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GMAT Quant Questions: Problem Solving

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

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

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

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

1. Problems with Averages

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

2. Distance, Rate, Time

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

3. Permutations & Combinations

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

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

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

5. Advanced Geometric Solids

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

6. Estimation questions

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

7. Difficult Dice Questions

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

8. Difference of Two Squares

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

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

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

10. Remainders

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

11. Work & Work Rate

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

12. Circle & Line Diagrams

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

13. Polygons

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

14. Set Problems, with Double Matrix Method

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

15. Set Problems, with Venn Diagrams

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

16. Scale Factor & Percent Change

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

17. Standard Deviation

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

18. Radicals

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

19. Function Notation

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

20. Algebraic Factoring

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

21. Hard Factorial Problems

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

22. Backsolving from the answers

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

23. Distance in the x-y plane

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

24. Pythagoras !

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

25. Lines in the x-y plane

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

26. Tricks for Calculating Combinations

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

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

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

28. Probability: AND & OR Rules

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

29. Probability: “at least” statements

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

30. Probability: counting problems

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

31. Hard counting problems

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

32. Probability: geometric probability

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

Also check out these GMAT Probability questions .

Other GMAT Practice Questions

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

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

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

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

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

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One response to “GMAT Quant Questions: Problem Solving”

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

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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

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

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

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Quantitative reasoning - problem solving.

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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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GMAT Problem-Solving Questions: Tips To Improve Scores

GMAT problem-solving questions in the quantitative section of the GMAT exam can be very challenging. However, if you prepare adequately and ensure that you use your time efficiently and effectively, you will improve your chances of achieving your desired target score in the GMAT exam. This article uses a few examples to create a quick summary of how best to go about finding solutions to problems in this section of your exam.

Let’s take a look at what you need to equip yourself in the process of preparing for this section of your GMAT exam.

What to Expect in GMAT’s Problem-Solving Section

There are two types of questions you’ll come across in the Quantitative Reasoning section of the GMAT exam: Problem-solving questions and data-sufficiency questions. Problem-solving questions make up at least half of the total number of questions you’ll come across in this section. Usually, the quantitative reasoning section contains 31 questions, which means approximately 15 of them will be problem-solving questions.

You will always have five options and one correct selection. The answer choices can be presented as numeric values, variables, or even ranges, and this is going to inform your strategy for solving these problems.

Strategic Implications of the Presentation

Take note of the format of choices in order to select an approach that is efficient and enables savvy mental calculation. For instance, if your answer choices are in the form of fractions, do your mental calculations as fractions, and if you are looking for a range of values, then don’t take a lot of time solving for a specific value. Usually, you’ll have 62 minutes to answer all 31 quantitative questions, which gives an average of 2 minutes per question. However, you have a maximum of 3 minutes for any question because some questions will take you a bit less than two minutes.

Check your pacing after every 10 quantitative questions, as this will help you to avoid clock-watching for every question.  The initial questions matter more according to the scaling of the exam, and, therefore, try to avoid mistakes here and be more methodical. It’s essential to spend a bit of time in this section. For the first 10 questions, spend about 24 minutes total for a ~2:24 average. You can look up after the first 10 questions and see if you have more or less than 38 minutes left.

For the second 10 questions, spend the recommended 2-minute average. This means you have to increase your speed as you go. After these 10 questions, check again to see if you have more or less than 18 minutes left. For the final 11, we are looking at roughly ~1:40 average per question. While you need these questions to complete the section, they don’t have as much impact on your overall score as the previous ones.

A good rule of thumb is to try to guess earlier on questions that you are not sure how to proceed with within the final 11 rather than trying to shortcut everything.

Simple Quantitative Problem-Solving Process

An example of a problem-solving question.

For many years, a surfeit of bears terrorized Yamhill neighborhoods. Then, Bill moved in, and every week he was able to safely relocate the greater of either ⅓ of the bears or 30 bears until a sustainable population of fewer than 30 bears remained in the town. If Yamhill had 270 bears upon Bill’s arrival, what was the number of bears in the sustainable population at the end of Bill’s relocation efforts?

The Problem-Solving Process

1. Set up your scratchpad listing choices vertically from A to E, including simple numbers if provided.

2. Skip to the end of the problem to identify sought values and label your choices as such.

 # Number of Bears at the end of relocation effort =?

3. Read from the beginning taking notes and completing obviously necessary calculations as you go.

• 270 bears at the start
• Relocate Great of ⅓ or 30 bears weekly until < 30 remaining
• \(270-\frac{1}{3}(270)=180\)
• \(180-\frac{1}{3}(180)=120\)
• \(120-\frac{1}{3}(120)=80\)
• \(80-30=50\)
• \(50-30=20\)

So option D is the correct answer.

Complex Quantitative Problem-Solving Question

If x and y are integers, and \(3x+3x+2=10y\), which of the following must be true?

• uppercase roman numerals
• I and III only
• II and III only
• I, II, and III

The Problem Solving process

1. Set up your scratchpad listing choices vertically from A to E.

4. Stop to consider all Four possible problems solving tactics

• Technical Math- Attempt first but abandon quickly if it becomes either not apparent or simple to you. In this case, it is apparent because you have been given the algebraic expression, but if it is not simple to you, then quickly abandon this approach.
• Logical estimation- Attempt at each step of every problem. Constantly eliminate things as much as you can so that when you are in a position where you have to guess, it is from one of two or three rather than from one of five.
• Plugging in value (modeling)
• Plugging in the choices(backsolving)

We can basically use a hybrid of ii-iv in our attempt to solve this problem.

5. Work the problem using your chosen tactic until only one choice is left.

  Note : Don’t fully calculate if not needed. For example, if you know your answer is greater than 6 and is negative, and  -12 is the only option that satisfies those conditions, then just pick -12. 

Always look for opportunities to use logical estimation.

• Note the Roman numeral format
• Which of the following must be true?
• \(3x+3x+2=10y\) (we know that x and y are integers, so we won’t use any fractions here)
• Let us consider the best approach at the moment for us: (a) Use technical math, (b) Plugging in values and Estimation

       5a. \(3x + 3x+2 =10y\)

         \(3x(1 +32) = 10y\)

          \(3x(10) = 10y\)

 This means that: 3x must  = 1, and 10y must = 10.

 x must = 0 (anything to the power of zero = 1) and y must = 1

Option D is the correct answer.

         5b.  If we are not familiar with this math, then we can look at the choices A-E and notice that iii is the most commonly occurring numerical. Then we can plug in x = 0. So if we find out that x cannot = 0 then the answer is A, and we are done.

If we plug in x = 0 then, \(3x(1 +32) = 10y\)

Then 1 0 = 10y is true if \(y = 1\) ( Option D )

In this way, we are able to solve the problem using logical reasoning without needing to know the technical math.

Set up the scratchpad listing the choices vertically from A through E. 

• Include simple numbers with the choices if the numbers are provided
• Note the format of choices to inform tactics and calculation

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

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

Read the question from the beginning as you take notes and perform the required calculations 

• If you see a clear path to solving a problem, take it!
• Most “certain but time-consuming” approaches could take you less than three minutes if you start working immediately.

Consider all four possible tactics for the most effective and efficient path to solving a problem at the moment. 

• Technical Mathematics 
• Logical Estimation
• Plugging in values (Modelling)
• Plugging in Choices(Backsolving)

Work the problem using your chosen tactic until only one option remains 

• Always be asking, “I’m I pressing for a solution?” If the answer is “No”, Estimate, Eliminate, Guess, and move on in less than 20 seconds. 
• Allow a maximum of a single calm reread, recalculate, or tactical reset before you must estimate, eliminate or guess 

If a rectangular parking lot with width 4 feet shorter than its length was extended into a square parking lot and doubled its area in the process, what would have been the original length of the parking lot?

Steps 1& 2

We list our choices & skip to the end, and label choices according to what we seek.

Original length

      Length = \(w+4\)

      Original area = \(w(w+4)\) 

      New width = \(w+4\)

      New are = \((w+4)2\)

The area was doubled. Therefore \(w(w+4)=\frac{1}{2}(w+4)2\)

$$w2+4w=\frac{1}{2}(w2+8w+16)$$

$$2w2+8w=w2+8w+16$$

Let’s collect like terms:

$$w2-16=0$$

$$(w+4)(w+4)=0$$

$$w = 4\ \text{or}\ -4$$

 Length cannot be negative, so w = 4

Original length = w+4, = 4+4 = 8(choice C)

If we plug in 8, then

$$\small{\begin{array}{lllll}\text{Original length} & \text{Original width} & \text{Original area} & \text{New width} & \text{New Area} \\ 8 & 4 & 32& 8 & 64=2(32) \\ \end{array}}$$

So option C) is our correct answer through a backsolving approach that might be a lot more straightforward than technical math and saves us quite a bit of time.

Go ahead and do more practice with all the possible tactics, you will get better and find what works for you best.

How Can You Prepare for the GMAT Problem Solving Questions?

GMAT problem-solving questions don’t test advanced mathematical concepts as one might expect. If anything, for most of the questions, you’re required to apply your knowledge of high school math, though this time around, in a more complex and analytical way. That means a little thinking out of the box, and mathematical reasoning should help you solve the problems without much struggle.

That said, here are a few tips that could be of great help in tackling questions in the problem-solving section of your GMAT exams.

Practice doing calculations without a calculator

It’s high time you get used to using scratch paper for calculations and double-checking your work just to make sure there are no errors. You’re not going to use a calculator for GMAT exams. So get used to making basic calculations by hand.

Plugin numbers

It’s essential to plug in real numbers for the variables in the equations so that it’s easy for you to work on the questions without feeling that they’re complex. Along the way, you might find two or more answers that match the numbers you’ve chosen. In such a case, try plugging in new numbers or solving the problem in a different way until you get a correct answer.

Use answer choices to work backward

If you’ve got an idea of where to start, go ahead and plug in an answer to work backward. In that way, you’ll easily eliminate the choices until you arrive at the correct answer. You can start with the middle choice, last, or the first answer in your guesswork. Somehow, you should finally get the correct choice provided you know your way around.

Avoid estimations by all means

When it comes to geometry questions, don’t rely on your eyes in estimating areas, lengths, angle sizes, or any form of measurement. This kind of visual estimation will see you fail in most of the questions, and this will affect your overall score.

Start with what you know

Keep in mind that GMAT exams will only require you to use high school-level math to answer the questions. Therefore, it’s advisable to start small on the questions by using what you know and break the problem into small steps that you can achieve with the little knowledge you have. In that way, you’ll be able to work towards an answer. 

Use high-quality study materials

The best way to prepare for your GMAT exams is by using real problem-solving practice questions from past exams or questions that specifically follow the GMAT format. At AnalystPrep , we provide lots of study resources for all the sections of your GMAT exams. You can get a GMAT study package with thousands of real problem-solving practice questions to help you prepare for your exams adequately. It’s a one-time investment that will see you improve your GMAT scores and consequently hit your targets.

GMAT problem-solving questions aren’t as hard as you can imagine. All you need to do is to practice adequately for the exams and brace yourself for the exams.

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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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GMAT Question Types

Quantitative Section

The Quant section consists of 21 Problem Solving (PS) questions, which are traditional multiple-choice math questions. You have 45 minutes for the section, giving you an average of just over 2 minutes per question . PS questions rely on various arithmetic and algebra concepts, both in word-problem and non-word-problem formats. Concepts are interspersed throughout the section; they do not appear in discrete blocks. Several questions, particular difficult questions, make use of multiple concepts .

Verbal Section

The Verbal section consists of 23 Critical Reasoning (CR) and Reading Comprehension (RC) questions. You have 45 minutes, giving you an average of just under 2 minutes per question . Expect 9 to 13 CR questions and 10 to 14 RC questions across 3 or 4 passages. The CR and RC questions are intermingled, except that all RC questions related to a given passage appear consecutively. Process of elimination is important on verbal questions, since they ask you to pick the best answer . You will often find it easier to eliminate three answers, whereas deciding between the other two may be trickier. Review all five answers, unless low on time, even if you come across one that you like.

Data Insights

The Data Insights section consists of 20 Data Sufficiency (DS) and Integrated Reasoning (IR) questions. You have 45 minutes, giving you an average of 2 minutes 15 seconds per question . Expect 5 to 8 DS questions and 12 to 15 IR questions, intermingled throughout the section. IR questions include four distinct question types: graphics interpretation, multi-source reasoning, table analysis, and two-part analysis. Most IR questions are accompanied by two or three sub-questions to answer.

Experimental Questions

Each section contains a few experimental questions that do not count towards your score and do not impact test adaptiveness. The GMAC is testing the validity of these questions before incorporating them into future GMAT administrations. Experimental questions do not have an assigned difficulty level , so you may encounter a question with difficulty that seems too easy or too hard given your performance. If so, such a question may be experimental. That said, you cannot identify which questions are experimental, nor should you spend any time trying to do so. Answer every question to the best of your abilities within the time constraints.

GMAT Prep Online Guides and Tips

2000+ gmat sample questions: practice every question type.

Practice questions are an essential part of any GMAT prep. But how do you find the best GMAT sample questions?

In this article, I’ll address what to look for in GMAT practice questions, the pros and cons of both official and unofficial GMAT test questions, and tips on creating an effective GMAT study plan using these resources.

What to Look for in GMAT Sample Questions

There are a wide variety of GMAT sample questions out there. How do you know if you’re using quality practice ones? These are a few of the characteristics of good GMAT practice questions, whether they’re official or unofficial.

#1: Same Format and Question Types as the Real GMAT

Once you start taking GMAT practice tests, you’ll get a feel for how GMAT questions should look: how long they are, what they look like on the screen, the topics they tend to cover, and the style in which they’re written, for example. In every section, there will also be a mix of question types: the quant section always includes both data sufficiency and problem-solving questions, while the verbal section always includes a mix of sentence correction, reading comprehension, and critical reasoning questions.

The GMAT example questions you choose as you prepare for the test should be as similar as possible to real questions written by the Graduate Management Admissions Council (GMAC). The closer you can get to simulating real testing conditions, including everything from visuals to question content, the more comfortable you’ll feel on the day of the test. Also, answering GMAT practice questions that are similar to those you’ll encounter on exam day will help you gauge your progress and potential GMAT score range accurately.

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#2: Computerized (and Hopefully Adaptive)

The GMAT is a computerized adaptive test (CAT), which means it adapts to the test taker’s skill level in real time to determine both their score and the mix of questions they’re given. Ideally, GMAT sample questions should follow this format, so you can be best prepared for what you’ll see and experience on test day. Practice resources in CAT format will usually advertise that fact prominently. If they don’t, they’re likely not in the format of the official GMAT.

Obviously not every resource you use will be in CAT format—for example, if you’re using a book to do drills on specific question types. But a sizable portion of your prep should be done using practice questions in CAT format.

#3: Accurate Difficulty Levels

The GMAT always includes a mix of easy, medium and difficult questions. How many you receive of each will depend partly on the computerized adaptive test: You’ll start with ‘medium’ questions, and if you answer those correctly, you’ll be given more difficult questions on average; if you answer them incorrectly, you’ll get easier questions on average. However, every test taker will receive some questions at all three difficulty levels.

Your selection of practice GMAT questions should be at the same difficulty level as the real GMAT test questions. As you prepare, you’ll be able to tell if your sample GMAT questions seem too easy or too difficult on average. Practicing with either too-difficult or too-easy questions might give you an inaccurate picture of your probable ultimate GMAT score, and could also leave you underprepared for the real GMAT.

#4: Organized by Skill and/or Difficulty

You should target your weaknesses when completing GMAT practice questions. You may struggle more with data sufficiency questions than with problem-solving questions on the quant section, for example, or you may do well on most geometry questions but wrestle more with trigonometry and algebra. Alternatively, you may have mastered easy questions across the board and might need to focus on medium and/or difficult questions instead.

Resources that offer customizable sets (based on question type, skills tested, and difficulty level) of GMAT practice questions, or that separate the questions according to those categories, will help you study more effectively and in a more organized fashion than ones that aren’t labeled according to type or that are randomly compiled. The more specifically each question is categorized, the more effectively you will be able to form a study plan that hones in on your specific problem areas.

Official GMAT Practice Questions

The Graduate Management Admissions Council (GMAC) releases a variety of practice resources that use official GMAT sample questions, either written by the test makers themselves or adopted from retired exams. For each resource, I’ll go over what’s included, its strengths and weaknesses, and the best way to make use of it in your prep.

#1: GMATPrep Software

The official GMATPrep Software is the best resource for GMAT practice questions available. It contains two full-length simulated computerized adaptive tests . Everything is written by GMAC, so you know you’re getting the real thing. You can take the two practice tests as many times as you like, but you’ll likely repeat some of the same questions if you take each one more than once.

You can customize your sets of practice questions, choosing 1-15 questions of each type (critical reasoning, sentence correction, and reading comprehension, for verbal) and difficulty (easy, medium, or difficult). In addition to the questions on the two practice tests, there are 90 additional practice questions available on the software.

The software also includes a detailed breakdown of GMAT question types and strategies, as well as a review of skills you’ll need for the quant section.

• It’s free for registered users of mba.com. Just create an account.
• The practice questions are identical in length, format, style, content, and visuals to what you’ll see on the GMAT.
• Answer explanations are step-by-step and in-depth, and you can go back and review or drill questions you previously got wrong as many times as you like.
• Detailed performance reviews break down what you’re getting wrong so you can hone in on your weak spots, including specific question types and skill sets
• Not much! The GMATPrep exams are great GMAT example tests. There aren’t many resources that can beat official questions under simulated testing conditions, and it’s free.
• However, there are only two full-length practice tests, so you’ll likely need to supplement these practice questions with other resources.
• Also, while the quant review is great, there isn’t a similar resource available on the software for the verbal section.

How to Use It:

• It’s best to start off your GMAT prep by taking one of the two full-length simulated tests on the GMATPrep software. Since the practice questions and score report are so realistic, the results will serve as a good barometer of your starting point.
• After you complete the rest of your prep with other practice questions, you should take the second GMATPrep practice test a few weeks before you take the GMAT. This will give you a good idea of where you stand before exam day.

#2: GMATPrep Question Pack 1

An official addition to the GMATPrep Software, the GMATPrep Question Pack contains 404 additional official questions.

You can create custom sets of practice questions of any length based on your needs. Each set of questions can be completed in either ‘exam mode’ (timed, under simulated test conditions) or ‘study mode’ (untimed). The Question Pack will cost you $29.99 to download.

• This resource contains practice questions that aren’t available in any other official prep materials.
• Your performance reviews for these practice questions will be integrated into your overall progress reports in the GMATPrep Software , allowing you to get an even more accurate picture of what your needs are in terms of prep.
• There isn’t much of a downside to official questions as a supplement to your overall prep.
• Once you’ve taken a few practice tests and figured out your weaknesses, create custom practice question sets that target your difficult spots (particular sections, question types, or question difficulty levels). These will serve as drills to beef up your skills in those areas.

#3: The GMATPrep Exam Collection

These are official additions to the GMATPrep Software. You can only get them once you’ve downloaded the original free software.

Each Exam Pack contains 90 additional practice questions (30 quantitative, 45 verbal, and 15 integrated reasoning), as well as two full-length computerized adaptive GMATs. Each Exam Pack costs $49.99.

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• In-depth diagnostics will let you know how you’re doing in comparison to your peers on every subsection of the test , as well as how your pacing could improve on each question type.
• Answer explanations offer step-by-step, detailed analyses of all practice questions.
• Not much (official GMAC questions are always helpful), except that they’re a bit pricey.
• These practice questions are a great first step after you take an initial diagnostic practice test, particularly if you’re still unsure of what exactly your weak spots are.
• You can use the two full-length CAT GMATs to gauge your progress throughout your prep. Alongside the official GMATPrep Software, you’ll have four full-length tests, so you can space them out to regularly check up on how your score is improving.

#4: GMAT Write

GMAT Write is a fairly new tool released by the makers of the GMAT, meant to help you with the analytical writing assessment. It includes two unique sample prompts for the analytical writing assessment section.

GMAT Write will time your essays (30 minutes each, just like on the real exam) and score them in real time according to the GMAC rubric. It costs $29.99 to download.

• The visuals and experience of writing the essay are highly realistic.
• The sample questions are written by GMAC, so you know they’re reliable.
• GMAT Write scores your essays according to the same criteria used on the real GMAT— ‘analyzes the issue,’ ‘supports ideas,’ ‘organizes a coherent idea,’ and ‘language control’ — in real time. It’s the only official GMAC tool that will score your sample essays.
• There are only two unique exam prompts included, which isn’t necessarily a lot of practice for $29.99.
• You won’t get any detailed feedback , just scores in each of the four categories used to assess GMAT essays.
• Use it alongside other practice tests. Many other resources only have integrated reasoning, verbal and quantitative practice questions, so adding a prompt from GMAT Write to your practice test will help you more closely simulated the experience of the actual GMAT.

#5: The  GMAT Official Guide 2018

The GMAT Official Guide 2018  is a comprehensive resource for GMAT prep. Included in your purchase ($19.95) is access (both online and in print) to over 900 official practice questions, access to an accompanying site where you can customize sets of practice questions, and online videos with plenty of GMAT tips and strategies.

• The questions are written by GMAC, so they’re high quality.  The online practice questions mimic the visuals of the real GMAT.
• The practice questions are organized in order of difficulty.
• The answer explanations and introduction sections (where key GMAT concepts get broken down) are too complex for non-advanced students. This is especially true for the quant and sentence correction questions.
• The online question bank only allows you to save ten practice sessions at a time, so if you plan on doing more, you’ll need to delete them before starting a new session.
• The online question bank is great for regular practice sessions. The question sets are customizable, and you can review them at any time.
• The book itself is a good resource to start your practice with after using the GMATPrep software as an initial diagnostic tool.

#6: IR Prep Tool

The Integrated Reasoning (IR) Prep Tool was introduced in 2014 to aid students specifically in the integrated reasoning section.

The tool includes 48 integrated reasoning questions total: 10 graphics interpretation questions, 15 multi-source reasoning questions, 15 two-part analysis questions, and eight table analysis questions.

You can create customized practice question sets, focusing on all question types or just one. You can also set the difficulty level for each practice question set. Once downloaded, you have unlimited use of the prep tool for six months. The IR Prep Tool can be downloaded for $19.99.

• A detailed ‘help’ section breaks down each integrated reasoning question type for you and gives tips on how to approach it.
• A time management tool tracks your average time on each question type and difficulty level, allowing you to work specifically on your pacing.
• The IR Prep Tool doesn’t give you a specific score estimation. Your official IR score will be between 1 and 8, but the IR Prep Tool gives you a score between 0 and 100 based on your performance and time management.
• There aren’t many resources out there specifically aimed at the integrated reasoning section, a frequent problem area for students, so this is a goldmine for students who have trouble with it.
• Use it to target and break down the integrated reasoning section into manageable chunks, particularly if you get overwhelmed by the fact that each question has multiple components.

#7: GMAT Focus Quantitative Diagnostic Tool

The GMAT Focus Quantitative Diagnostic Tool consists of a 24-question quantitative test (12 data sufficiency questions and 12 problem-solving questions ) that uses real questions from retired exams. It’s computer adaptive and follows the style and format of the actual GMAT quant section.

You can start and stop the test manually, but you have 45 minutes total to complete the practice questions.

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When you complete the test, the Focus Tool provides detailed answer explanations and an assessment of your strengths and weaknesses in terms of quant concepts.

Four unique tests are available. One test costs $29.99, and a three-test package costs $79.99.

• The GMAT Paper Tests are the only other GMAT practice resources that use real retired GMAT questions, making the Focus Tool the only computerized adaptive resource to do so. So you get the best of both worlds with this one: real practice questions from previous GMATs and simulated testing conditions.
• The detailed assessment of your performance, including a possible score range (more accurate than an exact score, since no one practice test will give you a perfect prediction of your ultimate GMAT score) and a breakdown of your performance by question difficulty, will tell you exactly which quant skills you need to work on before the GMAT.
• It’s a bit pricey for just 24 questions each.
• It’s not tied into the other GMAT prep resources, so your results won’t be integrated into your GMATPrep performance reports.
• After you complete one of the GMATPrep exams, this tool will help you hone in on the quant section . You’ll get an overall idea of your strengths and weaknesses in quant from the GMATPrep Software, but this tool will help you get much more specific about which skills to target in your quant prep.

#8: GMAT Paper Tests

The GMAT Paper Tests are real retired GMAT tests , written by GMAC. Each set (I, II, and III) contains three official GMAT tests, answer sheets, and a guide for converting your raw score into a scaled score. They’re available in downloadable PDF form. Each set costs $29.99.

• Most of the questions in these tests aren’t available in any of the other official GMAT practice tests or resources, so they’re especially good if you want some extra practice. This is a big plus: It’s somewhat difficult to find GMAC-authored questions that don’t overlap with other resources.
• Official questions are always a big positive in terms of GMAT prep!
• They’re on paper! You’ll have to score them yourself using the answer sheet, and it’s not computerized (obviously) or adaptive, so it doesn’t simulate any of the testing conditions.
• No answer explanations are included, just the answers themselves.
• You may want to order these if you’re a test-taker with a disability that may require an accommodation and using paper tests at home is easier for you during prep time.
• The GMAT Paper Tests might also serve you well if you’ve used all the other official sample GMAT questions and you want some additional prep. However, don’t rely on them to give you much info on your likely final GMAT score, since they aren’t in the official GMAT format. Use them to work through practice questions in your prep sessions instead.

Best Unofficial GMAT Practice Questions

Official GMAT questions are great, but they aren’t the only GMAT prep materials out there. There are also a variety of free and paid resources that offer quality GMAT practice questions. Here, I’ve included practice tests, books, and online question banks. For each unofficial resource, I’ll address how you can access it, its pros and cons, and the best way to incorporate it into your GMAT prep.

#1: Veritas Prep

You’ll need to create an account to access Veritas Prep’s GMAT Question Bank, but once you do, it’s completely free.

The Question Bank offers hundreds of realistic sample GMAT questions: quant, verbal, and integrated reasoning. It includes example questions of every type within those categories. Before you start your practice session, you can choose which kinds of questions you want to see. With one account, you’ll only see each practice question once.

Veritas Prep doesn’t give you an official estimated score, but it does give you an overall percentile , which measures how you did on a particular question set compared to other students who answered the same practice questions.

The Veritas Prep Question Bank is ideal for regular practice throughout your prep, particularly if you have varying amounts of time (you can do a short or lengthy session) and want to drill certain skill sets or question types . The questions from the bank aren’t in CAT format, but you can access one free computerized adaptive test through Veritas and six paid ones. Veritas Prep questions are some of the closest you’ll find to official GMAC-authored GMAT example questions.

Kaplan has a wide variety of GMAT resources, including in-person and online prep courses, but its GMAT Premier 2018  is its flagship GMAT prep tool. Your purchase includes access to over 1,000 GMAT practice questions, six full-length practice tests (one is in the book, and five are computerized adaptive tests available online), video tutorials, an online question bank with 200 GMAT sample questions and customizable quizzes, and a mobile app that allows you to study on the go.

GMAT Premier also includes a special section of forty advanced quant practice questions and in-depth answer explanations, which can help if you’re looking for a challenge in the quant department. The Kaplan practice questions are a bit harder than the ones in Princeton Review, but the verbal questions in particular still leave something to be desired in terms of difficulty level. The sentence correction questions in particular are easier than real GMAT questions. The Kaplan quant questions fare a bit better in terms of GMAT comparability.

Like Princeton Review, Kaplan is a good resource if you’re looking for a fairly solid overview and breakdown of the exam to start your prep (after you take your first diagnostic GMATPrep test). It’s not going to be as helpful if you’re looking for a comprehensive guide to the GMAT or a massive boost in your score.

#3: Manhattan Prep

With an account, you can take one full-length computerized adaptive Manhattan Prep test for free. Six additional ones are available for $49.99, which gives you one year of unlimited access.

You can take the Manhattan Prep practice GMATs timed or untimed, and you can take complete or partial practice exams depending on your time limit during prep. After you take all six, you can reset the questions to take more. Each test includes an in-depth assessment of your performance that analyzes your strengths, weaknesses, timing, and the difficulty levels you’ve mastered.

Manhattan Prep questions are mostly quite realistic in content and difficulty level. Though the visuals aren’t perfect, they are not too far from what you’ll see on the real exam.

I’d also like to point out one of Manhattan Prep’s best resources for students looking to challenge themselves in the quant section: Their GMAT Advanced Quant book includes strategies for tackling the trickiest quant questions and over 150 realistic practice questions. This is a great resource if you’re already doing well in the quant section and looking to bump yourself up to the next level.

#4: PowerScore

PowerScore’s main claim to fame is its trilogy of GMAT Verbal Bibles: Critical Reasoning, Sentence Correction, and Reading Comprehension, along with the PowerScore Verbal Bible , which covers the entire section. The books are available for $24.99 each or $69.99 as a trilogy.

PowerScore does an excellent job of breaking down each question type within the verbal section (a great resource for non-native English speakers and anyone who struggles with verbal questions), and the sample GMAT questions included in each book are consistent with the length, difficulty, and content of those on the GMAT. Though of course the practice questions here aren’t computerized or adaptive, each book does include access to a companion website that includes extra drills and practice questions.

The main downside to PowerScore is that, while the books offer great strategies and explanations of various question types, there aren’t a substantial number of actual practice questions . The Verbal Bible , for example, contains 31 critical reasoning questions, 77 sentence correction questions, and only eight reading comprehension questions. So while these resources are great reads for test-takers who are looking for in-depth answer explanations, they’re not fantastic for substantial extra practice or regular prep sessions.

#5: 800 Score Test

Providing a username and password will get you one full-length test on 800 Score Test for free. You can download five more for $39.95, which includes a comprehensive quant and verbal review, ten sample essay questions, access to online help, and in-depth video explanations of practice questions.

The visuals at 800 Score Test aren’t much like what you’ll see on the GMAT, but the practice questions themselves are high quality, particularly in the quant section. The verbal practice questions veer a little ‘off’ and aren’t as close to the real GMAT verbal section as the quant questions are, so if you’re especially looking to focus on verbal practice questions, this might not be your best bet.

The 800 Score tests are in CAT format, though, so even though the visuals are a bit lacking, they’re not the worst resource if you only want practice questions that simulate real testing conditions. Their Test Pacer tool lets you know what question you should be on to finish in time, which is very helpful for students who have trouble with consistent pacing.

#6: Princeton Review

Princeton Review’s Cracking the GMAT, available for $21.99 on Kindle, offers a breakdown of all GMAT sections (including integrated reasoning and the analytical writing assessment), along with six full-length computerized adaptive practice exams, over 180 practice questions organized by difficulty level, and drills for each test section. Cracking the GMAT Premier is $7 more and comes with more online resources, like extra practice tests, study strategies, and video tutorials.

Princeton Review offers a decent overview of each of the GMAT sections, though it only offers the grammar and math fundamentals, not anything in the way of more advanced concepts. Indeed, where it misses the mark is mainly in the difficulty of the practice questions: Nearly none of them are as difficult as actual GMAT questions. This is especially true in the critical reasoning and reading comprehension sections. So while Cracking the GMAT may help beginners who aren’t familiar with GMAT basics (especially to start off, since it’s not an intimidating text), it’s not enough for test-takers looking to break 700 or even 650.

#7: GMAT Club

Beyond its helpful GMAT forums, GMAT Club offers a variety of useful GMAT practice materials, including practice tests and question banks.

A few practice tests and question banks are free (no account required), but access to all of their customizable quizzes, bonus questions (over 1,572) and full-length tests will run you at least $79.99 for three months of use.

GMAT Club tests aren’t exactly in CAT format, as they don’t adapt to your performance as you go along, but they do follow CAT ‘logic’ and include a mixture of difficulty levels and question types that is consistent with what you’ll usually encounter in a computerized adaptive test. The quality of the visuals and practice question content is high, with practice questions closely resembling GMAC ones.

Difficult quant questions are one of GMAT Club’s specialties, which is important as many of the other top practice resources (Princeton Review and Kaplan, for example) trend a little easier: They claim that hundreds of their quant questions are at the 700+ scoring level. So if you’re looking to wow your prospective schools with your quant score, this might be a great resource.

#8: Manhattan Review

You have several options for free practice questions and other GMAT prep materials with Manhattan Review. With an account, you can access a fairly high-quality quantitative question bank in PDF ebook form, along with a vocabulary list (good for non-native English speakers) and another free ebook, GMAT in a Nutshell , that serves as an overall guide to the test and top strategies.

The Sentence Correction Guide, downloadable for free, boasts a solid grammar review of the concepts that are more often tested in sentence correction questions, but the sentence correction practice questions themselves aren’t all quite as difficult or complex as the real ones on the GMAT.

Manhattan Review also offers a full-length free practice test, which you can access with an account. It’s a computerized adaptive test. The questions here are good for extra practice, but the difficulty levels and visuals aren’t always consistent with the actual GMAT.

3 Top Tips for Creating a GMAT Study Plan

Once you’ve selected some practice GMAT questions, it’s time to set up a study plan. It’s important not just to find the best prep materials for you, but to use them to your advantage. Here are a few tips for using your prep materials as effectively as possible:

#1: Use the Two Official GMAC Tests on the GMATPrep Software First and Last

You should start your prep with one of the two full-length GMATPrep Software tests. Since they’re computerized adaptive tests with accurate visuals and questions written by GMAC, they’re the best possible indicator of your ultimate GMAT score. The first practice test will give you a good idea of where you stand and how to begin your prep. Unless you purchase more official GMAC practice tests, take the second free test from the software a few weeks before your exam date. This will give you a good idea of your score at the end of it all, and will let you know what to brush up on last-minute before the big day.

#2: Use Different Materials to Build Different Skills

Tailor the practice GMAT materials you select to your particular needs. For example, if you’re strong in quant but weaker in verbal (or a non-native English speaker), you might use Manhattan Prep, the GMAT Focus Quantitative Diagnostic Tool, or GMAT Club practice questions for your quant prep, since they all feature more advanced quant questions. You might start out more slowly in verbal, completing grammar reviews and drills from one of the PowerScore Bibles before delving more into practice questions. Mix and match resources according to your personal GMAT goals.

#3: Note Differences Between the Conditions of Your Practice and the Conditions of the Real GMAT

Not all of your GMAT practice questions need to be (or should be) in computerized adaptive form. Sometimes you’ll need to take your time to work through a particular question, complete a drill, or review concepts. But when you do take a full-length GMAT practice test, stick to the real testing conditions as much as you can: Use double-sided scratch paper, don’t use a calculator on the quant section, take the right amount of time for each section, and take eight-minute breaks between the integrated reasoning and quant sections and before the verbal section.

Some GMAT practice materials allow you to manually time yourself, take longer or unlimited breaks, or stop and start the test. Be mindful of these differences so you don’t learn to rely on conditions (such as a longer break) that won’t exist on the day of your exam.

What’s Next?

Looking for free full-length practice tests in addition to the best practice questions? You can find a list in our guide to the best free GMAT practice tests .

Our complete collection of GMAT practice tests provides a more comprehensive overview, in addition to reviews, of all available GMAT practice tests.

Finally our guide to how long to study for the GMAT will help you set up a time-effective study plan.

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Author: Laura Dorwart

Laura Dorwart is a Ph.D. student at UC San Diego. She has taught and tutored hundreds of students in standardized testing, literature, and writing. View all posts by Laura Dorwart

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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‘I Love The GMAT’: This GMAT Doctor Has Diagnosed More Than 4,000 Test Takers

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Chris Kane, head of test prep and a vice president of Menlo Coaching

In his 20 years of coaching people on the GMAT, Chris Kane has more than met Malcolm Gladwell’s popular dictum that it takes 10,000 hours to become an expert at something. Having guided and coached nearly 5,000 GMAT test takers, he boasts the accumulated knowledge and experience of a seasoned doctor treating health problems.

“Think of me as the GMAT Doctor who can figure out what a person is doing wrong on this test,” says Kane, the 53-year-old head of test prep and a vice president at Menlo Coaching . “When I get my knee replaced in five years, I am going to the person who has done the most knee replacements. It is the doctor who is in that sweet spot of having a lot of experience but is not set in his ways. He is not too old, and he is not too young.”

That would be Kane, who first entered the business of test prep in 2004 with Veritas Prep in New York City. “I have tutored brilliant people from all over the world, and I have seen every way you can think about these test problems,” he says. “People don’t get to learn from their students the way I have. The volume of tutoring is where I became an expert. That is the 10,000-hour business.”

‘I AM THE SUM TOTAL OF THE THOUSANDS OF PEOPLE I TUTORED’

Kane is that rare person whose eyes light up when talking about standardized tests, even more so when it’s the GMAT which he considers one of the best-designed standardized tests that anyone can take. “It is my job to diagnose what you need, prescribe the right drugs for improvement, and choose the problems that are going to help you the most,” he says, as if he were a practicing MD. “I am the sum total of the thousands of people I tutored.”

From an idyllic perch in Bar Harbor, Maine, a place known for its natural beauty in Acadia National Park, he tutors his students via Zoom. Though he spent nearly a decade tutoring students in their apartments and in New York’s investment banks, Kane is most at home in Maine where he has spent the last seven years in a house he built with his own hands.

When it comes to the debate between the GMAT and the GRE, Kane has a clear preference. He has a deep belief that the GMAT is an exquisite test. “I love the GMAT,” he says emphatically. “I love what it assesses. I know there are problems with standardized tests, but it is less true of the GMAT. When I think about the best standardized tests, it comes down to the GMAT and the LSAT. I have done this for 20 years because I believe what the GMAT is testing is very valuable. I see many false positives in standardized tests: people who did well and got lucky. But with the GMAT, I can think of literally a few cases.”

IF YOU GREW UP IN A LOWER SOCIOECONOMIC NEIGHBORHOOD, YOU ARE AT A DISADVANTAGE WITH THE GMAT

Chris Kane of Menlo Coaching

Of course, he has heard all the complaints about whether standardized tests in general are biased against women, minorities and international students who read and speak English as a second language. Kane agrees that there are unfair biases in the tests. “There are people who don’t do well but should be admitted to the top programs,” he believes.  

“Let’s imagine you are a brilliant kid growing up in a difficult school system in a lower socioeconomic neighborhood and you get a really bad education. You are at an immediate disadvantage with the quality of your underlying education.   To some degree, a standardized test is an assessment of your education broadly. It is pretty hard to re-learn a lot of the underlying math for a test like this, even if you are an incredibly brilliant person. It can be a little unfair in that regard.”

Regardless, he strongly believes that the GMAT, including the most recent shorter version of the test, is a superior exam to the GRE. “I have always said that a lot of the complaints with standardized tests are valid because they are poorly made,” believes Kane. “There is nothing worse than a poorly made standardized test, like state assessment exams. Teachers are frustrated because they have to teach to a test that is poorly made. When you have a well-made standardized test like the GMAT, that makes you think the right way, it’s great.”

WHY HE THINKS THE GMAT IS SUPERIOR TO THE GRE

Kane turns thumbs down on the GRE which has gained significant market share over the GMAT for business school admissions. “The GRE is too general a test in my opinion,” he says flatly. “It’s a test for people going to get MFAs in poetry and this huge range of graduate education so it’s a weird test that way. You are competing against people who are going on to do very different things. The quant section is less difficult to be sure and it feels a little bit more like a math test. There is less reasoning. When people struggle with the GMAT quant they can often do better on the quant GRE. The verbal is different. However, I am not sure how important that is for predicting a person’s success in business school. At its core. Some of the GRE content like geometry is so far removed from anything you do in business. So it is a weird choice for solving business problems.”

“The GMAT,” he continues, “predicts who is going to perform well in business school and who you want to sit next to in the top MBA programs. What they are assessing is the way you think. Are you hyper-vigilant and good at being critical? Can you deal with problem-solving? And at the same time, it is a test to make sure you have the requisite skills to get through a rigorous MBA program. “

There’s only one thing about the updated GMAT that he finds perplexing. The change in scoring has made it much more difficult to score above 750. A 750 on the old GMAT, which put a test taker in the 98th percentile, will convert to just a 695 on the new GMAT Focus Edition. Instead of a top score of 800, the new GMAT now has a top score of 805.

WHAT THIS GMAT TUTOR DOESN’T UNDERSTAND ABOUT THE GMAT FOCUS EDITION

“It’s the one part of this shift to the GMAT Focus edition that I have a hard time understanding.,” he says. “To get to that elite 49, you have to get an 84 on the new scale system and there are still six points above that to differentiate. You can take a little bit less time to prep and focus more on problem-solving skills. Data insights are still evolving. I am getting reports from students who say that the questions differed greatly from the practice tests. So that is still changing and they made some big changes in their question distribution. More data sufficiency now than before. It won’t settle into what it is going to be until the end of this year.”

One thing is certain: A mistake on the new test is more costly than ever before. “They are definitely using a new scoring algorithm with the new test that allows them to score you with fewer items,” says Kane. “You can’t make mistakes on this new test. You’ve got 21 questions on the quant side and if you miss easy or moderate questions it is really punishing because there are fewer items to assess. In chess, when you lose to a bad player, it really hurts you. When you lose to an easy-to-moderate question, it hurts you on a computer adaptive test. Your floor is much more important than your ceiling.”  

Another big difference in his view? “Before yo had to nail two sections, quant and verbal. The writing didn’t matter that much. Now you need to nail it on three different sections and if you have a bad day on one section your score is going to be negatively impacted. I am seeing more variability in scoring than before.”

Kane, who does one-on-one tutoring at $450 an hour as well as GMAT prep classes with Menlo’s Director of Tutoring Hailey Cusimano, says it doesn’t take all that much work to help a client achieve his or her goals. “I can usually provide what I need in no more than 14 hours of tutoring,” he says. “This is with a lot of self-study provided. As soon as a session is done, clients get their recording and I assign them a to-do list until the next session. Tutoring should have a super high-value takeaway. A great challenge is always trying to figure out how can I get the score up for this one person. I am going to work very hard to get you where you need to go. I am very confident in my approach.”

HOW TO TAKE A GMAT PREP COURSE OR GET KANE AS A TUTOR

DON’T MISS: ADVANCED GMAT PREPARATION FOR TOP PERCENTILE SCORES

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