gmat math problem solving

GMAT Quant Questions: Problem Solving

Note: GMAT Quant questions cover Problem Solving, and so much more. Be sure to use our GMAT Practice Test to test your knowledge of these concepts.

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

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

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

1. Problems with Averages

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

2. Distance, Rate, Time

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

3. Permutations & Combinations

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

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

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

5. Advanced Geometric Solids

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

6. Estimation questions

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

7. Difficult Dice Questions

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

8. Difference of Two Squares

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

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

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

10. Remainders

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

11. Work & Work Rate

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

12. Circle & Line Diagrams

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

13. Polygons

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

14. Set Problems, with Double Matrix Method

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

15. Set Problems, with Venn Diagrams

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

16. Scale Factor & Percent Change

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

17. Standard Deviation

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

18. Radicals

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

19. Function Notation

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

20. Algebraic Factoring

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

21. Hard Factorial Problems

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

22. Backsolving from the answers

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

23. Distance in the x-y plane

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

24. Pythagoras !

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

25. Lines in the x-y plane

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

26. Tricks for Calculating Combinations

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

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

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

28. Probability: AND & OR Rules

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

29. Probability: “at least” statements

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

30. Probability: counting problems

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

31. Hard counting problems

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

32. Probability: geometric probability

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

Also check out these GMAT Probability questions .

Other GMAT Practice Questions

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

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

Addendum to the table: A special note on Sentence Correction questions

Sentence Correction questions are the very shortest questions on the test, both in terms of word count and time. Ideally, you should complete any SC question in less than one minute. Make sure you set your speed for this question type carefully. And be aware that Sentence Correction questions do NOT have their own subsection in GMAT Verbal; instead, SC is mixed in with Critical Reasoning and Reading Comprehension on the GMAT.

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

View all posts

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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?

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

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Problem Solving

Concepts Tested on GMAT Problem Solving

The problems are based on arithmetic, algebra, and geometry math concepts. Any of these concepts can appear as a word problem, and in fact you should expect more than half of the PS questions to be presented as word problems . There is no 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 under arithmetic are certain types of word problems such as rate and work, mixture, sets, basic probability, and basic combinatorics.
• Algebra concepts on the test include solving linear equations, basic quadratic equations, and inequalities.
• Although most test takers see only 3 to 5 geometry questions on the GMAT, there are many types of geometry concepts that may appear: lines and angles, triangles, rectangles, circles, rectangular solids and cylinders, and coordinate geometry.

How to Approach GMAT Problem Solving

In approaching a problem, read the question carefully and fully understand what is asked. Harder questions are sometimes purposely worded in a confusing manner. For word problems, it is helpful to translate the information presented into equations or mathematical notation if possible. In working through the problem, make liberal use of the provided scratch board . Trying to perform calculations in your head can lead to careless mistakes. Be systematic in your approach, organize the information logically, and clearly label everything. This becomes more important as you tackle more difficult problems.

Before diving into the calculations, however, be sure to 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, perhaps some approximation will 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:

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, essentially 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, we must multiply price x quantity for each item, and then add the results. We are given the quantities, and can use our variables for the prices:

        Total bill = 50S + 270B

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 = 9B

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

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 and work through the math. We know that 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

Let’s now calculate the total bill, using the numbers we made up for the prices and the quantities provided in the problem.

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

Converting the fraction into a percent:

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.

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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.  

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Planning on applying to business school? Then you’re probably concerned about how well you will do on the GMAT, the Graduate Management Aptitude Test. Many students may find themselves to be particularly apprehensive about the GMAT’s Quantitative section, which focuses on mathematical calculations as well as data interpretation and analysis; however, with the right approach and tactics, you can familiarize yourself with the format of the GMAT Quantitative section, study the content it tests, and feel completely prepared for it on test day. 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 section consists of 37 multiple-choice questions and allows test-takers 75 minutes to answer them. Each of these multiple-choice questions is of one of two types: Problem Solving or Data Sufficiency. GMAT Problem Solving questions ask you to use your mathematical problem-solving skills to find the correct answer to a math problem, while Data Sufficiency questions ask you to analyze mathematical data presented in order to determine whether you have enough information to solve a problem, or what information is necessary to do so. Both of these question types may ask you problems concerning arithmetic, algebra, geometry, coordinate geometry, or a mix several of these categories together in a story problem that you must interpret in order to solve. Both may also test your ability to interpret charts, graphs, and figures. If you don’t know the answer to a GMAT Quantitative problem, whether you should guess or not is a somewhat complicated decision that you have to make based on your understanding of your own abilities. If, while studying, you have determined that you are likely to score quite highly on the GMAT Quantitative section, guessing on a question might bring your score down more than simply leaving the question blank; however, if you believe that you are not likely to score that well on the GMAT Quantitative section, the odds may be more in your favor, and you may want to guess on questions that you are not sure about. Varsity Tutors also offers resources like a  free GMAT Math Diagnostic Tests  to help with your self-paced study, or you may want to consider a  GMAT tutor . Any GMAT Quantitative study plan should include both Problem Solving questions and Data Sufficiency questions about a wide variety of mathematical topics. You should make sure to practice interpreting data in multiple forms, including equations, word problems, graphs, tables, and charts. You can practice questions of all of these different types by taking Varsity Tutors’ free GMAT Quantitative Practice Tests. Each Practice Test consists of ten to twelve problems, and you have the option to do problems of a range of types and topics in each practice test, or to hone in on one of the two GMAT Quantitative problem types, or a specific mathematical topic that you want to focus on and review. After taking a GMAT Quantitative Practice Test, you are presented with detailed statistics about your performance relative to other test-takers as well as your time management. In addition to the GMAT Math Practice Tests and  GMAT tutoring , you may also want to consider using some of our  GMAT Math Flashcards . You might also want to try one of the free Full-Length GMAT Quantitative Practice Tests, which ask you questions covering all of the concepts you’ll encounter during the course. The complete practice tests are a great way to get some practice as you check your skills. Once you finish the test, you’ll be shown a variety of statistics, step-by-step explanations of each question’s correct answer, and links to additional review exercises. These free online practice tests can help you build a custom GMAT study plan, as the results tell you which concepts you should focus on. This timesaving feature allows you to streamline your review. Once you’ve used some of the other Learning Tools to brush up on your skills, you can assess your progress by taking another Full-Length GMAT Quantitative Practice Test. By making the most of Varsity Tutors’ free GMAT Quantitative resources, you can study efficiently for the GMAT Quantitative section and feel fully prepared for it on test day!

Practice Tests by Concept

Data-sufficiency questions practice test, advanced data sufficiency practice test, algebra practice test, absolute value practice test, dsq: understanding absolute value practice test, equations practice test, dsq: solving equations practice test, exponents practice test, dsq: understanding exponents practice test, functions/series practice test, dsq: understanding functions practice test, inequalities practice test, dsq: solving inequalities practice test, linear equations, one unknown practice test, dsq: solving linear equations with one unknown practice test, linear equations, two unknowns practice test, dsq: solving linear equations with two unknowns practice test, simplifying algebraic expressions practice test, dsq: simplifying algebraic expressions practice test, solving by factoring practice test, dsq: understanding factoring practice test, solving quadratic equations practice test, dsq: solving quadratic equations practice test, arithmetic practice test, counting methods practice test, dsq: understanding counting methods practice test, decimals practice test, dsq: understanding decimals practice test, descriptive statistics practice test, arithmetic mean practice test, dsq: calculating arithmetic mean practice test, median practice test, dsq: calculating median practice test, mode practice test, dsq: calculating mode practice test, range practice test, dsq: calculating range practice test, discrete probability practice test, dsq: calculating discrete probability practice test, fractions practice test, dsq: understanding fractions practice test, percents practice test, dsq: calculating percents practice test, powers & roots of numbers practice test, dsq: understanding powers and roots practice test, properties of integers practice test, dsq: understanding the properties of integers practice test, ratio & proportions practice test, dsq: calculating ratio and proportion practice test, real numbers practice test, dsq: understanding real numbers practice test, sets practice test, dsq: understanding arithmetic sets practice test, avoiding common data sufficiency traps practice test, geometry practice test, circles practice test, chords practice test, dsq: calculating the length of a chord practice test, diameter practice test, dsq: calculating the length of the diameter practice test, dsq: calculating the ratio of diameter and circumference practice test, radius practice test, dsq: calculating circumference practice test, dsq: calculating the area of a circle practice test, dsq: calculating the length of a radius practice test, sectors practice test, dsq: calculating the angle for a percentage of a circle practice test, dsq: calculating the angle of a sector practice test, dsq: calculating the area of a sector practice test, dsq: calculating the length of an arc practice test, dsq: calculating the percentage of a sector from an angle practice test, coordinate geometry practice test, dsq: calculating the equation of a circle practice test, graphing practice test, dsq: graphing a function practice test, dsq: graphing a line practice test, dsq: graphing a logarithm practice test, dsq: graphing a point practice test, dsq: graphing a quadratic function practice test, dsq: graphing an exponential function practice test, dsq: graphing an ordered pair practice test, dsq: graphing complex numbers practice test, lines practice test, distance formula practice test, dsq: calculating the length of a line with distance formula practice test, midpoint formula practice test, dsq: calculating the endpoints of a line segment practice test, dsq: calculating the midpoint of a line segment practice test, other lines practice test, dsq: calculating the equation of a line practice test, dsq: calculating the slope of a line practice test, dsq: calculating whether point is on a line with an equation practice test, parallel lines practice test, dsq: calculating the equation of a parallel line practice test, dsq: calculating the slope of parallel lines practice test, dsq: calculating whether lines are parallel practice test, perpendicular lines practice test, dsq: calculating the equation of a perpendicular line practice test, dsq: calculating the slope of a perpendicular line practice test, dsq: calculating whether lines are perpendicular practice test, tangent lines practice test, dsq: calculating the slope of a tangent line practice test, x and y intercept practice test, dsq: calculating the equation of a curve practice test, dsq: calculating x or y intercept practice test, intersecting angles and lines practice test, dsq: calculating the angle of an intersection practice test, dsq: calculating an angle of a line practice test, dsq: understanding intersecting lines practice test, dsq: understanding rays practice test, polygons practice test, dsq: calculating an angle in a polygon practice test, dsq: calculating the area of a polygon practice test, dsq: calculating the length of a diagonal of a polygon practice test, dsq: calculating the length of a side of a polygon practice test, dsq: calculating the perimeter of a polygon practice test, quadrilaterals practice test, other quadrilaterals practice test, dsq: calculating an angle in a quadrilateral practice test, dsq: calculating the length of the diagonal of a quadrilateral practice test, dsq: calculating the length of the side of a quadrilateral practice test, dsq: calculating the perimeter of a quadrilateral practice test, dsq: calculating whether quadrilaterals are similar practice test, rectangles practice test, dsq: calculating the area of a rectangle practice test, dsq: calculating the length of the diagonal of a rectangle practice test, dsq: calculating the length of the side of a rectangle practice test, dsq: calculating the perimeter of a rectangle practice test, dsq: calculating whether rectangles are similar practice test, squares practice test, dsq: calculating the area of a square practice test, dsq: calculating the length of the diagonal of a square practice test, dsq: calculating the length of the side of a square practice test, dsq: calculating the perimeter of a square practice test, rectangular solids & cylinders practice test, cubes practice test, dsq: calculating the diagonal of a cube practice test, dsq: calculating the length of an edge of a cube practice test, dsq: calculating the surface area of a cube practice test, dsq: calculating the volume of a cube practice test, cylinders practice test, dsq: calculating the surface area of a cylinder practice test, dsq: calculating the volume of a cylinder practice test, prisms practice test, dsq: calculating the diagonal of a prism practice test, dsq: calculating the length of an edge of a prism practice test, dsq: calculating the surface area of a prism practice test, dsq: calculating the volume of a prism practice test, tetrahedrons practice test, dsq: calculating the length of an edge of a tetrahedron practice test, dsq: calculating the surface area of a tetrahedron practice test, dsq: calculating the volume of a tetrahedron practice test, triangles practice test, acute / obtuse triangles practice test, dsq: calculating an angle in an acute / obtuse triangle practice test, dsq: calculating if two acute / obtuse triangles are similar practice test, dsq: calculating the area of an acute / obtuse triangle practice test, dsq: calculating the height of an acute / obtuse triangle practice test, dsq: calculating the length of the hypotenuse of an acute / obtuse triangle practice test, dsq: calculating the length of the side of an acute / obtuse triangle practice test, dsq: calculating the perimeter of an acute / obtuse triangle practice test, dsq: calculating whether acute / obtuse triangles are congruent practice test, equilateral triangles practice test, dsq: calculating the area of an equilateral triangle practice test, dsq: calculating the height of an equilateral triangle practice test, dsq: calculating the length of the side of an equilateral triangle practice test, dsq: calculating the perimeter of an equilateral triangle practice test, right triangles practice test, dsq: calculating an angle in a right triangle practice test, dsq: calculating the area of a right triangle practice test, dsq: calculating the height of a right triangle practice test, dsq: calculating the length of the hypotenuse of a right triangle : pythagorean theorem practice test, dsq: calculating the length of the side of a right triangle practice test, dsq: calculating the perimeter of a right triangle practice test, dsq: calculating whether right triangles are congruent practice test, dsq: calculating whether right triangles are similar practice test, specific value data sufficiency practice test, word problems practice test, data interpretation practice test, diagrams practice test, dsq: understanding diagrams practice test, probability practice test, dsq: calculating probability practice test, discount practice test, dsq: calculating discounts practice test, interest problems practice test, dsq: calculating compound interest practice test, dsq: calculating simple interest practice test, measurement problems practice test, dsq: understanding measurement practice test, mixture problems practice test, dsq: understanding mixture problems practice test, profit practice test, dsq: calculating profit practice test, rate problems practice test, dsq: calculating rate practice test, dsq: understanding sets practice test, work problems practice test, dsq: understanding work problems practice test, yes/no data sufficiency practice test, problem-solving questions practice test, understanding absolute value practice test, solving equations practice test, understanding exponents practice test, understanding functions practice test, solving inequalities practice test, solving linear equations with one unknown practice test, solving linear equations with two unknowns practice test, understanding factoring practice test, understanding counting methods practice test, understanding decimals practice test, calculating arithmetic mean practice test, calculating median practice test, calculating mode practice test, calculating range practice test, calculating discrete probability practice test, understanding fractions practice test, calculating percents practice test, understanding powers and roots practice test, understanding the properties of integers practice test, calculating ratio and proportion practice test, understanding real numbers practice test, understanding arithmetic sets practice test, calculating the length of a chord practice test, calculating the length of the diameter practice test, calculating the ratio of diameter and circumference practice test, calculating circumference practice test, calculating the area of a circle practice test, calculating the length of a radius practice test, calculating the angle for a percentage of a circle practice test, calculating the angle of a sector practice test, calculating the area of a sector practice test, calculating the length of an arc practice test, calculating the percentage of a sector from an angle practice test, calculating the equation of a circle practice test, graphing a function practice test, graphing a line practice test, graphing a logarithm practice test, graphing a point practice test, graphing a quadratic function practice test, graphing a two-step inequality practice test, graphing an exponential function practice test, graphing an ordered pair practice test, graphing complex numbers practice test, graphing inverse variation practice test, calculating the length of a line with distance formula practice test, calculating the endpoints of a line segment practice test, calculating the midpoint of a line segment practice test, calculating the equation of a line practice test, calculating the slope of a line practice test, calculating whether point is on a line with an equation practice test, calculating the equation of a parallel line practice test, calculating the slope of parallel lines practice test, calculating whether lines are parallel practice test, calculating the equation of a perpendicular line practice test, calculating the slope of a perpendicular line practice test, calculating whether lines are perpendicular practice test, calculating the equation of a tangent line practice test, calculating the slope of a tangent line practice test, calculating the equation of a curve practice test, calculating x or y intercept practice test, calculating an angle of a line practice test, understanding intersecting lines practice test, understanding rays practice test, calculating an angle in a polygon practice test, calculating the area of a polygon practice test, calculating the length of a diagonal of a polygon practice test, calculating the length of a side of a polygon practice test, calculating the perimeter of a polygon practice test, calculating an angle in a quadrilateral practice test, calculating the area of a quadrilateral practice test, calculating the length of the diagonal of a quadrilateral practice test, calculating the length of the side of a quadrilateral practice test, calculating the perimeter of a quadrilateral practice test, calculating whether quadrilaterals are similar practice test, calculating the area of a rectangle practice test, calculating the length of the diagonal of a rectangle practice test, calculating the length of the side of a rectangle practice test, calculating the perimeter of a rectangle practice test, calculating whether rectangles are similar practice test, calculating the area of a square practice test, calculating the length of the diagonal of a square practice test, calculating the length of the side of a square practice test, calculating the perimeter of a square practice test, calculating the diagonal of a cube practice test, calculating the length of an edge of a cube practice test, calculating the surface area of a cube practice test, calculating the volume of a cube practice test, calculating the surface area of a cylinder practice test, calculating the volume of a cylinder practice test, calculating the diagonal of a prism practice test, calculating the length of an edge of a prism practice test, calculating the surface area of a prism practice test, calculating the volume of a prism practice test, calculating the length of an edge of a tetrahedron practice test, calculating the surface area of a tetrahedron practice test, calculating the volume of a tetrahedron practice test, calculating an angle in an acute / obtuse triangle practice test, calculating if two acute / obtuse triangles are similar practice test, calculating the area of an acute / obtuse triangle practice test, calculating the height of an acute / obtuse triangle practice test, calculating the length of the hypotenuse of an acute / obtuse triangle practice test, calculating the length of the side of an acute / obtuse triangle practice test, calculating the perimeter of an acute / obtuse triangle practice test, calculating whether acute / obtuse triangles are congruent practice test, calculating the area of an equilateral triangle practice test, calculating the height of an equilateral triangle practice test, calculating the length of the side of an equilateral triangle practice test, calculating the perimeter of an equilateral triangle practice test, calculating an angle in a right triangle practice test, calculating the area of a right triangle practice test, calculating the height of a right triangle practice test, calculating the length of the hypotenuse of a right triangle : pythagorean theorem practice test, calculating the length of the side of a right triangle practice test, calculating the perimeter of a right triangle practice test, calculating whether right triangles are congruent practice test, calculating whether right triangles are similar practice test, understanding diagrams practice test, calculating probability practice test, calculating discounts practice test, calculating compound interest practice test, calculating simple interest practice test, understanding measurement practice test, understanding mixture problems practice test, calculating profit practice test, calculating rate practice test, understanding sets practice test, understanding work problems practice test.

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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

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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).

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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.

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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.

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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.

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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.

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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

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GMAT Problem Solving: Technical Mathematics

While there are several ways of solving mathematical problems in the quantitative reasoning section of the GMAT, a time comes when the only reasonable tactic is technical mathematics. If you see a clearly technical math problem where no information is obscured behind opaque words, then technical math may be your only option. However, it is only going to require arithmetic, algebraic and geometric skills. The level of math on this test does not go beyond basic algebra II, which is really low in quadratic. Unfortunately, the GMAT does not necessarily associate technical mathematics with high-difficulty problems. You are not necessarily rewarded for completing some of the arithmetic or geometric technical math that you may consider difficult to do, especially at the beginning of your preparation. 

What are the strategic Implications of technical math in the Exam?

Always try the technical approach first because if you can do it, it’s probably the fastest. However, you must have a tight leash on this approach because as soon as it ceases to be both apparent and simple, you must abandon it quickly to keep up your pace.

• Apparent- If it is apparent, it means you can set up the math. Arithmetic is usually there implicitly. You need to ask yourself, “Can I create the algebra?” Or,” Can I construct the geometry?” If your answer to these questions is “Yes.” Then it is apparent. 
• Simple- This means you can solve the math with ease. Sometimes you may be given a problem, and although it is apparent, it is simple for you.

Note the numbering format in your question and choices to inform efficient calculations. For instance, do your calculations in fractions if your answer choices are in fractions and in decimals if your answer choices are in decimals. Make sure that you are math ambidextrous so that you don’t force yourself into a situation where you have to use a single specific number format for non-integer valuation all the time.

Technical Mathematics Problem Solving Process

Word problem example.

If Abby travels 4miles in minutes , and Barry travels 2miles in b minutes, which of the following represents the number of minutes it would take Callum to travel 10 miles at the average of Abby’s and Barry’s rates in terms of a and b ?

• \(\frac{2a+b}{10ab}\)
• \(\frac{2b+a}{10ab}\)
• \(\frac{10ab}{2a+b}\)
• \(\frac{10ab}{2b+a}\)

Problem Solving process

• You will need to set up your scratch pad by listing the choices A through E. 
• Skip to the end of the problem and identify what is sought, then label your choices as such. # no. Of minutes for c to travel 10 miles=?
• Read from the beginning, taking notes and setting up equations as you go. From the answer choices, you can tell that your answer should be an algebraic expression.

We can start with the formula: \(\text{rate}=\frac{\text{distance}}{\text{Time}}/ \text{time}=\frac{\text{distance}}{\text{rate}}\)

• Average rate: =\(\frac{4/a+2/b}{2}\)
• Process fraction: =\(\frac{4a+2b}{2ab}\)
• Simplify fraction: =\(\frac{2a+b}{ab}\)
• Solve for times as t: = \(\frac{10}{\frac{2a+b}{ab}}\)
• Multiply by reciprocal, \(t=\frac{10ab}{2a+b}\)

This matches choice E.

Remember that this needs to be both apparent and simple to you at the moment. If ever you get stuck while working through a word problem,  there may be an alternative approach that you can explore, but as you can see, it’s probably the fastest if you follow this technical approach.

Arithmetic Example

Square root of \(((27)(10) – (9)(15))\)

• \(3\sqrt{5}\)
• \(10\sqrt{3}\)

You will need to set up your scratch pad by listing the choices A through E. Include simple numbers. 

Note the format of choices to facilitate efficient manipulation. You cannot do an approximation in this case, you have to solve technically until you get the final answer. From the choice, you can see that we can have the answer in square root form. This will inform our approach, we have to remove common factors to simplify these roots.  

• Ignoring the root sign \(27\times10-9\times5\)
• 9 is a common factor \(9(3\times10-1\times5)\)
• Process parentheses \(9(30-5)=9\times25\)
• Put the radical back \(\sqrt(9\times25)=3\times5=15\)
• Distribute radical \(3\times5=15\)

There is no alternative approach to solving this problem. You have to use technical math, if you can’t find a way forward in this kind of arithmetic problem,  your best alternative is to make a guess and move on quickly.

Geometric Example

If the diameter of the circle above is 10, what is the area of the rectangle inscribed in the circle?

You will need to set up your scratch pad by listing the choices A through E, including simple numbers. There is no need to draw the figure on your scratchpad .

Skip to the end of the problem and identify the value (s) sought.

Write down formulas and avoid drawing as much as possible

Area of rectangle = lw

 Diameter = diagonal = 10

By Pythagoras theorem, diagonal 2 = l 2 + w 2

                    Area of rectangle = lw

                     Diameter = diagonal = 10

                     By Pythagoras theorem, diagonal 2 = l 2 + w 2

                     Pythagorean integers = 6 : 8 : 10

                         l = 6, w = 8, d = 10

                       Area of rectangle = 6 × 8 = 48

Therefore, for technical mathematics,  our problem-solving process will be: 

Set up a scratch pad listing your choices vertically A through E

• Note specific algebraic expressions or numbers in the choices 
• Note format of choices to inform tactics and calculations 

Skip to the end of the problem and label choices as sought value(s)

• Note if you are seeking specific or non-specific value
• Don’t auto-solve for individual values if you are seeking combined values.

Read from the beginning, take notes, and do the necessary calculations to maximize your efficiency. 

• If you can, take the technical math approach to solve the problem. 
• Abandon it quickly if, at any moment, it ceases to be both apparent and simple.

Sample Problem Solving question

If xy ≠ 0 and 3x 2 are 60 percent of 20 percent of y 3 , the value of y 3 is how many times the value of x 2 ? 

Set up your scratch pad by listing the choices A through E. Skip to the end of the problem and identify what is sought, then label your choices as such( y 3 is how many times the value of x 2 )

If \(\text{xy}≠0\)

$$(3x^{2}=0.6\times0.2\times{y}^{3})100$$

$$300x^2=6\times2\times{y}^3$$

$$(300x^2=12y^3)/12$$

$$25x^2=y^3$$

The correct answer is 25, choice E.

In this problem, the technical approach is relatively direct and expedient. You could plug in or take other alternative approaches here. But if you follow common constructs of algebra and simplification, you can reach the answer under the two-minute average per question allocated for the quantitative section.

Many GMAT test takers may shy away from technical math, however, as demonstrated above, sometimes it is the most efficient way to solve mathematical problems on the GMAT. At times, it is the only way. During your preparation for the exam, do some practice on technical math. keep it simple, and it may just save you some crucial seconds during your exam.

Best of luck as you prepare and, eventually, as you take your GMAT exam. Remember to take advantage of the GMAT study resources available on our website to prepare adequately for your exams. Practice makes perfect.

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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, the types of questions in gmat quant, problem-solving example 1, problem-solving example 2, problem-solving example 3, problem-solving example 4, problem-solving example 5, problem-solving example 6, problem-solving example 7, problem-solving example 8, gmat data sufficiency questions, memorize the data sufficiency answer choices.

• Value DS Example 1
• Value DS Example 2
• Value DS Example 3
• Yes/No DS Example 1

Yes/No DS Example 2

Yes/no ds example 3, 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 begin to 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, especially the Data Sufficiency questions, 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 question types are not.

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
• Geometry Problems
• 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.

Now, let’s discuss the GMAT quant question types.

In the GMAT quant section, you will encounter two main types of GMAT quant questions: Problem Solving (PS) and Data Sufficiency (DS) problems. Of the 31 questions in the quant section of the GMAT, roughly 20 will be PS questions and 11 will be DS questions.

Of the 31 questions in GMAT quant, roughly 20 are Problem Solving questions and 11 are Data Sufficiency questions.

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

GMAT Problem-Solving Questions

GMAT Problem-Solving 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 Problem Solving 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 now 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 expressions 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. Next, 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: Geometry

Subtopic: Area of a Rectangle

The length of a particular rectangle is twice its width. If the area of the rectangle is 72, what is its length?

First, we can define our two variables:

We know that the length of the rectangle is twice the width. This can be expressed as:

Next, we are told that the area of the rectangle is 72. Recall that the area of any rectangle is the product of its length and its width:

Lastly, we can substitute 2W for L to solve for W:

72 = 2W ✕ W

Note that we chose only the positive square root of 36 because the width cannot be negative.

Since L = 2W, we see that L = 2 ✕ 6 = 12, and so the length of the rectangle is 12.

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

Data Sufficiency (DS) questions differ in style from problem-solving questions. While in a problem-solving question, you must come up with a precise number answer, in Data Sufficiency questions, you must decide whether you have enough information to come up with a definitive answer.

A DS question usually provides information in a problem stem, a question, and two statements. Your job is to see whether one statement, either statement, or both statements are sufficient to answer the given question. If this seems a bit confusing, don’t worry. With practice, you can learn the logic underlying DS questions, and soon you’ll be a pro!

When solving Data Sufficiency questions, you must decide whether you have enough information to determine an answer.

Next, we will review the answer choices you should memorize for DS questions.

One thing that makes Data Sufficiency questions easier for us is that, although they always have five answer choices, those choices are the same for every question! Thus, it will serve you well to memorize the DS answer choices. Doing so is as important as memorizing math formulas or math shortcuts.

Here are the DS answer choices:

Answer A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Answer B: Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Answer C: BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Answer D: EACH statement ALONE is sufficient to answer the question asked.

Answer E: Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Memorize the DS answer choices.

Next, let’s discuss the first type of DS question: the value question.

The Value Data Sufficiency Question

We already know that in Data Sufficiency questions, we need to determine whether we have enough information to answer a particular question. In a value question, we need to determine whether we have enough information to generate a single numerical answer.

Let’s look at a few example question prompts below:

— What is the value of n – m?

— What is the hundredths digit of x?

— How many people work for company Q?

— What is the average of x and y?

— How many dollars did Marcus pay for his phone call?

In value Data Sufficiency questions, our job is to see if we have enough information to determine a single numerical value for the question asked.

Let’s now practice with some examples in which we will also provide full math solutions.

Value DS Example 1:

Subtopic: Don’t Divide by a Variable Whose Value Could Be Zero

What is the value of n?

1) n 2 = 24n

2) n > 0

Statement (1) Alone:

It might be tempting to divide both sides of the given equation by n. But recall that we cannot divide both sides of an equation by a variable unless we are sure that the variable can’t be equal to 0. In statement (1), we are told nothing about whether n is equal to 0. So, we have to do some other algebra to solve for n:

n 2 – 24n = 0

n(n – 24) = 0

We see that there are two solutions to the equation: n = 0 or n = 24. Thus, we cannot determine a unique value of n. Therefore, statement (1) alone is not sufficient to answer the question, “What is the value of n?” So, we can eliminate answer choices A and D.

Statement (2) Alone:

Knowing only that n is greater than 0 is not sufficient to determine a single value for n. Under this constraint, n could be any positive number. Therefore, statement (2) alone is also not sufficient to answer the question, and we can eliminate answer choice B.

Both Statements Together:

If we look at our algebra above, we can see that statement (1) tells us that n = 0 or n = 24. Statement (2), meanwhile, tells us that n > 0. Therefore, n cannot equal 0, meaning n must equal 24. Both statements, used together, give us sufficient information to answer the question.

Value DS Example 2:

Major Topic: Absolute Values

Subtopic: Evaluating Absolute Value Equations

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

1) y is a positive number

2) y 2 < 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.

Statement (1) says that y is a positive number. Both possible values of y are positive, so statement (1) by itself is not sufficient to determine a unique value for y. We can eliminate answer choices A and D.

We know that 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.

To illustrate this point, consider some possible values for y, as follows:

• If y is a negative number, then y 2 will always be positive, and thus y 2 will always be greater than y. Thus, in order to satisfy the inequality y 2 < y, we see that y cannot be negative.
• If y is a positive number greater than 1, then y 2 will always be greater than y. Thus, in order to satisfy the inequality, y also cannot be a positive number greater than 1.
• If y is a positive proper fraction, when a positive proper fraction is squared, this squared value is less than the value of the original fraction. Thus, we see that y 2 < y is true only if y is a positive proper fraction.

From the question stem, we determined that the two possible values of y are y = 1 and y = 1/3. Statement (2) tells us that y must be a positive proper fraction, and only one possible value of y meets this criterion: y = 1/3. Therefore, tatement (2) by itself is sufficient to answer the question. We can eliminate answer choices C and E.

Value DS Example 3:

Major Topic: Statistics

Subtopic: Standard Deviation

What is the standard deviation of Set T?

1) The mean of Set T is 10.

2) The largest data point in Set T is equal to the mean.

Many DS questions can be solved using math tricks, and this is one such question! Let’s evaluate each statement.

The mean of Set T is 10.

Just knowing the mean of Set T does not provide enough information to determine the set’s standard deviation. We can eliminate answers A and D.

The largest data point in Set T is equal to the mean.

When the largest data point in a set is equal to the mean, all the numbers in the set must be the same.

When all numbers in a data set are the same, the standard deviation of the set is equal to 0. Thus, the standard deviation of Set T is zero, and statement (2) alone was sufficient to answer the question.

Next, let’s discuss yes/no Data Sufficiency questions.

The Yes/No Data Sufficiency Question

The yes/no DS question is quite similar to its “value” counterpart. However, instead of determining whether we can find a singular numerical value from the given statements, we must determine whether we can definitively answer yes or no to the question posed. If we come up with an answer of “sometimes yes and sometimes no,” then the statement is not sufficient.

To determine sufficiency in a yes/no DS question, we must get a definitive yes or no answer.

Here are a few examples of yes/no DS question prompts.

— Is a > b?

— Is the integer n a prime number?

— Is x between 5 and 10?

— Is the mean greater than the median?

Let’s practice answering some Yes/No Data Sufficiency questions.

Yes/No DS Example 1:

Major Topic: Inequalities

Subtopic: Adding Inequalities

Is n > 17 – m?

1) n < 9

2) m < 8

Question Stem Analysis:

First, let’s rewrite the inequality in the question stem by adding m to both of its sides in order to put the variables on the same side. Thus, the question becomes: Is n + m > 17?

We know only that n < 9. So, without any information about the value of m, statement (1) is insufficient. Eliminate A and D.

We know only that m < 8. So, without any information about the value of n, statement (2) is insufficient. Eliminate B.

If n is less than 9 and m is less than 8, then the sum of n and m must be less than the sum of 9 and 8, which is 17:

n + m < 17

Thus, we can definitely say that the answer to the question “Is n + m > 17?” is no. The sum of n and m must be less than 17, not greater than it. Therefore, statements (1) and (2) together are sufficient to answer the yes/no question.

Subtopic: Divisibility

A researcher has a certain number of volunteers for conducting an experiment about memory loss after age 60. Can he evenly divide the volunteers into 3 groups?

1) If the researcher reduced the number of volunteers by 16 percent, he could evenly divide the volunteers into groups of 9.

2) If the researcher reduced the number of volunteers by 6 percent, he could evenly divide the volunteers into groups of 3.

Let’s let T represent the total number of volunteers. If the volunteers can be evenly placed into 3 groups, then T must be divisible by 3.

If the researcher reduces the number of volunteers by 16 percent, then he still has 84% of T, or (84/100)T volunteers remaining. We are told that this number of volunteers is evenly divisible by 9, so we can say that the expression (84/100)T / 9 yields an integer. Let’s simplify this expression:

(21/25)T / 9

(21 x T) / (25 x 9)

7T / 25×3

Thus, the expression 7T / 25×3 must also equal an integer, but 7 is not divisible by either 25 or 3. Thus, T must be divisible by both 25 and 3. Divisibility by 3 indicates that the researcher can divide the T participants into 3 equal groups.

Statement (1) is sufficient. We can eliminate answer choices B, C, and E.

If the researcher reduces the number of volunteers by 6 percent, then he still has 94% of T, or (94/100)T volunteers remaining. We are told that this number of volunteers is evenly divisible by 3, so we can say that (94/100)T / 3 is an integer. We can simplify this expression as we did in the analysis of statement (1):

(47/50)T / 3

(47 x T) / (50 x 3)

Thus, this simplified form is also an integer, but 47 is not divisible by either 50 or 3. Thus, T must be divisible by both 50 and 3. Because T is divisible by 3, the researcher again can divide those volunteers into 3 equal groups.

Statement (2) is sufficient. We can eliminate answer choice A.

Therefore, the correct answer is D. Each statement by itself allows us to answer the question.

Major Topic: Coordinate Geometry

Subtopic: Lines in the Coordinate Plane

Is (2, 5) on line k?

1) The y-intercept of line k is -2.

2) The slope of line k is positive.

In order to answer the question, we need to know more about line k.

If the y-intercept of line k is -2, then we know it passes through the point (0, -2), but it may or may not pass through the point (2, 5), depending on the slope of line k. Statement (1) is not sufficient. We can eliminate answer choices A and C.

Just knowing only that the slope of line k is positive is not sufficient for answering the question. There are many, many lines with positive slopes. We can eliminate answer choice B.

Even knowing both that the y-intercept of line k is -2 and that its slope is positive will not tell us whether the line passes through (2, 5). For instance, the equation y = x – 2 represents a line with a y-intercept equal to -2 and a positive slope equal to 1 that does not pass through the point (2, 5). The equation y = 3.5x – 2, meanwhile, represents a line that has a y-intercept equal to -2 and a positive slope equal to 3.5, and it does pass through the point (2, 5). Therefore, both statements together are not sufficient to answer the question.

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

There are two types of quant questions: Problem Solving (PS) and Data Sufficiency (DS).

• Problem-Solving questions are traditional multiple-choice questions.
• Data Sufficiency questions are logic-based questions that require the student to analyze two statements to determine whether either or both are sufficient to answer a posed mathematical question.

The two keys to success on GMAT quant are knowledge of the 21 topics that are tested and familiarity with the question types. In this article, we have provided you with 14 example questions covering both Problem Solving and Data Sufficiency questions.

Because DS questions are unique to the GMAT, you might feel that you need more practice with them. If so, you can read our article focused on Data Sufficiency questions and how to answer them .

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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.

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