gives your answer critical context and scale, showcasing the degree of challenge and strength of the accomplishment. That way, your answer is powerful, compelling, and, above all, thorough. 2. Describe a time where you made a mistake.

  24. 15 Logical Thinking Interview Questions and Answers

    Use examples from previous work or school experiences that highlight your ability to use logic and problem-solving skills effectively. Example: "There are many types of problems that can be solved using logical reasoning, including math problems, word problems, puzzles and riddles. In my last job as an accountant, I helped solve several math ...

  25. What Is A Fluid Intelligence Test

    Unlike crystallized intelligence, which relies on knowledge and experience, fluid intelligence is all about reasoning, abstract thinking, and solving new problems. Imagine being thrown into an escape room without any prior knowledge—you'd need fluid intelligence to find your way out. Key Characteristics of Fluid Intelligence. Abstract Reasoning