gmat math problem solving

• Skip to content

GMAT Prep Courses & Tutoring

Free GMAT Practice Questions

Practice makes perfect—or at least that's how the old saying goes—and it certainly applies to our free GMAT practice questions. Our Free Practice Questions are designed to give you the thorough understanding of how to go about solving a problem that you crave. Our thorough explanations show you what to expect from each GMAT question, detailing question-specific hurdles and common traps. Thankfully, our practice questions provide a wide variety of question types spanning across all sections, securing an abundance of insight-turned-strategy you can implement on test day to turn into high-scoring gold.

Manhattan Review prides itself in providing quality free practice questions to all prospective students, so please take a crack at the 52 free questions we have to offer as a courtesy to all GMAT learners. In the end, the only way to find out where you need your score to be is to discover where it currently is. Take advantage of this free resource that's sure to help you along your way to a high score.

You have not answered any question so far. You can answer all questions in a row (click on "All Questions") or only all questions of a particular section (click on that Section) or a single selected question (click on that Question).

GMAT is a registered trademark of the Graduate Management Admission Council (GMAC), which is unaffiliated with and does not endorse this website.

GMAT Math Problem Solving

Problem solving questions are standard 5-choice multiple choice questions.

How to approach problem solving questions

Practice your math problem solving skills with our 10 tests. You shouldn't need more than three lines of working for any problem. Redraw geometry figures on your scratch pad to include the information in the question.

Each test has ten questions and should take 12 minutes. Reading the explanations to the questions you get wrong will strengthen your fundamentals and remind you of important multiple choice techniques such as picking numbers and back solving.

Initially don't worry too much about the time until you have a feel for the type of questions. But, by the time you have done two or three tests you should start getting tough about the time you take.

Practice GMAT Problem Solving

• Practice Problem Solving Test 1
• Practice Problem Solving Test 2
• Practice Problem Solving Test 3
• Practice Problem Solving Test 4
• Practice Problem Solving Test 5
• Practice Problem Solving Test 6
• Practice Problem Solving Test 7
• Practice Problem Solving Test 8
• Practice Problem Solving Test 9
• Practice Problem Solving Test 10

Solve each problem and then click on the correct answer choice. Have a sheet of paper ready for any rough work.

• You may not use a calculator
• All numbers are real numbers

More information

If your fundamentals are weak and you need extra help check out our GMAT Books section.

Explore MBA Programs

While you’re preparing to ace the GMAT, look around for an MBA Program that meets your needs. You can also look at sub-specialties within an MBA degree to see if they align with your career goals:

• Human Resources
• Project Management
• Health Information Exchange
• The Functions of Management
• Krispy Kreme Inc Case Study
• The Comparative Advantage of Greece in the Era of Recession
• Business Desicion Making
• Ashford Computer Literacy Week 5
• Issc362 Quiz 1
• Professional Presence
• Business Model and Strategic Plan, Part I
• Religion in the Workplace: an Ethical Evaluation
• Social Performance of Organizations
• Hr Professional Map
• Introductory to Online Learning
• Community Conceptual Model
• Water Crisis in California
• Think Before You Ink
• Pillips Foods
• Individual Learning Project 2
• The Paradox of the Affordable Care Act
• The Use of Electricity and Magnetism in Our Future Transportation
• Family Values
• Steinway &Sons
• Cisco Internal Governance Case Study
• Cs 682 Assignment 1
• Ba Business
• Comparative Essay Original Creation of the Earth
• Corrections
• Fastcat Phase 3
• Breaching Experiment
• Leadership Skills
• Wgu Mmt2 It Strategic Solutions All 4 Tasks
• Case Study Analysis: Lufthansa: to Hedge or Not to Hedge…
• Distribution of Wealth
• Financial Ratios Analysis and Comparison Paper
• Legal Aspects to U.S. Health Care System Administration
• Behaviorism vs Cognitivism
• Alex Sharpe's Portfolio Solution
• Xyberspace Case Analysis
• The Gap of Generations
• French Revolution and Napoleonic Era Worksheet
• Situational Crime Prevention
• Social Network Final Paper
• Csi Analysis
• Essay: the Bad Seed
• Clothes R Us
• Compare and Contrast
• Taj Case Study
• Let's Go Travel Trailer
• Corporation (Fisch) Outline Penn Law
• Examining Theory Paper
• Carter Racing Case
• Zipcar Case Study
• Informative Speech Electriccars
• Deluxe Corporation Teaching Note
• Statistics Case Analysis
• Developing Professional Practice
• Experimentation02
• Creating a Personal Selling Philosophy
• Community Health
• Racism in College Football
• Industrialization After the Civil War
• Week 3 Case Study 2 Submission
• Peppercorn Dinning Casestudy
• Equal Economic Opportunity of Canadian Immigrants
• Database Records and Relational Data Worksheet
• Psych 625 Week 1 Individual Assignment Time to Practice
• Challenger Disaster
• Financial Analysis Proctor and Gamble
• Violation of Sec Rule 10-B-5 of the Federal Statue
• Integrated Distribuitors Integrated
• St. Jude Children's Hospital Outline
• Business Law
• Non-Verbal Communication Is More Effective Than Verbal Skills in the Workplace
• Starbucks in Japan
• Cipd 3dla Reflective Statement
• Csi Miami vs Csi Real Life
• Kingdom of Aksum
• Narnia Essay
• Seeing the Liberation of the Peon by Diego Rivera
• Importance of Homeostasis for Environment Change During Exercise
• Five Competitive Forces in the Biotechnology Industry and Its Economics Scenarios
• Business Plan
• Teamwork and Leadership in Remember the Titans
• Virtual Reality as Jaron Lanier Envisioned It.
• Escape Fire
• Inside Intel Inside
• Nokia Product Design Analysis
• Written Campaign Proposal: Bullying
• The Circle by Dave Eggers
• Coors' Balanced Scorecard
• Walmart Supply Chain
• Late Adulthood and Death Paper
• Valuation Quiz
• Technology Leading to Social Isolation
• C200 Managing Organizations and Leading People Task 2 C200
• M382 Exam 1study Guide
• Later Adulthood Development Report
• Balancing Ecosystems
• Financial Accounting
• The Billy Beane Case Study
• Marketing Assignment Canadian Apparel Federation
• Sands Corporation
• Westminster Company
• The Effectiveness of Vinegar as Battery
• Meet the Parents
• Cowgirl Creamery
• Informatics Needs Essay
• Plight of the Little Emperors
• Roles and Functions of Law
• Analysis of Silver Linings Playbook
• Accreditation Audit Task 4
• Person Centred Care
• Economic Principles
• Accounting Project
• Proton Supply Chain Challenges
• Victoria Secret
• Decision Analysis Task 2
• Common Sense Primary Source Critique
• Sociological Portrait Milestone 1
• Liston Mechanics Corp
• The Effects of War and Peace on Foreign Aid
• Marketing Excellence - Red Bull
• Informed Decision
• Nfl: Global Entry
• Risks in a Home Building Project
• Evaluating Truth and Validity Exercise
• Application of International Law
• Renaissance Time Capsule
• Chronic Obstructive Pulmonary Disease (Copd; Emphysema) Patho
• Operation Decision
• Culture Clash: Opportunity or Conflict?
• Reaction Paper
• Ethics in Criminal Justice Administration Analysis
• The Crucible - Self-Preservation
• Euro Watch Case Study
• Investure Llc and Smith College
• Employee Engagement
• Beaten by a Hair
• A Day in the Life of Alex Sander
• Nr 305 Health Assessment
• Abc Model of Crisis Intervention
• Comparison Islam/Sikhism
• Patterns in Nature Research Paper Infrared Tech
• P1 Unit 21 - Health and Social Care Level 3
• What Is Your Evaluation of the Effectiveness of the U.S. Health Care System in the Context of Delivery, Finance, Management, and/or Sustainability? What Are the Issues That Prompted a Need for Health Care Reform
• Sandals Marketing Mix
• Goventure Small Business
• West Point Cheating Incident Essay
• Finance Project
• Ethical Issues in Group Counseling
• Cis Data Communications Concepts Wans
• Malpractice
• E-Commerce Evolution
• Assistive Technology
• Vector Aeromotive Corporation Summary
• Mayo Clinic Case Study Memo
• Should Animals Be Used for Scientific Research?
• Speedster Athletics Case Study
• Exchanges with Industry Before Receipt of Proposals (4-4)
• Atha Corporation
• Application Theory
• Wgu Aft2 Accreditation Audit Task 2
• Iom Competencies Case Study
• Confucianism vs Legalism
• Private Law Firm – Pearson Specter
• GMAT Test Information
• GMAT Test Structure
• GMAT Scores
• GMAT Verbal
• sentence correction
• critical reasoning
• reading comprehension
• problem solving
• data sufficiency
• Integrated Reasoning
• MBA Rankings

* GMAT is a registered trademark of the Graduate Management Admission Council, which was not involved in the production of, and does not endorse, this product.

All content of site and tests copyright © 2024 majortests.com

• Virtual Writing Center
• CA Privacy Policy

GMAT Quant Questions: Problem Solving

Note: GMAT Quant questions cover Problem Solving, and so much more. To get more math practice, try our free GMAT practice test with accurate score prediction and subject-by-subject performance breakdown.

On the GMAT Quantitative section, the Problem Solving questions are just the familiar five-choice multiple choice math problems you have seen on every standardized test since well before puberty.  Here, you have discovered a veritable treasure chest of Problem Solving sample questions.  

Below is a link to thirty-two different articles on this blog, each with at least two Problem Solving questions.  The sample GMAT Problem Solving questions are often at the top of the article, although sometimes they are further down in the text.  The total number of sample Problem Solving problems available from this page is far more than 37, the total number of math questions you will see on a full Quantitative section of the GMAT. 

In each blog, the solutions & explanations to the sample questions are at the ends of the articles.  (If the topic is less than crystal clear for you, you may find the article itself enlightening.)

1. Problems with Averages

https://magoosh.com/gmat/math/gmat-averages-and-sums-formulas/

2. Distance, Rate, Time

https://magoosh.com/gmat/math/word-problems/gmat-distance-and-work-rate-formula/

3. Permutations & Combinations

https://magoosh.com/gmat/math/gmat-permutations-and-combinations/

4. Factors & Prime Factorizations ( five practice PS questions at the bottom of the article )

https://magoosh.com/gmat/math/arithmetic/gmat-math-factors/

5. Advanced Geometric Solids

https://magoosh.com/gmat/math/geometry/gmat-math-advanced-geometric-solids/

6. Estimation questions

https://magoosh.com/gmat/math/the-power-of-estimation-for-gmat-quant/

7. Difficult Dice Questions

https://magoosh.com/gmat/math/basics/gmat-probability-difficult-dice-questions/

8. Difference of Two Squares

https://magoosh.com/gmat/math/algebra/gmat-quant-difference-of-two-squares/

9. Sequences ( five PS practice questions scattered through article )

https://magoosh.com/gmat/math/word-problems/sequences-on-the-gmat/

10. Remainders

https://magoosh.com/gmat/math/basics/gmat-quant-thoughts-on-remainders/

11. Work & Work Rate

https://magoosh.com/gmat/2012/gmat-work-rate-questions/

12. Circle & Line Diagrams

https://magoosh.com/gmat/math/geometry/circle-and-line-diagrams-on-the-gmat/

13. Polygons

https://magoosh.com/gmat/math/geometry/polygons-and-regular-polygons-on-the-gmat/

14. Set Problems, with Double Matrix Method

https://magoosh.com/gmat/math/word-problems/gmat-sets-double-matrix-method/

15. Set Problems, with Venn Diagrams

https://magoosh.com/gmat/math/word-problems/gmat-sets-venn-diagrams/

16. Scale Factor & Percent Change

https://magoosh.com/gmat/math/geometry/scale-factors-on-the-gmat-percent-increases-and-decreases/

17. Standard Deviation

https://magoosh.com/gmat/math/standard-deviation-on-the-gmat/

18. Radicals

https://magoosh.com/gmat/math/algebra/simplifying-radical-expressions-on-the-gmat/

19. Function Notation

https://magoosh.com/gmat/math/arithmetic/function-notation-on-the-gmat/

20. Algebraic Factoring

https://magoosh.com/gmat/math/algebra/algebra-on-the-gmat-how-to-factor/

21. Hard Factorial Problems

https://magoosh.com/gmat/math/arithmetic/gmat-factorials/

22. Backsolving from the answers

https://magoosh.com/gmat/math/gmat-plugging-in-strategy-always-start-with-answer-choice-c/

23. Distance in the x-y plane

https://magoosh.com/gmat/math/geometry/gmat-coordinate-geometry-distance-between-two-points/

24. Pythagoras !

https://magoosh.com/gmat/math/geometry/pythagorean-triplets-to-memorize-for-the-gmat/

25. Lines in the x-y plane

https://magoosh.com/gmat/math/geometry/gmat-math-lines-slope-in-the-x-y-plane/

26. Tricks for Calculating Combinations

https://magoosh.com/gmat/math/gmat-math-calculating-combinations/

27. Parallel & Perpendicular Lines and Midpoints in the x-y plane

https://magoosh.com/gmat/math/geometry/gmat-math-midpoints-and-parallel-vs-perpendicular-lines/

28. Probability: AND & OR Rules

https://magoosh.com/gmat/2012/gmat-math-probability-rules/

29. Probability: “at least” statements

https://magoosh.com/gmat/math/basics/gmat-math-the-probability-at-least-question/

30. Probability: counting problems

https://magoosh.com/gmat/math/gmat-probability-and-counting-techniques/

31. Hard counting problems

https://magoosh.com/gmat/math/word-problems/gmat-counting-with-restrictions/

32. Probability: geometric probability

https://magoosh.com/gmat/math/geometry/geometric-probability-on-the-gmat/

Also check out these GMAT Probability questions .

Other GMAT Practice Questions

Magoosh has practice materials for all of the GMAT question types in GMAT Quantitative  and in GMAT Verbal. Look at the table below, and click the links for more practice!

And make sure you do practice questions that cover the most common GMAT Quant concepts too.

Mike served as a GMAT Expert at Magoosh, helping create hundreds of lesson videos and practice questions to help guide GMAT students to success. He was also featured as “member of the month” for over two years at GMAT Club . Mike holds an A.B. in Physics (graduating magna cum laude ) and an M.T.S. in Religions of the World, both from Harvard. Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike’s Youtube video explanations and resources like What is a Good GMAT Score? and the GMAT Diagnostic Test .

View all posts

More from Magoosh

Leave a Comment

Please leave any questions or suggestions in the comments, we try our best to respond within a few days! Your email address will not be published.

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

One response to “GMAT Quant Questions: Problem Solving”

this work is fantastics job, i need more of the solved problems

Problem Solving

Concepts Tested on GMAT Problem Solving

The problems are based on various arithmetic and algebra math concepts, many of which are presented as word problems. There is no geometry, trigonometry, or calculus on the GMAT. All numbers used are real numbers; irrational numbers are not used.

• Arithmetic concepts on the test include number properties, fractions, percents, ratios, exponents and roots, and basic statistics. Also included are certain types of word problems such as rate and work, mixture, sets, probability, and basic combinatorics.
• Algebra concepts on the test include linear equations, basic quadratic equations, absolute values, and inequalities.

How to Approach GMAT Problem Solving

Read the question carefully and fully understand what is asked. Harder questions may be purposely worded in a confusing manner. For word problems, it is often helpful to translate the information presented into equations or in a tabular format. Make liberal use of the provided scratch board , as performing calculations in your head can lead to careless mistakes. Be systematic in your approach, organize the information logically, and clearly label everything. This becomes even more important as you tackle hard difficultly problems.

Before diving into calculations, examine the five answer choices for clues . Incorrect answers are typically not random numbers, but are instead created to ensnare test takers who make a careless mistake or fall into a common trap. Consider the format of the answers, so you know what you are working towards. Look for any similarities or differences amongst the available answers. If the answer choices are numbers that are far apart, some approximation may make for easier calculations .

Sample GMAT Problem Solving Question

Let’s try a sample problem. Attempt the problem on your own before viewing the answer and explanation.

A hospital purchased 50 stethoscopes and 270 boxes of tongue depressors from a medical supply company. If the price of each stethoscope was nine times the price of each box of tongue depressors, what percent of the total bill was the price of one stethoscope?

        (A) 0.8%         (B) 1.0%         (C) 1.25%         (D) 1.45%         (E) 2.0%

Explanation to Problem

There are three general approaches to this word problem: conceptual, algebraic, and plugging-in numbers. Let’s discuss each in turn.

Conceptual approach:

The conceptual approach, likely to be taken by advanced students, is the fastest. Since the question focuses on the price of a stethoscope, we can convert the total tongue depressor cost into an equivalent stethoscope cost. The price of each stethoscope is nine times the price of each box of tongue depressors (side note – we can safely assume that all stethoscopes are equally-priced and that all tongue depressor boxes are equally-priced). Thus nine tongue depressor boxes cost the same as one stethoscope.

Divide 270 (the number of tongue depressor boxes) by nine to calculate that the cost of these 270 boxes is equivalent to the price of 30 (270 ÷ 9) stethoscopes. Therefore, the total bill is equivalent to the cost of 80 stethoscopes: the 50 stethoscopes bought plus 30 more (representing the 270 tongue depressor boxes). As a result, one stethoscope is \(\frac{1}{80}\) of the total bill.

We now need to convert this into a percent. But first let’s review the other two approaches, to make the conceptual approach more understandable.

Algebraic approach:

This approach, likely to be taken by intermediate students, puts the conceptual approach into algebraic form. For this algebra word problem, let’s assign variables to the unknowns:

         S = price of one stethoscope          B = price of one box of tongue depressors

To calculate the total bill, multiply Price × Quantity for each item and then add the results. We are given the quantities, and can use our variables for the prices:

        Total bill = 50 S + 270 B

We are told that the price of each stethoscope is nine times the price of each box of tongue depressors. Using our variables, we can write an equation to express this relationship:

         S = 9 B

A common mistake is to write this equation backwards, as B = 9 S . Since stethoscopes are more expensive, however, we need to make the bigger value S equal to nine times the smaller value B . A small number B cannot equal a big number S times 9.

Since the question asks about stethoscopes and not tongue depressors, we want to get rid of B , the variable that we don’t care about. To do this, isolate B and substitute it away. Divide both sides of our equation by 9 (same as multiplying both sides by \(\frac{1}{9}\)).         \(\frac{1}{9}\) S = \(\frac{1}{9}\)(9 B ) = B

Now let’s do an algebraic substitution into the total bill equation:         Total bill = 50 S + 270(\(\frac{1}{9}\) S ) = 50 S + 30 S = 80 S

The question asks: the price of one stethoscope is what percent of the total bill ? We are looking for a percent, as further verified by the format of the answers. When calculating a percent, a good approach is to form a fraction with the “is” number on top and the “of” number on the bottom:         Percent = \(\frac{\text{is}}{\text{of}}\) = \(\frac{\text{stethoscope price}}{\text{total bill}}\) = \(\frac{S}{80S}\) = \(\frac{1}{80}\) (since the S variable cancels out)

We’ll convert this into a percent after reviewing the plugging-in numbers approach.

Plugging-in numbers approach:

This approach is likely to be taken by less-advanced students, but is actually a great approach for this problem. When the answers represent a ratio or percent, and we don’t have specific numbers provided within the problem, then a very good technique is to pick numbers to work through the math. The price of each stethoscope is nine times the price of each box of tongue depressors, so let’s pick easy numbers. We do not need to worry about whether the numbers are accurate in the real world, just whether the numbers meet the relationship described in the problem.

        Tongue depressor box = $1         Stethoscope = $9

Now calculate the total bill, using the price numbers we made up and the quantities provided in the problem.

        Total bill = 50 × $9 + 270 × $1 = $450 + $270 = $720

The question asks: the price of one stethoscope is what percent of the total bill? As mentioned in the algebraic approach, we can calculate the percent by forming a fraction with the “is” number on top and the “of” number on the bottom:         Percent = \(\frac{\text{is}}{\text{of}}\) = \(\frac{\text{stethoscope price}}{\text{total bill}}\) = \(\frac{$9}{$720}\) = \(\frac{1}{80}\) (since 9 goes into 72 eight times)

Converting the fraction into a percent:

There are several approaches to convert \(\frac{1}{80}\) into a percent. Worst case, we could do long-hand division. But there are a couple faster approaches.

Notice that \(\frac{1}{80}\) = \(\frac{1}{8}\) × \(\frac{1}{10}\). We recommend that students memorize the decimal equivalents of common fractions. So we should ideally know that \(\frac{1}{8}\) = 0.125. Multiplying by \(\frac{1}{10}\) is the same as moving the decimal one place to the left, resulting in 0.0125. Converting a decimal into a percent is done by moving the decimal two places to the right, so 0.0125 = 1.25%.

Another good shortcut takes advantage of the fact that a percent is equivalent to a fraction with a denominator of 100. How can we turn our denominator of 80 into 100? We can increase 80 by 25%, the same as multiplying 80 by 1.25. To leave the value of our fraction unchanged, we must multiply numerator and denominator by the same number.         \(\frac{1}{80}\) = \(\frac{1(1.25)}{80(1.25)}\) = \(\frac{1.25}{100}\) = 1.25%

Finally, if we are very short on time and don’t see an easy way to do the conversion, we could at least quickly eliminate three answers by recognizing that:         \(\frac{1}{100}\) < \(\frac{1}{80}\) < \(\frac{1}{50}\)  →  \(\frac{1}{100}\) < \(\frac{1}{80}\) < \(\frac{2}{100}\)  →  1% < \(\frac{1}{80}\) < 2%

Our correct answer has to be somewhere between 1% and 2%, leaving only answers C and D. As we have seen above, C is the correct answer.

This site uses various technologies, as described in our Privacy Policy, for personalization, measuring website use/performance, and targeted advertising, which may include storing and sharing information about your site visit with third parties. By continuing to use this website you consent to our Privacy Policy and Terms of Use .

We are experiencing sporadically slow performance in our online tools, which you may notice when working in your dashboard. Our team is fully engaged and actively working to improve your online experience. If you are experiencing a connectivity issue, we recommend you try again in 10-15 minutes. We will update this space when the issue is resolved.

4 Tips to Tackle GMAT Math Problem Solving Questions

GMAT Problem Solving questions make up roughly half of the 31 questions in the GMAT's Quantitative section. That means you’ll typically see 15 or 16 Problem Solving questions. Perfecting your approach and pacing on these questions can go a long way toward improving your score on the GMAT .

GMAT Problem Solving the GMAC Way

In Problem Solving questions, you need to solve a math problem and pick the correct answer from among five answer choices. Let’s review what GMAC says about Problem Solving questions.

The Quantitative section tests three broad content areas:

All of the rules and concepts from these areas that are tested are generally covered in high school mathematics classes. The Problem Solving format is designed to test basic mathematical skill and understanding of elementary concepts from the three content areas. Moreover, Problem Solving also tests the ability to reason quantitatively, solve quantitative problems, and interpret data presented in the form of graphs. In other words, some GMAT Problem Solving questions are really just testing your ability to follow the rules. Other GMAT Problem Solving questions, the ones that test your ability to reason quantitatively, are testing your ability to determine which rules apply before you start solving. 

Read More: GMAT Practice Questions

Tips for GMAT Math Problems

1. remember what the gmat tests..

Some GMAT questions entice you to use math that is actually more sophisticated than you really need for the GMAT. It’s not that you can’t solve the questions using sophisticated math. It’s just that doing so may take more time than you really have. However, there’s often a simpler—and faster—approach that involves little more than some basic math. Keeping that in mind can be a clue to look for a more straightforward approach. That’s particularly true of the problems that aim to test your quantitative reasoning ability.

2. Practice working with different forms of numbers.

The GMAT really doesn’t care that much about testing your raw calculating ability. As a result, the test-writers tend to use numbers in the problems that make the math work out nicely. But, you still need to think about the easiest way to do the calculation. For example, if you needed to find 75% of a number, would you multiply by 0.75 or by ¾? If you’re solving a GMAT question, you probably want to choose the fraction because it’s much more likely that you are finding 75% of 400 than 423. 

Read More: GMAT Sentence Correction Tips

3. Use the answer choices for help.

When you solved math problems in school, you probably didn’t have answer choices from which to choose. Teachers tend to care more about the work that you do to solve a problem than the actual answer that you get. The GMAT, of course, cares only that you select the correct answer. By providing answer choices, the GMAT actually gives you more ways to solve the problem. In many cases, you may be able to just test out the answers until you find the one that works.  In other cases, you may realize that there are only one or two answers that even make sense. This kind of question may require no calculations at all if you pay attention to the answer choices!

4. Study the wrong answers.

Remember that the GMAT test-writers study the way that test-takers make mistakes. The GMAT test-writers use that knowledge to come up with wrong answers. In fact, they can increase the difficulty of a problem simply by including more wrong answers that are based on the common mistakes test-takers make when solving a particular problem. So, study the wrong answers! If you can determine what sort of mistake would lead to an included wrong answer, you can use that knowledge towards avoiding those sorts of mistakes on the problem solving questions.

Practice for the GMAT Math Section

Take a GMAT practice test with us under the same conditions as the real thing. You'll get a personalized score report highlighting your strengths and areas of improvement.

START A FREE PRACTICE TEST

• GMAT  
• Business School  

Find MBA Programs Matched to Your Interests

Explore our featured business schools to find those that are looking for students like you.

Top Online MBA Programs

On a mission to increase your salary? Our Top 50 Online MBA ranking is based on academics, career outcomes, tech platforms, and more.

Best Career Prospects

Find out which schools have the best track records for getting students jobs—and the highest starting salaries.

Top Schools for Entrepreneurship

Ready to build your own business from the ground up? Check out these 50 graduate programs.

Free MCAT Practice Test

I already know my score.

MCAT Self-Paced 14-Day Free Trial

Enrollment Advisor

1-800-2REVIEW (800-273-8439) ext. 1

1-877-LEARN-30

Mon-Fri 9AM-10PM ET

Sat-Sun 9AM-8PM ET

Student Support

1-800-2REVIEW (800-273-8439) ext. 2

Mon-Fri 9AM-9PM ET

Sat-Sun 8:30AM-5PM ET

Partnerships

• Teach or Tutor for Us

College Readiness

International

Advertising

Affiliate/Other

• Enrollment Terms & Conditions
• Accessibility
• Cigna Medical Transparency in Coverage

Register Book

Local Offices: Mon-Fri 9AM-6PM

• SAT Subject Tests

Academic Subjects

• Social Studies

Find the Right College

• College Rankings
• College Advice
• Applying to College
• Financial Aid

School & District Partnerships

• Professional Development
• Advice Articles
• Private Tutoring
• Mobile Apps
• International Offices
• Work for Us
• Affiliate Program
• Partner with Us
• Advertise with Us
• International Partnerships
• Our Guarantees
• Accessibility – Canada

Privacy Policy | CA Privacy Notice | Do Not Sell or Share My Personal Information | Your Opt-Out Rights | Terms of Use | Site Map

©2024 TPR Education IP Holdings, LLC. All Rights Reserved. The Princeton Review is not affiliated with Princeton University

TPR Education, LLC (doing business as “The Princeton Review”) is controlled by Primavera Holdings Limited, a firm owned by Chinese nationals with a principal place of business in Hong Kong, China.

• Menlo Coaching
• Practice Questions
• Problem Solving
• Sign up for GMAT Prep

July 4th Sale on GMAT Prep! 20% Off GMAT Prep Course Enrollment (Ends July 8)

Sample GMAT Problem Solving Questions

We’ve already covered why studying with official practice questions is the best way to prepare for the GMAT .  But even if you come up with the correct answer to an official problem, you still might not understand the underlying principles used to create that particular question, leaving yourself open to traps and pitfalls set by the test writers.  In the explanations below, I will use some of the core tenets of the Menlo Coaching GMAT curriculum to breakdown two official GMAT problem solving questions and provide important principles for correctly attacking this question type in the future. 

Multiple choice “problem solving” questions are, to most students, familiar, yet they generally do not approach them properly. To succeed on these questions, you obviously need the requisite knowledge related to the content area being tested—math skills related to arithmetic, algebra, etc. However, it is just as important to read carefully, leverage every hint, and choose the right strategy (backsolving, number picking, conceptual thinking, etc.) People think of multiple-choice problem solving questions as just plain math questions, but this GMAT sample question shows that they are much more than that. Take a look at the following questions, and check out our problem solving video below.

GMAT Problem Solving, Sample Question #1

Rates for having a manuscript typed at a certain typing service are $5 per page for the first time a page is typed and $3 per page each time a page is revised. If a certain manuscript has 100 pages, of which 40 were revised only once, 10 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed?

Finish the GMAT in 10 Weeks with Our Study Schedule

GMAT Problem Solving, Sample Question #2

A certain airline’s fleet consisted of 60 type A planes at the beginning of 1980. At the end of each year, starting with 1980, the airline retired 3 of the type A planes and acquired 4 new type B planes. How many years did it take before the number of type A planes left in the airline’s fleet was less than 50 percent of the fleet?

Sample GMAT Questions by Topic

• Data Sufficiency: Practice for the GMAT with Official Data Sufficiency Sample Questions
• Data Insights: How to Approach Data Insights: Practice Questions and Explanations
• Reading Comprehension: How GMAT Reading Comprehension Questions Mislead Test Takers: Practice Questions and Explanations
• Critical Reasoning: How to Succeed Against Official GMAT Critical Reasoning Questions

Need even more problem solving help? Read our guest post on MBA.com to learn why, in GMAT problem solving, flexibility is key! Plus, practice with more official GMAT problem solving questions from Poets&Quants.

Book a GMAT Strategy Call with Hailey

Replies in 24 hours

[email protected]

✓ Get feedback on your profile as a test-taker

✓ Ask questions about strategy, timelines, or the GMAT itself

✓ Learn what you need to work on to improve your score

✓ Find out whether you’d be a fit with live classes or private tutoring

• Exam Prep >
• Prepare for Business School >
• Business School & Careers >
• Explore Programs >
• Connect with Schools >
• How to Apply >
• Help Center >
• About the Exam
• Register for the Exam
• Plan for Exam Day
• Prep for the Exam
• About the Executive Assessment
• Register for the Executive Assessment
• Plan for Assessment Day
• Prepare for the Assessment
• NMAT by GMAC
• Shop GMAT™ Official Prep
• About GMAT™ Official Prep
• Prep Strategies
• Personalized Prep Plan
• GMAT Mini Quiz
• Executive Assessment Exam Prep
• NMAT by GMAC Exam Prep

Prepare For Business School

• Business Fundamentals
• Skills Insight

Business School & Careers

• Why Business School
• Student Experience
• Business Internships
• B-School Go
• Quiz: Are You Leadership Material?
• MBA Return on Investment (ROI) Calculator
• Estimate Your Salary
• Success Stories
• Diversity and Inclusion
• Women in Business

Explore Programs

• Top Business School Programs
• Quiz: Which Post Graduate Program is Right for You?
• Quiz: Find the Best Program for Your Personality
• Business School Rankings
• Business Master's Programs
• MBA Programs
• Study Destinations
• Find Programs Near Me
• Find MBA Programs
• Find Master's Programs
• Find Executive Programs
• Find Online Programs

Connect with Schools

• About GradSelect
• Create a GradSelect Profile
• Prep Yourself for B-School
• Quiz: Can You Network Like An MBA?
• Events Calendar
• School Events
• GMAC Tours Events
• In-Person Events
• Online Events

How to Apply

• Apply to Programs
• The Value of Assessments
• Admissions Essays
• Letters of Recommendation
• Admissions Interviews
• Scholarships and Financing
• Quiz: What's Your Ideal Learning Style?

Help Center

• Create Account
• Exams & Exam Prep
• GMAT Exam Prep

GMAT Problem Solving: Flexibility is the Key

Chris Kane - Menlo Coaching

Chris Kane is a mba.com Featured Contributor.

Of the five different question types you will encounter on the GMAT exam, Problem Solving feels the most familiar to test-takers. After all, most of us have done a considerable number of multiple-choice math questions in our academic careers, so this format is not new. However, what most people don’t understand about these particular “math” questions is that the GMAT does not exist to assess who is the best at math; rather, it exists to assess who is good at creative problem solving, who reads carefully and pays attention to details, who leverages every hint and resource at their disposal, who remains critical and finds contrarian cases – in other words, who possesses the skills required to excel in business school. 

Having the requisite math knowledge and a high level of fluency with the underlying concepts and skills tested in Problem Solving is obviously important, however, scoring even above the 50th percentile on the GMAT quant section requires much more than core math knowledge and fluency.

As I discuss in my previous article , GMAT test writers embed a set of critical thinking and logic skills in GMAT Data Sufficiency that make those questions feel like much more than just math problems. Because GMAT Data Sufficiency questions are more unusual to students, Problem Solving questions feel more like good old-fashioned high school level math problems, but a closer look shows they too involve much more.

Tip #1: Read Carefully! 

As I emphasize over and over with GMAT quantitative questions (both Data Sufficiency and Problem Solving), there is a lot of clever difficulty hiding in the wording and the details of the question. A long career teaching the GMAT has proved to me that people are not good at dealing with this type of difficulty. Overall, people preparing for the GMAT are not used to multiple choice math problems that are designed to “trick” you and elicit certain mistakes unrelated to the math. In business, it really doesn’t matter if you know how many positive factors 441 has, but it sure does matter if you misread a contract or fall for some con or trap set by a competing business!

If you don’t learn to focus on this more devious type of difficulty in your preparation, you will miss countless GMAT quant questions for which you understand the math principles, but still get the question wrong because it is assessing other attributes. Consider a few examples of cleverly worded question stems from official problems (one data sufficiency and two problem solving examples) that show how GMAT question writers assess who reads carefully and who pays attention to details:

• The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first three minutes. Did the phone call last longer than 15 minutes?

A vast majority of people get this Data Sufficiency question wrong because they interpret the highlighted portion as meaning $0.75 per minute for the first 3 minutes. It doesn’t say that, but you expect it to! If you think the first 3 minutes cost $2.25, you have fallen for the trap and you get the question wrong.

• A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.10. For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount. What is the total fine for a book on the fourth day it is overdue?

Many students miss this question as well, again due to interpretation. People think you are calculating the fine per day and adding it to the previous day, but it is a cumulative fine that you are supposed to be calculating. This problem seems so simple, but it must be difficult somehow and indeed it is…all relating to reading carefully and following the instructions properly.

• A worker carries jugs of liquid soap from a production line to a packing area, carrying 4 jugs per trip. If the jugs are packed into cartons that hold 7 jugs each, how many jugs are needed to fill the last partially filled carton after the worker has made 17 trips?

When people miss this, it is almost never because of the math. After 17 trips, the worker has carried 68 jugs, which divided by 7 gives you a remainder of 5. You feel good about hammering out the math quickly and pick 5 because that is the remainder. But wait a second…the question wasn’t asking for that! It was asking for how many more jugs are needed to fill the carton . That is 2 not 5. Again, you would not believe how many students get this question wrong, mainly because they are being too casual in their approach.

If you want to succeed in GMAT Problem Solving and differentiate yourself from the competition, you must develop an strong focus on wording and recognize when that is the primary difficulty in a question. Always make sure you are answering the proper question and never forget little details or restrictions provided in the question stem. If you do this well, you will be amazed how much higher your quant score can go. Once you become a pro at interpretation and stop falling for wording traps, then you must try to master the hardest part of Problem Solving: choosing the right approach. 

Tip #2: Be Flexible in Your Approach

I believe the most important component to success in GMAT Problem Solving is learning how to choose the best strategy for getting a solution quickly and efficiently – and be flexible in that choice. This decision will always be hard on these multiple-choice questions, but you can get a lot better at it with practice and good coaching.

There are numerous ways to solve GMAT problem solving questions: you can use algebra or other “traditional” math approaches; you can pick numbers to remove abstraction in percent or variable word problems; you can use conceptual thinking or logic (what I call the Leather Chair approach); you can actively leverage the answer choices (i.e. backsolving). 

When GMAT Problem Solving questions are created, they are designed to push people who always approach questions the same way. Business schools want creative, flexible problem solvers, not rote math machines! As an example: a hard 700+ level Problem Solving question on the exam will make you use fairly hard math (algebra, arithmetic, etc.) to go most of the way to the answer, but then the only way to get it correct at the end is to leverage the answers. The problem can’t be solved without answer choices to leverage, yet the “math machine” student will knock his or her head against the computer trying to solve the problem in a vacuum without actively using the answers. More commonly, questions are created in which one approach is extremely difficult or time consuming, while another approach is quite simple. 

Before you jump headfirst into a problem, always take the time to consider which approach will work best. You will not always make the right choice initially, but your instincts will become better and better as you complete more GMAT official practice problems. Remember: You can’t be a one-trick pony on this test if you want to score highly!

To become more flexible in your approach, you must practice and master all the different ways available to solve a GMAT Problem Solving question:

• When there are variables in answer choices or the original number does not matter (for example, in percent questions), it is often much easier to pick your own numbers, solve, and then find the correct answer using those numbers. Are you fluent with this technique and have you practiced it with numerous questions?
• When using the answers (i.e., backsolving) is required or makes the problem much easier, do you recognize this and use the answers actively?
• Are you good at solving problems conceptually from your leather chair when such an approach is available? 
• Are you ready to just do the math when that is the best or only way to solve a problem?

Mastering all these techniques and training yourself to be flexible with them is essential to success and requires active practice during your preparation. 

Tip #3: Know What You Need to Know

After reading the question carefully and considering the best approach for solving it, you then need to execute some type of underlying math calculations or apply particular math concepts. As I mentioned earlier, it is essential that you have a thorough understanding of these concepts and a high level of fluency with the necessary calculations. Most students need to do considerable work on this in their preparation, but it is important to remember that the underlying math concepts used to create these questions are not particularly difficult – most people just haven’t used them in a while so the concepts are rusty.

The best way to improve this fluency is to do full official GMAT problems so that you practice three separate things: reading carefully and interpreting wording correctly, choosing the best approach to the problem, AND solving the underlying math components quickly and efficiently. After every official GMAT Problem Solving question that you do, ask yourself three questions:

1. Why did I really get this question wrong? Was it because I didn’t understand a math concept or because I fell for some other trap?  Did I choose the right approach?

2. If I was slow on the problem, what led to the pacing issue and how can I improve my speed next time?

3. Overall, what repeatable takeaways exist from this problem and how can I apply those to future questions?

Remember: Don’t Mistake Activity for Achievement. You can do a lot fewer problems in your preparation if you always isolate the proper takeaways. To do this effectively, make sure to use official problems that help you develop all the different skills required in GMAT Problem Solving, not simply the underlying math.

GMAT Problem Solving Best Practices

Let’s summarize a set of GMAT Problem Solving best practices and then apply them to one full problem:

1. Very carefully assess the question , looking out for wording traps and noting any important restrictions or details in the problem (for instance, if it says “x is a positive even integer,” focus on how that changes the answer to the question compared to the case in which x was not restricted to being an integer, positive, and even).

2. Look out below! After analyzing the question stem, look carefully at the answers and consider how those answers will dictate your approach to the problem and what action is actually required to choose one of them. What hints do the answer choices give you for how to best attack the problem? 

3. Spend a considerable amount of time deciding what approach you should use . Is number picking a valid option? How actively can I leverage the answers? Are there any conceptual shortcuts? Do I just need to grind out some math? As a rule, people jump into questions too quickly and your first inclination for how to solve most GMAT Problem Solving questions will be wrong.  

4. Make sure you are leveraging every little hint provided by both the question stem and the answers. Often these questions are almost impossible to solve if you don’t leverage all the given clues. As an example, maybe it is impossible to actually solve for the correct answer, but fairly easy to prove that 4 answers are incorrect. 

5. After choosing an approach, be ready to pivot quickly if that approach is not working . It is hard to always choose the proper approach initially, and sometimes the best approach only becomes clear once you have dug into a problem.

6. Execute any basic calculations or conceptual math quickly and efficiently . Avoid unnecessary calculations and learn how to avoid careless errors when doing computations (mental math and focusing on the given answers is often helpful).

7. Before selecting your answer and hitting “Next,” do two things: (a) reread the question stem and make sure you are answering the proper question and (b) ask yourself if there is truly a reward in your answer (i.e., is it tricky enough to differentiate yourself from other smart test takers). In doing these two simple things, you will avoid trap answers and false negatives on the exam – questions you should have gotten correct but didn’t.

Sample GMAT Problem

Consider the following problem and try to solve it yourself in a few minutes using the best practices above:

During the four years that Mrs. Lopez owned her car, she found that her total car expenses were $18,000. Fuel and maintenance costs accounted for 1/3 of the total and depreciation accounted for 3/5 of the remainder. The cost of insurance was 3 times the cost of financing, and together these two costs accounted for 1/5 of the total. If the only other expenses were taxes and license fees, then the cost of financing was how much more or less than the cost of taxes and license fees

(A) $1,500 more

(B) $1,200 more

(C) $100 less

(D) $300 less

(E) $1,500 less 

Explanation:

Let’s go through the question applying the best practices in the same order as described above:

1.   With so much convoluted wording in this question stem, you should recognize that proper interpretation is key and wording tricks will surely be present. The first thing you should notice is that it says “3/5 of the remainder” not the “total” in the 2nd line, so you will need to account for that in your calculations. Additionally, you should note that there are many components to this question, so you better slow down and execute each part carefully.

2.   The answer choices don’t provide too many hints, but there a few takeaways: you will not be able to backsolve (they are asking for a difference) and it must be easy to make computational mistakes with that difference, since 2 answers say “more” and three say “less”. Make sure you calculate the difference carefully.

3.   For the approach, I have already noted that backsolving is not an option nor is number picking because you must work with the given total of $18,000. This question will require an algebraic approach and setting up those equations and/or calculations properly will be key.

4.  Carefully using all the provided information, let’s execute the math:

The last step is to figure out the amount of taxes and licensing fees (let’s use T for that sum):

• M = $6000, D = $7200, and I + F = $3600.
• That is $16,800, which leaves $1200 for T.
• The question is asking for the difference between T and F, so you can see that F ($900) is $300 less than T ($1200).

Correct answer is thus D.

5. (and 6/7) There was no need to pivot in your approach at any point since you must just do the calculations carefully in this problem. It is very important that you re-read the question and you double check that no careless errors were made in the calculations to get there. People get this question wrong because there are so many steps and thus many opportunities to make calculation mistakes or interpretation mistakes. Note: all of the calculations in this problem can easily be done mentally, so if you are writing much down beyond the totals for each component in this problem, you should work on your calculation fluency.

Final Thoughts

To succeed in Problem Solving you must learn how to be flexible and creative in your approach to each problem, and you must focus on precision in wording. Everyone understands that you must possess the requisite math knowledge to do well, but in general people spend too much time on raw math and not enough time on math + everything else that makes these questions difficult (and relate more to what GMAC is really trying to assess with this exam). 

While it is smart to start your studying process with some raw math skills work, make sure you quickly move into full official GMAT problems, so you can work not just on the underlying math, but also on “everything else.” With the right type of preparation , you can master all the different elements required to succeed in GMAT Problem Solving questions and knock your quant score out of the park!

Chris Kane is an mba.com Featured Contributor.  

SUNDAY QUIZZES!    GRE Quiz (20 Questions) at 9:30am ET / 7pm IST   |   GMAT Quiz (30 Questions) at 10:30am ET

Practice thousands of GMAT questions with top expert solutions.

Identify and improve upon mistakes efficiently using our Error Log.

Get the latest tips and news from our top GMAT professionals.

- it’s free and easy!

Problem Solving (PS)

View after sorting.

• GMAT Exam Info
• What's Tested on the GMAT
• What's a Good GMAT Score?
• How to Register for the GMAT
• GMAT Study Plans
• Creating Your Study Schedule
• Applying to Business School
• GMAT Question of the Day
• GMAT Pop Quiz
• GMAT 20-Minute Workout
• Free GMAT Practice Test
• GMAT Math Sheet
• GMAT Prep Courses

What's Tested on the GMAT: Quantitative Section

The GMAT Quantitative Section is designed to test your quantitative reasoning—your ability to think logically about quant concepts. It covers basic math concepts, including arithmetic, algebra, statistics, and more but it’s not truly a math test (though it can certainly feel like it). The section contains only one problem type: Problem Solving.

You will need to relearn many of the quant skills you first learned in high school (or earlier!). And you’ll need to learn strategies for approaching Problem Solving questions, as efficiently as possible.

Finally, you do not get a calculator on the Quant section of the GMAT—so you will have to do your math work by hand.

What is the Breakdown of GMAT Quant questions?

• Time limit: 45 minutes
• Number of problems: 21
• Average time per problem: 2 minutes
• Problem type: Problem Solving

You’ll have 45 minutes to answer 21 Quant problems or an average of 2 minutes per problem.

[ RELATED: GMAT Practice Tests ]

What Math Skills are Tested on the GMAT?

• Arithmetic, including number properties, percents, fractions, and ratios
• Algebra, including exponents, linear equations, quadratics, and functions
• Statistics, including mean, median, and standard deviation
• Story problems and number properties

Problems may be written in “pure math” form or in “story” form, so you’ll also need skill in translating a story into the necessary math concepts to solve.

While you do need to know various rules and formulas, the GMAT is explicitly designed to allow you to take advantage of shortcuts—estimation, testing out a few real numbers, and so on. The GMAT isn’t all that interested in precise calculations; rather, the test mimics the real-world usage you can expect in business school and the working world.

For example, business schools are interested in knowing whether you understand quant concepts well enough to do some quick back-of-the-envelope calculations to determine a rough answer to the CEO’s question—7,500 is good enough; 7,462.39 is unnecessary. Or whether you are able to realize that the sales forecast numbers your coworker just handed you don’t make logical sense—even though you haven’t performed the precise calculations yourself.

[ RELATED: GMAT Math Basics ]

FREE PREMIUM CONTENT

Gmat math quicksheet.

Unlock access to our free GMAT Math Quicksheet

How Problem Solving Works

Problem Solving (PS) is the classic multiple-choice math problem: They give you some info, they ask you a question, and they give you five answer choices with numbers or variables in them. 

Unlike DS, you are actually going to have to solve the math to get to the answer. But PS will at least feel a lot more familiar right from the start.

Be careful, though! Because PS problems feel more familiar, you’re going to be more tempted to use the textbook solution methods you learned in school. But a lot of PS problems can be solved much more efficiently by using various test-taking strategies—estimating, testing out some real numbers, trying the answers. 

Standardized tests are literally built (on purpose!) for you to take advantage of these strategies to save time. In fact, someone who tries to solve all of the math problems in the “old school” way will most likely run out of time before they can finish the test. The GMAT is not really a math test. In the real world, it’s good enough to know that revenues were up approximately 10% this quarter; if you take the time to calculate and tell your boss that revenues were up 9.843% this quarter, she’s going to think that you’re wasting your time.

How to Train Yourself to Think Like an Executive

As you get ready for the GMAT, train yourself out of your “old school” mentality and into your “executive mindset” mentality: What’s the quickest, easiest way to get to the answer—without making a mistake?

Problem Solving GMAT Practice Question

At a particular school, 65% of the students have taken language classes. Of those students, 40% have studied more than one language. If there are 300 students at the school, how many have studied more than one language?

First, read the question and jot down the information given:

• 65% → LC (abbreviation for language class)
• 40% OF 65% → more than one LC

Glance at the answers (before doing any work.). They’re pretty spread apart, indicating that you can estimate at least a little.

The first step is to figure out how many students take language classes. 65% is a little less than two-thirds (or 66.7%), so use two-thirds to estimate. Two-thirds of 300 is 200, so approximately 200 students have taken language classes.

Is that value, 200, a little bit of an overestimate or a little bit of an underestimate?

Because the real percentage (65%) is a little less than the percentage actually used (two-thirds, or 66.7%), the value of 200 is a little bit greater than whatever the exact 65% figure would be. In other words, 200 is a little bit of an over estimate.

Next, here’s the source of one of the trap answers. The 40% who have taken more than one language class is not 40% of the total number of students. Rather, it’s 40% of just the 65% who’ve taken language classes. So the next step is to take 40% of the 200 figure.

That’s not a terribly hard calculation to do…but get out of your “old school math” mindset. Don’t do calculations that you don’t absolutely have to do! 40% is less than 50%, so 40% of 200 has to be less than 100.

Answer and Explanation

The correct answer is (A). 78. Only one answer choice is less than 100.

What if the answers had instead been these:

In that case, you can still do the first estimation (using two-thirds rather than 65%), but calculate more precisely on the second step. Here’s how:

• 40% of 200 is the same as 4(10%) of 200
• 10% of 200 = 20
• 4(10%) of 200 = (4)(20) = 80

80 is a little bit of an overestimate (since you overestimated on the first step), so the correct answer in the second set of answers is the one that’s a little less than 80—answer (B) 78.

To calculate percentages quickly, find benchmarks like 50%, 10%, 5%, 1% first, and then multiply or add them up to get to the percentage that you want. If you needed 12%, for example, then you could find 10% and 1% and then add up 10% + 1% + 1%.

[ RELATED: Quantitative Strategies for the GMAT ]

How GMAT Scoring Works

The GMAT Quantitative section is scored on a scale from 6 (low) to 51 (high). Most schools want to see a score of at least 40 and the most competitive schools are typically looking for a Quant score of 45 or higher.

Your Quant, Verbal, and Data Insights scores are also combined into your Total score, which ranges from 205 (low) to 805 (high). The Total score is the score that schools care about most (followed by your Quant score, for most schools). An average GMAT score is about 545; top-10 business school programs report average scores for their students in the 665 to 695 range.

Review What’s a Good GMAT Score to learn how to determine what kind of goal score will help to make you competitive at your target programs.

You might also like

Call 1-800-KAP-TEST or email [email protected]

Prep for an Exam

MCAT Test Prep

LSAT Test Prep

GRE Test Prep

GMAT Test Prep

SAT Test Prep

ACT Test Prep

DAT Test Prep

NCLEX Test Prep

USMLE Test Prep

Courses by Location

NCLEX Locations

GRE Locations

SAT Locations

LSAT Locations

MCAT Locations

GMAT Locations

Useful Links

Kaplan Test Prep Contact Us Partner Solutions Work for Kaplan Terms and Conditions Privacy Policy CA Privacy Policy Trademark Directory

• Skip to content

Free GMAT Test Questions

Welcome to our Question Bank!

You have not answered any question so far. There are 50 free practice questions in our database in total, which you can answer and will improve your skills.

You can answer all questions in a row (click on "All Questions") or only all questions of a particular section (click on that Section) or a single selected question (click on that Question).

All Questions

Quantitative reasoning - problem solving.

Quantitative Reasoning - Data Sufficiency

Verbal Reasoning - Critical Reasoning

Verbal Reasoning - Reading Comprehension

Verbal Reasoning - Sentence Correction

GMAT is a registered trademark of the Graduate Management Admission Council (GMAC), which is unaffiliated with and does not endorse this website.

Should You Take a Prep Class?

Wouldn't it be great to know the average GMAT score of the business school of your dreams? You've studied hard for the GMAT, but are you fully sure of what ...

How to Choose a Prep Course

Adaptive Testing Explained

  How to Master GMAT Problem Solving

Updated for the new gmat in 2024.

To master GMAT Problem Solving, you’ll need to develop the following skills: 

A firm grasp of basic, high school math concepts

The ability to avoid careless errors

Good time management

A flexible and creative mindset

Although GMAT Problem Solving questions are rooted in fundamental, high school-level math concepts, they often require a limber approach that you can’t find in any textbook. Our tips for GMAT Problem Solving will help you thrive on these questions – no matter what the exam throws at you.

What Topics Are Tested in GMAT Problem Solving?

The following are some of the most common math topics that appear in GMAT Problem Solving questions:

●  Arithmetic                                    ●  Rates

●  Algebra                                         ●  Probability

●  Geometry                                     ●  Combinatorics

●  Exponents                                    ●  Statistics

●  Percents                                       ●  Number Properties

●  Ratios

The first step to mastering GMAT Problem Solving is to develop accuracy on algebra, arithmetic, and number properties. Since those three topics appear in more than two-thirds of GMAT quant questions, students should give them priority when developing GMAT Problem Solving study plans.

Although many students obsess over the more exotic topics listed above (such as combinatorics, probability, and rates), these topics collectively represent less than 10% of GMAT Problem Solving questions. So if you need to make a big improvement in your GMAT Problem Solving performance, spend the bulk of your time developing your accuracy on algebra, arithmetic, and number properties.

Avoiding Careless Errors on GMAT Problem Solving

The GMAT is an adaptive exam, which means that when you answer GMAT questions correctly, the test will give you harder questions as you move through the section. If you get a bunch of easy Problem Solving questions wrong, on the other hand, your quant score will plummet. For this reason, avoiding careless errors on easy questions is essential to mastering GMAT Problem Solving. 

The best way to avoid careless mistakes is to practice the following three steps on every GMAT Problem Solving question you tackle: 

Read carefully . Many students miss GMAT Problem Solving questions not because they fail to understand the math, but because they miss a key detail in the question.

Plot an efficient path forward . There are usually several different ways to solve any given GMAT Problem Solving question. If you take a few moments to think through your options before jumping in, you’re more likely to choose an efficient path that avoids tortuous algebra and arithmetic – and you’re far less likely to make a careless error.

Check your work as you go . Don’t wait until the end of the problem to check your work. By catching careless errors as soon as possible, you’ll make the best use of your precious time and energy. 

How to Master Time Management on GMAT Problem Solving

The best time management strategy for GMAT Problem Solving is to avoid wasting time on questions that you can’t solve efficiently. Because the GMAT is an adaptive test, most test-takers will answer 30-50% of all quant questions incorrectly – even if they ultimately get an excellent quant score. So you’ll need to be prepared to guess and move on when you’re overmatched by a GMAT Problem Solving question. 

The best approach to GMAT Problem Solving is to read the question twice, and then plot your path forward towards a solution. If you think you’re on track for an efficient answer to the question, great – solve the question, double-check your work to avoid silly mistakes, and continue to the next question. But if you don’t see a good path forward on a GMAT quant question, then you’ll want to guess and move on quickly. 

By following this strategy, you’ll spend the majority of your 62 minutes actually solving problems, and waste relatively little time clawing away at questions that you likely wouldn’t get right anyway.

Another benefit of good time management is that you won’t find yourself rushing towards the end of the section. Rushing often leads to careless errors, and as we’ve already discussed, careless errors will seriously damage your GMAT Problem Solving performance. 

For more, check out this video on how to manage your time on adaptive tests like the GMAT. 

Developing a Flexible Approach to GMAT Problem Solving

While a strong understanding of fundamental math concepts is essential, you’ll need more than just content knowledge to master GMAT Problem Solving. In fact, students often perform better on GMAT Problem Solving when they stop thinking of it as “math” and start thinking of it as “quantitative reasoning.” 

For most high school students, math is taught as sequences of mechanical steps to be memorized and followed. GMAT Problem Solving questions, on the other hand, often come with a twist. By presenting familiar math topics in unfamiliar contexts, they challenge students to be both flexible and creative in their approach.

Consider the following problem as an example:

If you think of this as a mechanical “math question,” you’ll follow some well-worn steps here: find some common denominators, add the fractions, and THEN compare the sums. But if you’re thinking of the GMAT as “quantitative reasoning,” maybe you’ll try something quicker, smarter, and less arithmetic-intensive. 

For instance, since we’re just looking for the greatest value, we don’t care what that value actually is. As long as we know that it’s larger than the other four expressions, we’ve found the correct answer. So since the question is asking for the greatest of the five answer choices, you can just compare pairs of answer choices, and knock off anything that’s the smaller of the two. 

Let’s start with (D) and (E). It’s easy to see why (E) is larger than (D) once you notice that 1 – ½ = ½, so (D) is gone.

Similarly, (B) looks a lot like (E), except that the denominators in (B) are squared – and since larger denominators mean that the fractions must be smaller, we can cross off (B). The same argument holds for (C) – it’s clearly smaller than (E) as well. And then (A) has smaller denominators than (E) – so (A) is your answer.

Overall, if you’re thinking of GMAT Problem Solving as a set of narrow mathematical tasks, then you’re barking up the wrong tree. Once you start looking for opportunities to apply flexible logic and identify multiple solution paths, then you’re on the right track.

Want to learn more about GMAT Quant?

Misplaced GMAT Math Anxiety

When to Guess & When to Skip GMAT Questions

What Test Sections Are on the GMAT?

A 12-minute video on how to approach the GMAT Data Insights section

Our free, complete GMAT video course

Featured Videos

How to Manage Time on an Adaptive Test Like the GMAT

How to Spend the Last Two Weeks of GMAT Prep

How to Overcome Test Anxiety on the GMAT

GMAT vs. GRE

Quant Ep. 1: Arithmetic

CR Ep: 1 How to Approach GMAT Critical Reasoning

RC Ep 1: How to Approach GMAT Reading Comprehension

SC Ep. 1: How to Approach GMAT Sentence Correction

GMAT Prep Online Guides and Tips

What math is on the gmat topics, questions, and review.

The Quantitative section of the GMAT strikes fear into the hearts of many test takers who haven’t taken a math class in years. If you’re one of those test takers, you shouldn’t worry! You can totally handle the math in this section.

While the Quantitative section is challenging, it doesn’t test especially advanced concepts. This guide will show you what math is on the GMAT, along with key tips on how to prepare.

First, let’s discuss a general overview of GMAT math.

GMAT Math Section: An Overview

The GMAT Quantitative section is your third section on the GMAT. You’ll take it after the 30-minute Analytical Writing Assessment, 30-minute Integrated Reasoning section, and an optional eight-minute break.

The Quantitative section is the first adaptive section on the GMAT, meaning that the questions change to match your ability level. You’ll start out with some medium level GMAT math questions, and the problems will get easier or harder depending on how you’re doing.

Not sure how or what to study? Confused by how to improve your score in the shortest time possible? We've created the only Online GMAT Prep Program that identifies your strengths and weaknesses, customizes a study plan, coaches you through lessons and quizzes, and adapts your study plan as you improve.

We believe PrepScholar GMAT is the best GMAT prep program available , especially if you find it hard to organize your study schedule and don't want to spend a ton of money on the other companies' one-size-fits-all study plans.

The GMAT math section will continue to give you customized questions to get a more and more accurate measure of your skills. This adaptive format allows for comparable scores across different tests, plus it enhances security since no two tests look exactly the same.

You’ll get 31 GMAT math questions in 62 minutes, leaving you with approximately two minutes per question. Unlike the Integrated Reasoning section, you won’t have access to a calculator. You will get some note boards and markers to write out your work.

While you’ll need to know a variety of math concepts for this section, you’ll only see two question types. Read on to learn what they are.

GMAT Math Questions: 2 Types

There are just two types of Quantitative questions, and they’re interspersed throughout the section in random order. The two types are problem solving questions and data sufficiency questions.

Typically, about two-thirds of GMAT math questions will be problem solving and one-third will be data sufficiency. However, this proportion could change depending on how many experimental questions you get of each type.

Problem solving questions are just like any other typical question you’d get on a math test. They may ask you to solve an equation, figure out a word problem, or answer questions on a graph.

Each question has five answer choices, and there’s only one right answer for each. Where these questions do get tricky is when they require multiple steps or abstract thinking.

Here’s one example of a problem solving question on the Quantitative section of the GMAT.

The second type of Quantitative question, data sufficiency problems, are more unusual. These questions present you with a math problem followed by two pieces of information. You don’t have to solve the problem, but rather indicate whether one or both statements give you “sufficient data.”

Here’s an example of a GMAT math data sufficiency problem.

The answer choices for data sufficiency questions are always the same as the ones you see above. You don’t need to solve the initial problem. You just need to know if you could solve the problem based on the given information.

While there are only two question types in the Quantitative section, there are quite a few more concepts that show up. Below, you’ll find an overview of the tested GMAT math concepts, along with sample problems for each one.

What Math Is on the GMAT Quantitative Section?

As you read above, the Quantitative section doesn’t require you to be a mathematician. Your GMAT math review won’t involve advanced calculus or trigonometry. In fact, the GMAT math topics  don’t get much more advanced than high school-level algebra.

The main challenge for a lot of people, then, is reviewing concepts that they studied in the past but haven’t used in a long time. The main skills you need to answer both question types involve arithmetic, algebra, geometry, and word problems.

Let’s take a closer look at the topics within each of these skill areas as outlined by the official GMAT Prep Software , starting with arithmetic.

GMAT Math Topics in Arithmetic

You’ll get a variety of problems that require skills in arithmetic. You shouldn’t have to do particularly advanced calculations, since you won’t have use of a calculator, but the questions may require some strategic problem solving and complex thinking.

Want to improve your GMAT score by 60 points?

We have the industry's leading GMAT prep program. Built by Harvard, MIT, Stanford, and Wharton alumni and GMAT 99th percentile scorers, the program learns your strengths and weaknesses and customizes a curriculum so you get the most effective prep possible.

For arithmetic math in the Quantitative section, you should be familiar with

• Properties of integers
• Real numbers
• Ratio and proportion
• Powers and roots of numbers
• Descriptive statistics
• Counting methods
• Discrete probability

The problem below, for example, is a problem solving GMAT math question that involves fractions and percents. 

This second sample problem is a data sufficiency question that calls on your arithmetic and logic skills.

GMAT Math Topics in Algebra

In addition to arithmetic, another major skill area is algebra. As part of your GMAT math review, you definitely want to get work with algebraic expressions and solve for variables. You should be comfortable with

• Variables and algebraic expressions
• Manipulating algebraic expressions
• Solving linear equations with one unknown
• Solving two linear equations with two unknowns
• Solving equations by factoring
• Solving quadratic equations
• Inequalities
• Absolute value

The sample question below is a typical problem solving question that involves an algebraic expression with two variables and an exponent.

Data sufficiency questions may also call on your algebra skills, like in the practice question comparing two variables below.

GMAT Math Topics in Geometry

You won’t find quite as many questions on geometry as on arithmetic and algebra, but they definitely still come up. To prepare, you should study the following concepts:

• Lines and angles
• Polygons (convex)
• Quadrilaterals
• Rectangular solids and cylinders
• Coordinate geometry

This problem solving question, for instance, asks about properties of triangles.

This data sufficiency question requires you to have some understanding of angles and how they relate to one another.

GMAT Word Problems

Word problems may call on arithmetic, algebra, or geometry skills, plus they require careful reading to identify exactly what the problem is asking you to do.

Want to Identify YOUR GMAT Strengths and Weaknesses?

Our proprietary GMAT Diagnostic Assessment creates a customized study plan for you that takes you from registration all the way to test day! It is included with every account and proven to significantly maximize your score .

Get your personalized assessment as part of your 5 day risk-free trial now:

You might be asked to calculate simple interest or compound interest, calculate rate, or measure profits. You also may have to work with data from a table, line chart, bar graph, scatter plot, or pie graph. Finally, a question may ask you to analyze sets, as presented in Venn diagrams, or analyze probability.

These are some typical concepts you need to understand to solve GMAT word problems.

• Work (these questions typically show the rates at which a person and a machine work alone, and you’ll have to compute the rate at which they work together, or vice versa)
• Mixture (in these problems, substances with different characteristics are combined, and you’ll need to determine characteristics of the resulting mixture)
• Measurement
• Data interpretation

This problem solving practice question asks you to calculate how fast the Earth travels around the sun. You need to convert miles per second into miles per hour.

This data sufficiency question is a word problem that calls on your arithmetic and logic skills.

Knowing what math is on the GMAT is an important first step, but what else can you do to prepare for the Quantitative section? Read on for six key tips on getting ready for GMAT math.

How to Review Math for the GMAT: 6 Key Tips

How can you get ready for the problem solving and data sufficiency questions on the Quantitative section? What can you do to review concepts that you may not have seen since high school?

Read on for six tips to guide your GMAT math review.

#1: Review the Fundamentals

As you read above, GMAT math doesn’t involve particularly advanced concepts. You won’t need calculus, trigonometry, or any college-level mathematics.

Your first step in preparing, then, should be to review fundamental math concepts. You need to have a solid foundation of key concepts in arithmetic, algebra, and geometry, plus a firm grasp of logic and analysis that will help you solve word problems.

Make sure your study materials offer a thorough review of all tested concepts, and take time to work through the lessons.

#2: Drill With Realistic Practice Questions

As you review key concepts, you should reinforce your understanding with GMAT math practice problems. Even though the math in the Quantitative section isn’t particularly advanced, the questions are still challenging.

They often require complex thinking and multiple steps. Even if you know how to calculate the area of a right triangle or solve a quadratic equation, you need to make sure you can apply that knowledge to GMAT math questions.

By drilling with realistic practice questions, you’ll learn how to apply your math knowledge to the GMAT. The best practice questions come from the official test makers, as on the GMAT Prep Software. Third party test prep companies, like Kaplan and Manhattan Prep, also offer useful practice questions and tests.

As you answer the questions, take notes on anything that confuses or trips you up. Take time to read answer explanations and find the source of your confusion.  By understanding your mistakes, you can take specific steps to fix them.

#3: Take Timed Practice Tests

After you’ve done initial concept review and tried out some practice problems, you should set aside time to take a timed GMAT practice test. Find a quiet place, take a practice test with a computer adaptive format, and give yourself 62 minutes to complete the section.

After you’ve finished the practice test, take time to review any questions that you got wrong or felt unsure about. Try to locate the source of your error.

Were you running out of time? Did you misunderstand what a question was asking you to do? Did you make an arithmetic mistake? Were you unfamiliar with a concept? Did you simply make a careless error?

By figuring out where you went wrong, you can take the right steps to fix it for next time. The practice test will not only help you figure out what concepts you need to review, but it will also give you feedback on your pacing. Doing well on the Quantitative section requires you to work quickly and efficiently, and taking practice tests will help you improve your test taking rhythm.

#4: Memorize Data Sufficiency Answer Choices

Data sufficiency questions are weird; there’s no doubt about it. You won’t really see questions like them anywhere but on the GMAT.

To minimize confusion, you should familiarize yourself with the answer choices before test day. You’ll always see the same five answer choices that ask whether statement 1, statement 2, both, or neither give you sufficient information to solve the problem.

Remember that you don’t need to solve these problems, but rather indicate whether you have enough information to solve them. Memorize the answer choices before test day so you know exactly what you’re looking for in each data sufficiency problem and don’t have to waste time reading through or trying to differentiate between the answer choices.

#5: Write Out Your Work

As goes the mantra of high school math teachers everywhere, make sure to show your work. You can’t use a calculator in the Quantitative section, and mental math will only get you so far.

You’ll get note boards and markers in the testing center to write out your work. You should definitely use them to work through the challenging, often multi-step problems.

Try to be neat and organized so you don’t run out of room or make a careless error. If your answer doesn’t match any of the answer choices, then you may need to comb through your work to find the calculation mistake. Try to keep everything legible to make things easier on yourself.

These note boards won’t be graded and are entirely for your own use. You can use them on any of the GMAT sections, but they’re especially helpful when solving math problems.

#6: Practice, Practice, and Practice Some More

As a skill like any other, GMAT math demands a lot of dedicated practice. Whether or not you consider yourself a “math person,” you should set aside time to review concepts, answer sample questions, and take practice tests.

Not only will you sharpen your math skills, but you’ll also become a more efficient test-taker who can handle answering 31 questions in 62 minutes. Don’t get discouraged, but know that you can improve with effort, time, and a customized study plan.

GMAT Math Questions: Final Points

To prepare for the Quantitative section of the GMAT, you should focus on fundamental concepts of arithmetic, algebra, and geometry, plus you need to prepare for word problems. You’ll answer two types of questions, the straightforward problem solving questions and the more unusual data sufficiency questions.

After months of GMAT math review, you can go into the test familiar with these question types. You can hone your time management skills by taking timed practice tests. You’ll also find that the math section gets more and more manageable as you answer lots of GMAT practice questions.

You don’t need to be a math person to do well on the GMAT Quantitative section, but you do need to spend time preparing. With enough effort, you can sharpen skills that you first developed in high school and get yourself ready to conquer GMAT math.

What’s Next?

Now you’re an expert in GMAT math, but do you know what the rest of the exam looks like? Check out  our guide to the full GMAT structure and format , along with examples of each question type across the test.

Do you know how the GMAT is scored? Check out our complete guide to GMAT scoring , and then head to this article to see how section and total scores correspond to percentiles.

The GMAT is a daunting test, but how hard is it, really? This article tackles that complicated question to show you just how challenging you can expect the GMAT to be.

Was this helpful? Sign up for FREE GMAT and MBA guides!

Share this:.

• Click to share on Twitter (Opens in new window)
• Click to share on Facebook (Opens in new window)
• Click to share on Google+ (Opens in new window)

Author: Rebecca Safier

Rebecca graduated with her Master's in Adolescent Counseling from the Harvard Graduate School of Education. She has years of teaching and college counseling experience and is passionate about helping students achieve their goals and improve their well-being. She graduated magna cum laude from Tufts University. View all posts by Rebecca Safier

GMAT Math Help

Study concepts, example questions, & explanations for gmat math.

• GMAT Quantitative Reasoning
• Data-Sufficiency Questions
• Advanced Data Sufficiency
• Absolute Value
• DSQ: Understanding absolute value
• DSQ: Solving equations
• DSQ: Understanding exponents
• Functions/Series
• DSQ: Understanding functions
• Inequalities
• DSQ: Solving inequalities
• Linear Equations, One Unknown
• DSQ: Solving linear equations with one unknown
• Linear Equations, Two Unknowns
• DSQ: Solving linear equations with two unknowns
• Simplifying Algebraic Expressions
• DSQ: Simplifying algebraic expressions
• Solving by Factoring
• DSQ: Understanding factoring
• Solving Quadratic Equations
• DSQ: Solving quadratic equations
• Counting Methods
• DSQ: Understanding counting methods
• DSQ: Understanding decimals
• Descriptive Statistics
• Arithmetic Mean
• DSQ: Calculating arithmetic mean
• DSQ: Calculating median
• DSQ: Calculating mode
• DSQ: Calculating range
• Discrete Probability
• DSQ: Calculating discrete probability
• DSQ: Understanding fractions
• DSQ: Calculating percents
• Powers & Roots of Numbers
• DSQ: Understanding powers and roots
• Properties of Integers
• DSQ: Understanding the properties of integers
• Ratio & Proportions
• DSQ: Calculating ratio and proportion
• Real Numbers
• DSQ: Understanding real numbers
• DSQ: Understanding arithmetic sets
• Avoiding Common Data Sufficiency Traps
• DSQ: Calculating the length of a chord
• DSQ: Calculating the length of the diameter
• DSQ: Calculating the ratio of diameter and circumference
• DSQ: Calculating circumference
• DSQ: Calculating the area of a circle
• DSQ: Calculating the length of a radius
• DSQ: Calculating the angle for a percentage of a circle
• DSQ: Calculating the angle of a sector
• DSQ: Calculating the area of a sector
• DSQ: Calculating the length of an arc
• DSQ: Calculating the percentage of a sector from an angle
• Coordinate Geometry
• DSQ: Calculating the equation of a circle
• DSQ: Graphing a function
• DSQ: Graphing a line
• DSQ: Graphing a logarithm
• DSQ: Graphing a point
• DSQ: Graphing a quadratic function
• DSQ: Graphing an exponential function
• DSQ: Graphing an ordered pair
• DSQ: Graphing complex numbers
• Distance Formula
• DSQ: Calculating the length of a line with distance formula
• Midpoint Formula
• DSQ: Calculating the endpoints of a line segment
• DSQ: Calculating the midpoint of a line segment
• Other Lines
• DSQ: Calculating the equation of a line
• DSQ: Calculating the slope of a line
• DSQ: Calculating whether point is on a line with an equation
• Parallel Lines
• DSQ: Calculating the equation of a parallel line
• DSQ: Calculating the slope of parallel lines
• DSQ: Calculating whether lines are parallel
• Perpendicular Lines
• DSQ: Calculating the equation of a perpendicular line
• DSQ: Calculating the slope of a perpendicular line
• DSQ: Calculating whether lines are perpendicular
• Tangent Lines
• DSQ: Calculating the slope of a tangent line
• x and y intercept
• DSQ: Calculating the equation of a curve
• DSQ: Calculating x or y intercept
• Intersecting Angles and Lines
• DSQ: Calculating the angle of an intersection
• DSQ: Calculating an angle of a line
• DSQ: Understanding intersecting lines
• DSQ: Understanding rays
• DSQ: Calculating an angle in a polygon
• DSQ: Calculating the area of a polygon
• DSQ: Calculating the length of a diagonal of a polygon
• DSQ: Calculating the length of a side of a polygon
• DSQ: Calculating the perimeter of a polygon
• Quadrilaterals
• Other Quadrilaterals
• DSQ: Calculating an angle in a quadrilateral
• DSQ: Calculating the length of the diagonal of a quadrilateral
• DSQ: Calculating the length of the side of a quadrilateral
• DSQ: Calculating the perimeter of a quadrilateral
• DSQ: Calculating whether quadrilaterals are similar
• DSQ: Calculating the area of a rectangle
• DSQ: Calculating the length of the diagonal of a rectangle
• DSQ: Calculating the length of the side of a rectangle
• DSQ: Calculating the perimeter of a rectangle
• DSQ: Calculating whether rectangles are similar
• DSQ: Calculating the area of a square
• DSQ: Calculating the length of the diagonal of a square
• DSQ: Calculating the length of the side of a square
• DSQ: Calculating the perimeter of a square
• Rectangular Solids & Cylinders
• DSQ: Calculating the diagonal of a cube
• DSQ: Calculating the length of an edge of a cube
• DSQ: Calculating the surface area of a cube
• DSQ: Calculating the volume of a cube
• DSQ: Calculating the surface area of a cylinder
• DSQ: Calculating the volume of a cylinder
• DSQ: Calculating the diagonal of a prism
• DSQ: Calculating the length of an edge of a prism
• DSQ: Calculating the surface area of a prism
• DSQ: Calculating the volume of a prism
• Tetrahedrons
• DSQ: Calculating the length of an edge of a tetrahedron
• DSQ: Calculating the surface area of a tetrahedron
• DSQ: Calculating the volume of a tetrahedron
• Acute / Obtuse Triangles
• DSQ: Calculating an angle in an acute / obtuse triangle
• DSQ: Calculating if two acute / obtuse triangles are similar
• DSQ: Calculating the area of an acute / obtuse triangle
• DSQ: Calculating the height of an acute / obtuse triangle
• DSQ: Calculating the length of the hypotenuse of an acute / obtuse triangle
• DSQ: Calculating the length of the side of an acute / obtuse triangle
• DSQ: Calculating the perimeter of an acute / obtuse triangle
• DSQ: Calculating whether acute / obtuse triangles are congruent
• Equilateral Triangles
• DSQ: Calculating the area of an equilateral triangle
• DSQ: Calculating the height of an equilateral triangle
• DSQ: Calculating the length of the side of an equilateral triangle
• DSQ: Calculating the perimeter of an equilateral triangle
• Right Triangles
• DSQ: Calculating an angle in a right triangle
• DSQ: Calculating the area of a right triangle
• DSQ: Calculating the height of a right triangle
• DSQ: Calculating the length of the hypotenuse of a right triangle : Pythagorean Theorem
• DSQ: Calculating the length of the side of a right triangle
• DSQ: Calculating the perimeter of a right triangle
• DSQ: Calculating whether right triangles are congruent
• DSQ: Calculating whether right triangles are similar
• Specific Value Data Sufficiency
• Word Problems
• Data Interpretation
• DSQ: Understanding diagrams
• Probability
• DSQ: Calculating probability
• DSQ: Calculating discounts
• Interest Problems
• DSQ: Calculating compound interest
• DSQ: Calculating simple interest
• Measurement Problems
• DSQ: Understanding measurement
• Mixture Problems
• DSQ: Understanding mixture problems
• DSQ: Calculating profit
• Rate Problems
• DSQ: Calculating rate
• DSQ: Understanding sets
• Work Problems
• DSQ: Understanding work problems
• Yes/No Data Sufficiency
• Problem-Solving Questions
• Understanding absolute value
• Solving equations
• Understanding exponents
• Understanding functions
• Solving inequalities
• Solving linear equations with one unknown
• Solving linear equations with two unknowns
• Simplifying algebraic expressions
• Understanding factoring
• Solving quadratic equations
• Understanding counting methods
• Understanding decimals
• Calculating arithmetic mean
• Calculating median
• Calculating mode
• Calculating range
• Calculating discrete probability
• Understanding fractions
• Calculating percents
• Understanding powers and roots
• Understanding the properties of integers
• Calculating ratio and proportion
• Understanding real numbers
• Understanding arithmetic sets
• Calculating the length of a chord
• Calculating the length of the diameter
• Calculating the ratio of diameter and circumference
• Calculating circumference
• Calculating the area of a circle
• Calculating the length of a radius
• Calculating the angle for a percentage of a circle
• Calculating the angle of a sector
• Calculating the area of a sector
• Calculating the length of an arc
• Calculating the percentage of a sector from an angle
• Calculating the equation of a circle
• Graphing a function
• Graphing a line
• Graphing a logarithm
• Graphing a point
• Graphing a quadratic function
• Graphing a two-step inequality
• Graphing an exponential function
• Graphing an ordered pair
• Graphing complex numbers
• Graphing inverse variation
• Calculating the length of a line with distance formula
• Calculating the endpoints of a line segment
• Calculating the midpoint of a line segment
• Calculating the equation of a line
• Calculating the slope of a line
• Calculating whether point is on a line with an equation
• Calculating the equation of a parallel line
• Calculating the slope of parallel lines
• Calculating whether lines are parallel
• Calculating the equation of a perpendicular line
• Calculating the slope of a perpendicular line
• Calculating whether lines are perpendicular
• Calculating the equation of a tangent line
• Calculating the slope of a tangent line
• Calculating the equation of a curve
• Calculating x or y intercept
• Calculating an angle of a line
• Understanding intersecting lines
• Understanding rays
• Calculating an angle in a polygon
• Calculating the area of a polygon
• Calculating the length of a diagonal of a polygon
• Calculating the length of a side of a polygon
• Calculating the perimeter of a polygon
• Calculating an angle in a quadrilateral
• Calculating the area of a quadrilateral
• Calculating the length of the diagonal of a quadrilateral
• Calculating the length of the side of a quadrilateral
• Calculating the perimeter of a quadrilateral
• Calculating whether quadrilaterals are similar
• Calculating the area of a rectangle
• Calculating the length of the diagonal of a rectangle
• Calculating the length of the side of a rectangle
• Calculating the perimeter of a rectangle
• Calculating whether rectangles are similar
• Calculating the area of a square
• Calculating the length of the diagonal of a square
• Calculating the length of the side of a square
• Calculating the perimeter of a square
• Calculating the diagonal of a cube
• Calculating the length of an edge of a cube
• Calculating the surface area of a cube
• Calculating the volume of a cube
• Calculating the surface area of a cylinder
• Calculating the volume of a cylinder
• Calculating the diagonal of a prism
• Calculating the length of an edge of a prism
• Calculating the surface area of a prism
• Calculating the volume of a prism
• Calculating the length of an edge of a tetrahedron
• Calculating the surface area of a tetrahedron
• Calculating the volume of a tetrahedron
• Calculating an angle in an acute / obtuse triangle
• Calculating if two acute / obtuse triangles are similar
• Calculating the area of an acute / obtuse triangle
• Calculating the height of an acute / obtuse triangle
• Calculating the length of the hypotenuse of an acute / obtuse triangle
• Calculating the length of the side of an acute / obtuse triangle
• Calculating the perimeter of an acute / obtuse triangle
• Calculating whether acute / obtuse triangles are congruent
• Calculating the area of an equilateral triangle
• Calculating the height of an equilateral triangle
• Calculating the length of the side of an equilateral triangle
• Calculating the perimeter of an equilateral triangle
• Calculating an angle in a right triangle
• Calculating the area of a right triangle
• Calculating the height of a right triangle
• Calculating the length of the hypotenuse of a right triangle : Pythagorean Theorem
• Calculating the length of the side of a right triangle
• Calculating the perimeter of a right triangle
• Calculating whether right triangles are congruent
• Calculating whether right triangles are similar
• Understanding diagrams
• Calculating probability
• Calculating discounts
• Calculating compound interest
• Calculating simple interest
• Understanding measurement
• Understanding mixture problems
• Calculating profit
• Calculating rate
• Understanding sets
• Understanding work problems

The Graduate Management Admissions Test is a hurdle that many potential business students must face. The Quantitative Reasoning portion is probably the more feared section of the GMAT for most examinees. Many examinees will have flashbacks to high school or undergraduate math, and may anticipate complicated mathematical questions, elaborate graphs, and intimidating geometry. Whether you need  GMAT tutoring in Atlanta ,  GMAT tutoring in Houston , or  GMAT tutoring in San Francisco , working one-on-one with an expert may be just the boost your studies need.

The GMAT Quantitative Reasoning exam does in fact test challenging mathematical concepts that you may have not seen in some time. However, with proper preparation, you can face the questions with confidence. The section consists of thirty-seven questions administered over seventy-five minutes. Of these, you can anticipate about two-thirds to be fairly straightforward questions consisting of a problem you are asked to solve by choosing the correct answer from multiple presented options. 

The remaining questions are of a second type that is a bit more abstract. These are called the sufficiency questions, which ask you to make a judgment. Is enough information provided for you to be able to solve the question, or can you not determine the answer based on what you are told? Consider the following simple question:

If X and Y are positive integers, what is their sum?

1. X and Y have a difference of 50

2. X is the product of (Y/2) x 4

In answering this question, your challenge is to determine if you can figure out the sum of X and Y using just the information in either point 1 or point 2, if you need both point 1 and point 2 together to be able to solve the problem, or if you need more information than is provided in point 1 and point 2 taken together.

Most students find that the additional consideration of sufficiency to make these problems much more challenging than the relatively straight-forward problem-solving questions. Some students may consider these sufficiency questions to be the hardest questions they attempt on test day. Varsity Tutors also offers resources like a  free GMAT Math Practice Tests  to help with your self-paced study, or you may want to consider a  GMAT tutor .

The GMAT Quantitative Reasoning exam is tests your ability to think critically and to reason. Developing these skills through practice, collaboration, and reflection can be far superior to any shortcuts to a higher score. Consider working with tutors who have their own history of success with the GMAT Quantitative Reasoning test, as they can often help you fast track your initial progress substantially. In addition, explore Varsity Tutors’ free GMAT Math resources. You may find that our GMAT Math Help page is a great place to get started in improving your understanding of challenging mathematical concepts or question types like sufficiency questions. Our GMAT Math Help provides example problems which are answered and fully explained, allowing you to walk through the process of solving a challenging question as guided practice. We organize our GMAT Math Help content in differing levels of specificity, so whether you want to see examples of sufficiency questions in general or questions specifically about factoring, you can do so easily. After improving your understanding of the question types and concepts that you find to be most challenging, you can practice answering these types of problems on your own by using our other free GMAT Math resources. In addition to the GMAT Math Help Section and  GMAT tutoring , you may also want to consider using some of our  GMAT Math Flashcards .

The skills that the GMAT’s Quantitative Reasoning section tests are the same skills that are demanded in management programs and in managerial careers. You can give yourself a major advantage in the future by investing time and effort now. Also, consider that the GMAT is one of the only objective ways for admissions officers to evaluate different candidates. Your college may be dramatically different from the college of another applicant in terms of grading scale or grading rigor. A substantial difference in GPA may not be indicative of a difference in ability, and the GMAT is the best way for you to demonstrate your capacity for learning and success in an objective and convincing way. You can view the GMAT Quantitative Reasoning exam as an opportunity to showcase your abilities instead of simply one more hurdle to overcome. Take advantage of this chance to demonstrate why you belong in one of the best business schools!

Tired of practice problems?

Try live online GMAT prep today.

All GMAT Math Resources

GMAT Math Problems with Solutions

If you are currently studying for the GMAT and are in the thick of your prep, you already know the importance of practicing GMAT math problems. To help with your practice, we’re presenting you with a representative selection of GMAT math problems with solutions. Of course, practicing the questions here is just a start. If you need more practice after completing what we offer in this article, please check out the Target Test Prep Online GMAT Course .

Here is what we’ll cover in this article:

An overview of the gmat quant topics, each major gmat quant topic can be broken down into subtopics, problem-solving example 1: quadratic equations, problem-solving example 2: number properties, problem-solving example 3: exponents, problem-solving example 4: general word problems, problem-solving example 5: rates, problem-solving example 6: percents, problem-solving example 7: combinations and permutations, problem-solving example 8: absolute value, what’s next.

Before we jump into examples of GMAT math questions, let’s discuss some key basics of GMAT quant.

The Topics Tested in GMAT Quant

Here is the good news regarding the topics in the GMAT quantitative section. They are similar to those you studied in high school. So, as you jump into your GMAT math prep or even take practice tests, I’m sure many concepts and techniques will come back to you.

However, as you may have already discovered, the math questions you see on the GMAT are not the same types of questions you saw in high school. The GMAT will test your ability to evaluate math analytically. So, you will train new math “muscles” as you learn GMAT quant .

Although the topics tested on the GMAT are similar to those you saw in high school, the ways in which the questions are asked may not be familiar.

Here is the list of the quant topics tested on the GMAT.

• Basic Arithmetic Problems
• Algebra Problems
• Quadratic Equations
• Number Properties
• Inequalities
• Absolute Values
• General Word Problems
• Work Problems
• Unit Conversions
• Overlapping Sets
• Combinations and Permutations
• Probability
• Coordinate Geometry

It’s important to understand that each of these 21 major math topics includes a number of subtopics.

I often speak with students seeking GMAT math help. In those conversations, I help them analyze their math weaknesses. Most students will look at the macro list and say something like “I struggle with Number Properties.” While such statements are helpful, it’s much more important to understand students’ struggles on a more granular level.

For example, Number Properties includes many subtopics, such as even/odd numbers, positive/negative numbers, divisibility, remainders, the least common multiple, and the greatest common factor, to name a few. It’s possible that a student could excel in some of these subtopics and not in others. So, simply identifying that you struggle with Number Properties, at the end of the day, provides limited information.

Thus, when you’re analyzing your GMAT quant skills, it’s important to look at how you perform on a subtopic, not just a broad area of quant!

There are 21 major quant topics on the GMAT, but each main topic includes multiple subtopics.

Let’s now discuss GMAT problem-solving questions in a bit more detail.

GMAT Problem-Solving Questions

The GMAT Quantitative Reasoning section presents you with 21 problem-solving questions, and you have 45 minutes to answer them. GMAT Problem-Solving (PS) questions are a type of question with which you are likely already familiar. This multiple-choice question type presents five answer choices: A, B, C, D, and E, and there is only one correct answer for each question.

Any concept could be tested in a PS question, including all 21 topics we listed previously. To get a feel for how the GMAT presents these questions, let’s do some GMAT PS practice questions. You’ll notice that each sample question is categorized by major topic and subtopic.

Major Topic: Quadratic Equations

Subtopic: The Difference of Squares

What is the value of 998^2 – 2^2?

If we recognize this question as a difference of squares, we can solve it in less than 30 seconds, doing all the calculations in our heads.

We can recall the fact that, for any numbers a and b, a^2 – b^2 = (a – b)(a + b), we can apply this equation to the expression in the question stem, with a = 998 and b = 2. Thus, we can re-express 998^2 – 2^2 as follows:

998^2 – 2^2 = (998 – 2)(998 + 2) = (996)(1,000) = 996,000

Note that we could have instead solved this question by performing the unwieldy and time-consuming calculation of 998^2, and then subtracting 4. But, instead, by knowing and applying the difference of squares concept, we have avoided the risk of making an arithmetic mistake, and we’ve gained valuable extra time for solving later questions in the quant section.

Major Topic: Number Properties

Subtopic: Units Digit Patterns

What is the units digit of 7^15?

When we raise the base 7 to successive integer powers, a pattern of the units (ones) digit is revealed. Let’s determine that pattern now by calculating the first few powers of 7.

7^1 = 7 units digit is 7

7^2 = 4 9 units digit is 9

7^3 = 34 3 units digit is 3

7^4 = 2,40 1 units digit is 1

7^5 = 16,80 7 units digit is 7

So, we see that the units digits of powers of 7 have a repeating pattern of 4 numbers: 7-9-3-1. Thus, every 4th exponent has the same units digit. For example, we see that 7^4, 7^8, 7^12, … etc., will all have the same units digit of 1.

Therefore the most straightforward way of determining the units digit of 7^15 is to find an exponent that is a multiple of 4 close to 15. We know from our pattern that 7^16 must have a units digit of 1. Now, using the pattern 7-9-3-1, we know that 7^15 must have a units digit of 3.

Major Topic: Exponents

Subtopic: Solving Exponential Equations by Combining Exponential Expressions With Like Bases

If 16 x + 2 * 8 6 = 32 6 , then x is equal to which of the following?

First, notice that we can’t combine any of the expressions in the equation until we re-express the terms with like bases. In this case, the current bases, 16, 8, and 32, can all be expressed as powers of 2. So, we will use the facts that 16 = 2^4, 8 = 2^3, and 32 = 2^5 to rewrite the equation.

16 x + 2 * 8 6 = 32 6

(2 4 ) x + 2 * ( 2 3 ) 6 = ( 2 5 ) 6

2 4x + 8 * 2 18 = 2 30

So now that all terms in the equation have the same base, we can combine them, using the fact that when we multiply two terms with like bases, we add the exponents:

2 4x + 8 + 18 = 2 30

2 4x + 26 = 2 30

We can now use the fact that when we have two exponential expressions with like bases on either side of an equation, we can equate the exponents.

4x + 26 = 30

Major Topic: General Word Problems

Subtopic: Age Problems

Marla is 20 years older than Angelina. In 5 years, Marla will be 3 times as old as Angelina. What will Marla’s age be in 3 years?

First, let’s define our two variables:

M = Marla’s age today

A = Angelina’s age today

Next, we can write two equations from the information presented in the problem stem.

Since Marla is 20 years older than Angelina, we have:

M = A + 20 (equation 1)

Since in 5 years, Marla will be 3 times as old as Angelina, we have:

M + 5 = 3(A + 5)

M + 5 = 3A + 15

M = 3A + 10 (equation 2)

Next, from equation 1, we can substitute A + 20 for M in equation 2, and then solve for A:

A + 20 = 3A + 10

Finally, we see that Angelina is 5 years old. Thus, Marla is currently 5 + 20 = 25 years old. So, in 3 years, Marla will be 28 years old.

Major Topic: Rates

Subtopic: Average Rates

Paul walks from home to work at a rate of 5 mph and bikes home from work along the same route at 12 mph. What is his average speed for the round trip?

Since we have an average rate question we can use the following formula:

average rate = total distance / total time

Since the distance is the same in both directions, we can use a smart number to represent the one-way distance. A good number to use would be one that is divisible by both 5 and 12, so we can let the distance each way = 60.

So, the time going to work is 60/5 = 12, and the time going home from work is 60/12 = 5.

Finally we can determine the average rate:

average rate = (60 + 60)/(12 + 5)

average rate = 120/17

Major Topic: Percents

Subtopic: Percent Translations

If p is 500 percent of q, and q is 400 percent of z, then z is what percent of p?

First, we can note that 500% of a number is equivalent to 5 times that number, and 400% of a number is equivalent to 4 times that number. With these facts in mind, we can create two equations:

p = 5q (equation 1)

q = 4z (equation 2)

We can substitute 4z for q in equation 1:

p = 20z (equation 3)

Now, to find out what percent z is of p, we can divide these two quantities and multiply the result by 100:

Finally, we can simplify this expression if we use equation 3, plugging in 20z for p:

z/p ✕ 100 = z/20z ✕ 100 = 1/20 ✕ 100 = 100/20 = 5

Thus, z is 5% of p.

Major Topic: Combinations and Permutations

Subtopic: Choosing Multiple Items in a Combination Problem

A treasure chest contains 5 different rubies, 4 different emeralds, and 3 different diamonds. If a pirate picks 5 jewels from the chest, 3 of which are rubies, how many possible ways exist for him to pick the jewels?

First, he chooses 3 rubies out of 5. Since the order doesn’t matter, we use combinations to count the number of possibilities. Recall the formula for a combination choosing k objects out of n objects is nCk = n! / k!(n-k)!. Thus, the number of ways to choose just the 3 rubies is:

5C3 = 5! / 3!(5-3)! = 5! / 3!(2)! = 5x4x3x2x1 / 3x2x1x2x1 = 20 / 2 = 10

Now, there are 2 remaining choices to make, and there are 7 non-rubies remaining in the chest. Thus, the number of ways to choose the 2 jewels out of 7 is:

7C2 = 7! / 2!(7-2)! = 7! / 2!5! = 7x6x5x4x3x2x1 / 2x1x5x4x3x2x1 = 42 / 2 = 21

There are 10 ways to choose the rubies and 21 ways to choose the remaining jewels.

Therefore, the total number of ways to choose the 5 jewels is 10 ✕ 21 = 210.

Major Topic: Absolute Value

Subtopic: Evaluating Absolute Value Equations

If |3y – 2| = 1 and y^2 < y, then what is the value of y?

First, we can solve this absolute value equation for two cases: when (3y – 2) is positive and when (3y – 2) is negative, as follows:

Case 1: 3y – 2 is positive.

3y – 2 = 1

Case 2: 3y – 2 is negative.

-(3y – 2) = 1

-3y + 2 = 1

The absolute value equation has two solutions: y = 1 and y = 1/3.

Now, we don’t know which value of y to choose as the answer. We use the given fact that y^2 < y. Let’s test each possible answer, either y = 1 or y = 1/3.

If y = 1, then y^2 = 1. Thus, y cannot be equal to 1.

If y = 1/3, then y^2 = (1/3)^2 = 1/9, and we see that since 1/9 < 1/3 , then y^2 < y.

Thus, the correct answer is 1/3.

We could have skipped these last steps by recalling a fact from Number Properties: The only way that y 2 can be less than y is if y is a positive proper fraction — that is, if y is between 0 and 1.

Now that we have practiced many problem-solving questions, let’s shift the conversation to Data Sufficiency questions.

GMAT quant covers 21 major math topics from the disciplines of arithmetic, algebra, coordinate geometry, number properties, and statistics.

The 21 questions in the Quantitative Reasoning section are all 5-option multiple-choice problem-solving questions. In this article, we have looked at 8 example questions that run the gamut of topics that you might encounter in the GMAT quant section.

The two keys to success on GMAT quant are knowledge of the 21 topics that are tested and familiarity with what you might encounter. In this article, we have provided you with 8 example questions covering Problem Solving questions.

Another subtopic from Number Properties that challenges many students is divisibility. Read this article to review the divisibility rules and how the GMAT tests them .

You May Also Like...

About The Author

Jeffrey Miller is the head GMAT instructor for Target Test Prep. Jeff has more than fourteen years of experience in the business of helping students with low GMAT scores hurdle the seemingly impossible and achieve the scores they need to get into the top 20 business school programs in the world, including HBS, Stanford, Wharton, and Columbia. Jeff has cultivated many successful business school graduates through his GMAT instruction, and will be a pivotal resource for many more to follow.

Leave a Reply Cancel Reply

Save my name, email, and website in this browser for the next time I comment.