problem solving gmat

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10 top tips for gmat problem solving questions.

For many test takers, the quantitative section of the GMAT is particularly daunting. The challenging section includes two types of questions: data sufficiency and problem solving. While data sufficiency questions are undoubtedly the more notorious question type, GMAT problem solving questions can also be quite tricky.

In this guide, I’ll give you an in-depth look at GMAT problem solving questions. First, I’ll cover what they are and what types of math they cover. Then, I’ll give you the top 10 tips for acing GMAT problem solving questions. Finally, I’ll walk you through solving five sample problem solving questions spanning a variety of topics.

What Are GMAT Problem Solving Questions?

Problem solving GMAT questions assess how well you can solve numerical problems, interpret graphs and tables, and evaluate information. In plainer language, problem solving GMAT questions are the “traditional” math question type that you’ll see on the GMAT quant section.

While there isn’t a set number of problem solving questions that you’ll see on the GMAT, you can bet that the quant section will be divided just about 50/50 between problem solving and data sufficiency questions. There are 31 total questions on the GMAT quant section, so you there will be either 15 or 16 problem solving questions on the GMAT quant section.

Problem solving questions look a lot like the math questions you’ve seen on other tests. GMAT problem solving questions are all multiple choice questions, with five different answers. Depending on the content tested, problem solving questions may be presented as an equation, a word problem, a diagram, a table, or a graph.

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Contrary to popular belief, the GMAT quant section doesn’t test on advanced math concepts. The quant section tests your content and analytical knowledge of basic math concepts, such as arithmetic, algebra, and geometry. The same holds true for GMAT problem solving questions – you’ll be asked to apply your knowledge of high school math concepts to questions that are presented in a more challenging and analytical way. For more information about the concepts covered on the GMAT quant section, check out our guide to GMAT quant .

10 Tips for Mastering GMAT Problem Solving Questions

Here are the top tips that you can use to master GMAT problem solving questions.

#1: Master the Fundamentals

GMAT problem solving questions only test high school math concepts. In many ways, this is good news. You’ll have likely encountered every type of math you’ll see on the GMAT before you start studying. Just because the math on the GMAT is relatively basic, however, doesn’t mean that it’s not tricky.

The GMAT tests basic math concepts in complicated ways. Problem solving GMAT questions often ask you to use more than one skill at one time, so you need to have strong mastery of many different concepts.

The key to GMAT problem solving mastery, then, lies in mastering the fundamentals.  Memorize the exponent rules. Memorize common roots and higher powers. Memorize the formulas for finding area of different shapes. Know how to find mean, median, mode, and standard deviation without blinking an eye. Thoroughly understanding the material covered on the GMAT will save you time and boost your score on test day.

#2: Practice Doing Calculations Without a Calculator

As I mentioned, you won’t be able to use a calculator on the GMAT. As such, y ou should prepare for problem solving GMAT questions without using a calculator to ensure that you’re used to making basic calculations by hand.

Get used to using scratch paper for calculations and double-checking your work to make sure there are no errors. In particular, make sure that you spend time practicing multiplying and dividing fractions and decimals without a calculator, as you’ll have to do both on the GMAT. The more non-calculator practice you get in before test day, the better prepared and more comfortable you’ll be.

#3: Use High-Quality Practice Materials

The best way to prepare for the GMAT is by using real GMAT problem solving questions to practice, since they’re the only questions that simulate the GMAT’s style and content with 100% accuracy.  The problem-solving questions have a unique style and logic that many unofficial resources struggle to replicate. Fortunately, there are a ton of real GMAT questions available , and some are even free !

You’ll likely want to supplement each of these resources with other third party tools to help you study. Make sure that any books or online materials you’re using are accurate, useful, and well-respected. A good way to check about the reliability of a book or resource is to read reviews of the resource on Amazon or forums like Beat the GMAT or GMAT Club. We’ve also reviewed the best GMAT books and the best GMAT online resources (coming soon) for you.

#4: Plug In Numbers

You can solve many GMAT problem solving questions by plugging in real numbers for the variables in equations.  Look for questions that have algebraic answers, or questions that ask for the values of algebraic expressions instead of just the values of variables when plugging in numbers. For instance, consider the following question.

If x < y < 0, which of the following is greatest in value?

e. 2y – x

For this question, you can pick real numbers that fit the parameters of the question (such as y = -2 and x = -3), and then plug them into each answer to see which answer has the greatest value.

Here are a few tips for plugging in numbers. First, try to use easy, whole integers that fit the constraints of the question. Second, if the question is asking you to determine a value, you can use the numbers yo’ve plugged in to find the matching answer. If the answers are also algebraic terms, keep plugging in your numbers until you get a match. Third, be careful when you’re plugging in numbers! Make sure you go through every one of the answers, as you may find two answers that match with the numbers you’ve chosen. If that’s the case, try plugging in new numbers or solving the problem in a different way, until you’ve only gotten one correct answer.

The writers of the GMAT know that people generally pick positive, whole numbers to plug into their equations. Don’t forget about negative integers, positive and negative fractions, positive and negative decimals, etc., when plugging in numbers to solve a question.

#5: Work Backwards Using Answer Choices

The GMAT normally arranges answer choices in the ascending numerical value on the quant section. Consider the following example, which we’ll go into more depth on in the next section.

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When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000 dollars. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?

Notice how the answer choices are written in ascending numerical value. This arrangement means that you can try to plug in an answer and work backwards if you’ve got no idea where to start on a particular question. I’d suggest plugging in the middle answer, so that way you’ll know whether you need to go higher or lower with your answer. You can also use this method to decide which answers to try to plug in next, as well as automatically eliminate the other answers.

#6: Don’t Rely on Your Eyes

When tackling geometry questions, don’t rely on your eyes to estimate angle sizes, lengths, or areas of figures. Instead, use the numbers provided and your own mastery of geometry concepts. Geometry figures aren’t always drawn to scale, and assuming they are can get you into trouble.

You’ll never encounter a GMAT quant question that you can answer simply by visual estimation. GMAT problem solving questions are designed so that you have to use the information in the question, as well as any information in the diagrams, graphs, charts, or tables, to help you solve the question. That means that you won’t be able to see a triangle and estimate the length of one of its sides just by looking at it. You’ll need to use the information in the question to help you

#7: Remember That the Numbers Will Work Out

The writers of the GMAT know that you’re not allowed to use a calculator on the quant section. That means that you’ll be able to solve every question using your mastery of fundamental math concepts, a pencil, and scratch paper. If you’re working yourself into a quagmire of exceedingly complicated calculations, stop, take a breath, and reassess the question. You’re likely over-thinking something.

#8: Use What You Know

No matter how difficult the question may look, remember that you’ll only need to use high school level math to answer it. Start small on questions by using what you know. If you break the problem down to small steps, beginning with what you know, you’ll be able to work towards an answer.

Consider the following sample diagram, which I’ll go into more depth about in the next section.

When you’re approaching GMAT problem solving questions, make sure you’re using all the information in the question and any corresponding charts, tables, or diagrams to find your answer.

#9: Practice Your Timing

One of the keys to success on the GMAT quant section is being able to quickly solve complex math problems.  If you can solve most problem solving questions in a minute or less, you’ll have plenty of time leftover to spend on more difficult questions.

To improve your timing, practice with a timer when you’re working on practice sets. Give yourself two minutes to solve every question in your practice set, and see how that feels. Slowly decrease the amount of time you’re giving yourself, until you’re averaging one minute on most questions.

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#10: Use Flashcards to Help You Memorize Important Formulas

As I mentioned in previous tips, you won’t get to use a formula cheat sheet on the GMAT. You’ll have memorize all the formulas you expect to need on test day. You should spend time before test day memorizing the formulas that you’ll see on the GMAT.

Using flashcards is a great way to build your knowledge so that you can quickly recall and use important formulas on test day. Flashcards help you learn to quickly and accurately remember information by forcing you to focus on one small piece of information at a time. Flashcards are also highly portable, and easy to carry with you so that you can practice when you have downtime, such as on your commute to and from work or school. There are many free GMAT flashcard resources out there, but it’s always best to make your own flashcards. In our guide to the best GMAT flashcards , we review the best GMAT flashcard resources out there, as well as tell you the best way to study using flashcards.

5 Sample Problem Solving GMAT Questions

These five samples questions will help you see the types of concepts covered in GMAT problem solving questions. Please note: there’s a lot of content covered in GMAT problem solving questions. While I picked sample questions that represent a wide range of topics covered by GMAT problem solving questions, there are many more content areas that you’ll see on the test.

Problem Solving Sample Question #1

We know that Leo paid $87.50 of import tax on the total value of an item in excess of $1,000.

Let’s start by saying that x stands for the total value of the item. We also know that x ≥ 1000, because Leo had to pay import tax on the part that was in excess of $1,000.

So, (x – 1000) can represent the part that Leo had to pay the 0.7% import tax on.

We can therefore write the equation:

0.7(x – 1000) = 87.50

Multiply both sides by 0.7 to isolate x, which yields us:

X – 1000 = 1250

Add 1000 to both sides to isolate x which yields us:

X = 1250 + 1000

The correct answer is C. You could also get the right answer by plugging in the different values. As I mentioned in the tips section, start with the middle number. In this case, plugging in C would yield you the correct answer. However, if it didn’t, you’d be able to use that information to eliminate other answers and decide what to plug in next, as discussed in the earlier tip.

Problem Solving Sample Question #2

If the average (arithmetic mean) of the four numbers 3, 15, 23, and (N+1) is 18, then N =

This question requires us to understand how to find the arithmetic mean. You find the arithmetic mean of a set of values by dividing the sum of all the values by the total number of values. So, in this case, that yields us the following equation:

3 + 15 + 32 + (n + 1)/4 = 18

3 + 15 + 32 + (n+1) represents the sum of all the values.

4 represents the total number of values.

Now, let’s simplify this equation. In order to isolate n, let’s first multiply each side by 4, which yields us the new equation:

3 + 15 + 32 + (n +1) = 72

We can simplify that equation to get:

51 + N = 72.

Then we can solve for n by subtracting 51 from both sides.

N = 72 – 51

The correct answer is C.

Problem Solving Sample Question #3

This question is all about interpreting graphs. The question asks us to determine the difference between the highest and lowest tides.

First, let’s start off by determining the highest tide. The highest tide seems to be at 11:30 a.m., which is 2.2 ft.

The lowest tide is 0.5 feet below the baseline, which occurs at 6 pm.

Therefore, the equation to express the difference between the heights is [2.2 – (-0.5)] = 2.7 ft.

The correct answer is E.

Problem Solving Sample Question #4

A flat patio was built alongside a house as shown in the figure above. If all angles are right angles, what is the area of the patio in square feet?

You calculate the area of a rectangle by multiplying length x width. 35 x 40 = 1400 ft.

Now, because the patio is missing a portion where it intersects with the house, we have to find the area of that missing portion. From the diagram, we can see that the part where the patio intersects with the house is a square with the dimensions 20 ft by 20 ft.

We can find the area of that square by multiplying length times width, so 20 x 20 = 400 ft.

Now to find the area of the patio, we simply subtract 1400 – 400 = 1000 ft.

The patio has an area of 1000 square feet.

Problem Solving Sample Question #5

Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 10 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?

Let’s start off by defining what we know.

We know that Mark sold 10 less boxes than n. We can express the number of boxes that Mark sold as n – 10.

We know that Ann sold 2 less boxes than n. We can express the number of boxes that Ann sold as n – 2.

We also know that they each sold at least one box of cookies. Thus, we can say that n – 10 ≥ 1 and n – 2 ≥ 1.

Thus, we know that n ≥ 11, because we need at least 11 boxes to make Mark’s statement (n – 10 ≥ 1) true.

We also know that they sold less than n boxes. We can express this as:

(n – 10) + (n – 2) < n. If we solve through for n in this equation, we get that n < 12.

We therefore know that n ≥ 11 and n < 12, which tells us that n = 11.

The correct answer is A.

Review: How to Attack Problem Solving GMAT Questions

GMAT problem solving questions are more traditional than data sufficiency questions. You’ll see concepts presented in a straightforward way that is very similar to how you’ve seen math questions posed on other standardized tests.

But that doesn’t mean these questions are easy or simple! Problem solving questions cover a wide range of math concepts, from algebra to geometry to number properties and more. Work on mastering fundamental math concepts so that you can work quickly and successfully through problem solving questions on test day.

What’s Next?

There’s a lot of content covered on the GMAT quant section, so if you’re looking for specific tips on tackling a part content area check out some of our other guides (such as our guides to GMAT percents , probability , and geometry ). These guides will help you build up the fundamental knowledge you need to succeed on the GMAT.

Feel like you’ve gotten the hang of GMAT problem solving questions, but wondering what’s up with the other half of the GMAT quant section? Data sufficiency questions are undoubtedly a bit strange, and very different stylistically from any traditional math question you’ve encountered on other standardized tests. Check out our guide to data sufficiency questions  to learn more about this unique question type and how to master it.

Wondering how to build in practice on problem solving questions to your GMAT studying? Look no further than our comprehensive GMAT study plan article . In this guide, you’ll find four different GMAT study plans designed to maximize your time and boost your score. You’ll learn how much time you should devote to each section of the test and get recommendations on resources you can use to supplement your practice.

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Author: Hayley Milliman

Hayley Milliman is a former teacher turned writer who blogs about education, history, and technology. When she was a teacher, Hayley's students regularly scored in the 99th percentile thanks to her passion for making topics digestible and accessible. In addition to her work for PrepScholar, Hayley is the author of Museum Hack's Guide to History's Fiercest Females. View all posts by Hayley Milliman

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• Practice Questions
• Problem Solving

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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. 

The multiple choice “problem solving” questions, one of the two types of GMAT math questions, are the most familiar, yet students 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

• GMAT Data Sufficiency Questions
• GMAT Sentence Correction Questions
• GMAT Reading Comprehension Questions
• GMAT Critical Reasoning Questions

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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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GMAT Problem Solving Questions

Last Updated on November 27, 2023

Whether you are taking the current version of the GMAT or the new GMAT Focus, GMAT Problem Solving questions are the majority of the GMAT quant questions you will see. Thus, to get a great score on the GMAT, you must be able to crush this question type. In this blog, we will discuss the essence of GMAT Problem Solving questions and look at some GMAT Problem Solving sample questions and their solutions. (If you need data sufficiency help, we’ve covered that in a separate article .) If you need more practice after completing what we offer in this article, please check out the Target Test Prep online GMAT course .

Here are the topics we’ll cover:

What is a gmat problem solving question, the gmat quant topics.

• GMAT Problem Solving Example 1
• GMAT Problem Solving Example 2
• GMAT Problem Solving Example 3
• GMAT Problem Solving Example 4

GMAT Problem Solving Example 5

What’s next.

Let’s begin with a discussion of what a GMAT Problem Solving question is.

The good news is that GMAT Problem Solving questions are identical to the multiple-choice questions you’ve seen since your days of doing basic math questions. As such, a Problem Solving (PS) question presents the answer choices A, B, C, D, E and has just one correct answer. On the current version of the exam, PS questions make up about two-thirds of the questions in the GMAT quantitative section. So, you’ll see about 21 PS questions.

On the GMAT Focus, PS questions are actually their own section, which consists of 21 GMAT math questions. So, whether you are taking the traditional GMAT or GMAT Focus, you need to know GMAT Problem Solving questions!

There are 21 Problem Solving questions on GMAT Focus and around 21 Problem Solving questions on the standard GMAT.

Now, let’s discuss the quant topics you may see covered in GMAT Problem Solving questions.

If you are somewhat new to the exam, you may wonder, what the heck is tested in the GMAT quant section? Most of what is tested on the GMAT is math that you likely saw at one time in your life. So, rather than learning things from scratch, you can build back up the quant muscles you previously had. Sure, those concepts are tested slightly differently on the GMAT, but in general, there should not be many math topics that are completely new to you.

There is a high likelihood that you are familiar with most of the math topics tested on the GMAT.

Let’s list the topics tested:

• GMAT Arithmetic Questions
• Fractions and Decimals
• Number Properties
• GMAT Algebra Problems
• Quadratic Equations
• GMAT Number Properties
• Exponents and Roots
• Inequalities
• Absolute Values
• Word Problems
• Rate Problems
• Work Problems
• Unit Conversions
• Ratios and Proportions
• Overlapping Sets
• Permutations and Combinations
• Probability
• GMAT Geometry Questions
• Coordinate Geometry

Note that Geometry is not included in the GMAT Focus.

Now that we are familiar with the basics of a GMAT Problem Solving question and the topics those questions may involve, let’s get into our GMAT problem-solving practice.

In the sections that follow, we will first present a topic, and then show how it can be presented in a GMAT PS question.

GMAT Problem Solving Topic 1: Number Properties – Factorial Divisibility

The first example is based on the topic of factorial divisibility, which is one of many integer properties. The nice thing about factorial divisibility is that, although it appears to be a difficult topic, it’s actually quite simple once we learn to use a very cool strategy for this type of question.

For example, let’s say you need to determine the maximum value of n for the expression (14!) / (2^n) such that the result is an integer. To determine the max value of n, we do the following:

First, divide 14 by 2, and note the quotient while ignoring any remainder:

14/2 has a quotient of 7.

Next, divide 14 by 2^2 = 4, and note the quotient while ignoring any remainder:

14/4 has a quotient of 3.

Next, divide 14 by 2^3 = 8, and note the quotient while ignoring any remainder:

14/8 has a quotient of 1.

Next, divide 14 by 2^4 = 16, and note the quotient while ignoring any remainder:

14/16 has a quotient of 0.

Since we have found a quotient of zero, we can stop. The final step is to add up all the quotients; that sum is the maximum value of n. So, the maximum value of n is 7 + 3 + 1 = 11.

Use the strategy provided above to solve factorial divisibility problems.

Let’s practice with an example.

GMAT Problem Solving Example 1:

What is the greatest integer j, such that 240! / 4^j is an integer?

First, we divide 240 by 4^1, noting the quotient and ignoring the remainder:

240 / 4 = 60

Now we divide the quotient 60 by 4^2, noting the quotient and ignoring the remainder:

60 / 4^2 = 60 / 16 = 3

Now we divide the quotient 3 by 4^3, noting the quotient and ignoring the remainder:

3 / 4^3 = 3 / 64 = 0

Because the quotient is 0, we stop.

The value of j is the sum of all the quotients, so we have:

60 + 3 + 0 = 63

This tells us that there are 63 fours in 240!

Thus, we know that the largest value of j that allows 240! / 4^j to be an integer is j = 63.

Next, let’s discuss a topic from inequalities.

GMAT Problem Solving Topic 2: Inequalities – Combining Equations and Inequalities

One of the first things you will learn on the GMAT is solving for the value of the two variables contained in two equations, you often use the substitution method, which functions just as it sounds like it would. We also use this process when we have one equation and one inequality containing two variables.

For example, let’s say we have the following:

Equation: y = 2x – 1

Inequality: 3x + 4y > 25

If we want to know what is true about x, we do the following:

Since y = 2x – 1, we can substitute 2x – 1 for y in the inequality 2x + 4y > 25. Doing so gives us:

2x + 4(2x – 1) > 25

2x + 8x – 4 > 25

10x > 29

x > 29/10

Thus, we know that x is greater than 2.9.

When working with inequalities and equations, we can substitute the equation into the inequality.

Let’s practice with one more example.

GMAT Problem Solving Example 2:

If 2x – 4y = -10 and 5x – 3y < 3, then which of the following must be true?

• y < 28 / 13
• y < 53 / 17
• y > -28 / 13

The answer choices indicate that we need to get an answer for y, so we will first solve the equality to get x in terms of y.

2x – 4y = -10

2x = 4y – 10

x = 2y – 5

We now substitute 2y – 5 for x into the inequality and solve for y:

5(2y – 5) – 3y < 3

10y – 25 – 3y < 3

GMAT Problem Solving Topic 3: Rates – Converging Rate Questions

As you study rates on the GMAT, you will discover that there are many ways in which rate questions may be presented. Thus, you’ll want to become familiar with each type and know the associated formula for each one. If you can apply the appropriate GMAT math strategies to rate questions, you’ll be in a great place come test day.

We do not have the time to cover each type of rate question in this article, but we will focus on a common type, the converging rate question.

A converging rate is when two people or things head toward each other on a parallel path. An important characteristic of converging rates is that when two objects converge (or meet), the total distance that originated between them is equal to the sum of the individual distances of the two objects. Thus, we use the following formula:

Distance of Object 1 + Distance of Object 2 = Total Distance Traveled

When two objects meet, the sum of their individual distances is equal to the total distance they traveled from their respective starting points.

Let’s practice how we would use this formula with an example.

GMAT Problem Solving Example 3:

The distance between Philadelphia and Boston by train is 311 miles. Train A departs Philadelphia at 12:00 PM, traveling to Boston at a constant speed of 50 miles per hour. Train B departs Boston at 12:30 PM and heads toward Philadelphia on a parallel track at a constant speed of 60 miles per hour. How far has Train A traveled at the moment the trains meet?

We see that this is a converging rate question, as two trains are traveling toward each other (on parallel tracks!).

Let’s let r1 = Train A’s rate, t1 = Train A’s time, and d1 = Train A’s distance traveled.

Similarly, we will let r2 = Train B’s rate, t2 = Train B’s time, and d2 = Train B’s distance traveled.

The individual distance traveled by Train A will be:

r1 x t1 = d1 (Equation 1)

The individual distance traveled by Train B will be:

r2 x t2 = d2 (Equation 2)

Because the distance between the two cities is 311 miles, we can say that: the sum of the individual distances is equal to the total distance:

d1 + d2 = 311

We can substitute Equation 1 and Equation 2 into Equation 3, as follows:

r1 x t1 + r2 x t2 = 311

Substituting the known information for the rates of the two trains, we have:

50 x t1 + 60 x t2 = 311 (Equation 4)

We have two variables and only one equation, so we need additional information about the relationship between the two times. Because Train B left half an hour after Train A, its travel time is half an hour less than Train A’s. Thus, we see that t2 = t1 – 0.5, and we substitute this into Equation 4 and solve:

50 x t1 + 60 x (t1 – 0.5) = 311

50 x t1 + 60 x t1 – 30 = 311

110 x t1 = 341

Since Train A traveled for 3.1 hours, we substitute this value into Equation 1:

50 x 3.1 = d1

Train A traveled 155 miles.

Next, let’s discuss how to find the median of a large set of data.

GMAT Problem Solving Topic 4: Statistics – Finding the Median of a Large Set of Data

If you have ever studied how to determine the median of a set of data, you may recall that it’s a pretty simple process when you have a small set of data, as you can manually calculate it pretty easily. However, what do you do when you have a large set of data? Don’t worry; there’s an excellent way to determine the median, even in a large set!

To determine the place where the median falls in a set of data in ascending or descending order, we use the following formula, where n represents the total number of values in the set:

position of the median = (n + 1) / 2

Keep in mind that this formula works when the number of data points is odd and when it’s even, but in slightly different ways. Let’s do two quick examples that illustrate the difference.

Median Example With an Odd Number of Numbers

What is the median of -4, -3, 0, 1, 4, 6, 10, 11, 15?

Since there are nine numbers in the ordered set, we can determine the position of the median as follows:

position of the median = (9 + 1) / 2 = 5

So, the median is the 5th number in the set when counting from lowest to highest. Thus, the median is 4. Now let’s look at a set with an even number of numbers.

Median Example With an Even Number of Numbers

What is the median of -4, -3, 0, 1, 2, 6, 10, 11, 15, 19?

Since there are ten numbers in the set, we can determine the position of the median as follows:

position of the median = (10 + 1) / 2 = 5.5

Since the median cannot be in the “5.5 position” of the set, we calculate the average of the number in the fifth and sixth positions. The number in the fifth position is 2, and the number in the sixth position is 6. The average of those two numbers is 8/2 = 4. So, the median is 4.

The position of the median of an ordered data set is found by using the formula: position of median = (n + 1) / 2, where n is the number of values in the set.

GMAT Problem Solving Example 4:

At a candy shop, there are sixteen candies costing $1 each, twenty candies costing $2 each, and forty candies costing $3 each. What is the median cost of the candies?

Let’s calculate the position of the median for the 76 candies:

Position of median = (n + 1) / 2 = (76 + 1) / 2 = 77 / 2 = 38.5

We know that the median is the average of the 38th and 39th data values.

We don’t have the 77 data values listed individually, but we know that we are looking for the 38th and 39th data values. We see that the first 16 values are all $1, and the next 20 values (the 17th through 36th values) are all $2. The next 20 values (the 37th through the 66th values) are all $3.

Thus, we see that both the 38th and the 39th data values are each $3. Thus, the median is $3.

Next, let’s discuss one final GMAT Problem Solving topic: three-part ratios.

GMAT Problem Solving Topic 5: Ratios – Three-Part Ratios

Three-part ratios are one of the more challenging topics tested in ratios. Three-part ratio problems generally present two two-part ratios with a shared term represented by different numbers in each ratio.

For example, we may be given the following two ratios concerning the number of cartons of white milk, chocolate milk, and strawberry milk in a New York deli.

White to Chocolate = 3 to 2

White to Strawberry = 5 to 4

In the first ratio, the number of cartons of white milk is represented by 3. In the second ratio, the number of cartons of white milk is represented by 5. However, we need the number of cartons of white milk to be represented by the same number in both ratios before we can combine the two ratios into a single three-part ratio.

The LCM of 3 and 5 is 15. Thus, we’ll be able to combine the ratios if we create two equivalent ratios such that both have the number of cartons of white milk represented by 15:

White to Chocolate = 3 to 2 = 3 × 5 to 2 × 5 = 15 to 10

White to Strawberry = 5 to 4 = 5 × 3 to 4 × 3 = 15 to 12

Now that both equivalent ratios have the same number, 15, representing the number of cartons of white milk, we can create the following three-part ratio:

White : Chocolate : Strawberry = 15 : 10 : 12

To convert two two-part ratios to one three-part ratio, use the LCM of the common item shared by both ratios.

Let’s now try a Problem Solving example dealing with this concept.

At a farm, the ratio of horses to ponies is 10 : 7, and the ratio of goats to ponies is 3 : 2. If there are 60 horses at the farm, how many goats are there?

The common connection in the two ratios is ponies, so we need to find the LCM of the two “ponies” numbers, which are 7 and 2. Thus, the LCM is 7 x 2 = 14.

We can now convert the first ratio of horses to ponies, 10 : 7, to one in which the number of ponies in the ratio is 14, by multiplying by 2:

Horses to ponies = 10 to 7 = (10 x 2) to (7 x 2) = 20 to 14

Similarly, to convert the goats : ponies ratio, currently 3 : 2, such that the number of ponies in the ratio is 14, we multiply the ratio by 7.

Goats to ponies = 3 : 2 = (3 x 7) to (2 x 7) = 21 to 14

The three-part ratio can now be stated as horses : ponies : goats = 20 : 14 : 21.

There are 60 horses at the farm. If we multiply the three-part ratio by 3, we obtain the equivalent ratio of horses : ponies : goats as 60 : 42 : 63. Thus, there are 63 goats at the farm.

Whether you are registered for the GMAT or the GMAT Focus Edition, Problem Solving questions will constitute a large part of the quantitative portion of your exam. The more exposure you have to the various topics tested by PS questions, the better prepared you’ll be on test day.

In this article, we have focused on 5 examples of PS questions you might encounter on the GMAT or the GMAT Focus. They have come from the major topics of Number Properties, Inequalities, Rates, Statistics, and Ratios. They represent only a small proportion of the topics and subtopics that you need to master in order to get a great score on the GMAT.

The PS questions we covered in this article represent only a small proportion of the topics and subtopics that you need to master in order to get a great score on the GMAT. Check out our article that introduces additional GMAT PS math questions for more practice and expert tips!

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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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GMAT Sample Questions

Want a preview of the question types you'll face on the GMAT? Try your hand at the GMAT practice questions below. Then, check your answers against our in-depth explanations to see how you did.

We pulled these GMAT sample questions from our book Cracking the GMAT and from our test prep course materials. For more GMAT practice, take a full-length practice test with us held under the same testing conditions as the real thing. Find out how you'd score, and get  a personalized score report from us that shows your strengths and weaknesses.

• GMAT Verbal Questions 
• GMAT Math Questions
• GMAT Integrated Reasoning Questions 
• Essay Prompt 

Below you'll find sample GMAT questions covering the three question types you'll encounter on the Verbal section: Sentence Correction , Critical Reasoning, and Reading Comprehension.

GMAT Sentence Correction Questions

1. In order to better differentiate its product from generic brands, the cereal company first hired a marketing firm that specializes in creating campaigns to build brand awareness and then retools its factory to produce a variety of different shapes of cereal. (A) then retools its factory to produce a variety of different shapes of cereal (B) retools its factory to produce a variety of different shapes of cereal (C) then retooled its factory to produce a variety of different shapes of cereal (D) then will retool its factory to produce a variety of different shapes of cereal (E) then produces a variety of different shapes of cereal through retooling its factory

Answer: (C) The actions of the cereal company are not in parallel form. First the company hired then it retools . Eliminate choice (A). Choice (B) still has the same error. Choice (D) changes the verb form incorrectly to the future tense. Choice (E) rewrites the sentence but retains the error.

[+] See the Answer

2. Believed to be one of the first widely read female authors of the Western world, Christine de Pizan's masterwork The Book of the City of the Ladies , was written in 1405 and is a history of the Western world from the woman's point-of-view. (A) Believed to be one of the first widely read female authors of the Western world (B) Written by one of the first widely read female authors of the Western world (C) One of the first widely read female authors of the Western world, as some believe (D) Written by what some believe as one of the first widely read female authors of the Western world (E) Believed by some as one of the first works by a widely read female author in the Western world

Answer: (B) As written, this sentence has a misplaced modifier error: the book, The Book of the City of the Ladies isn't believed by anyone to be an author— Christine de Pizan is. Choices (A) and (C) repeat that error and can be eliminated. Choices (B) and (D) both change the introductory phrase to clearly refer to a written work, but choice (D) uses the incorrect idiom believe as instead of the correct form, believe to be . Choice (E) repeats that idiom error.

GMAT Critical Reasoning Questions

1. One food writer wrote that reducing the amount of animal products in one's diet can contribute to better health and well-being. Based on this claim, some people are completely eliminating meat from their diets in order to be healthier. The argument above relies on which of the following assumptions?

Answer: (B) The argument states that some people are eliminating meat from their diets because reducing the amount of animal products in one's diet can lead to better health. Meat is only one type of animal product, however. The argument assumes that by eliminating meat, the people are reducing the total amount of animal products in their diets. Choice (A) addresses increasing the amount of vegetables and grains, but the argument just deals with animal products. Choice (B) correctly addresses the people who are eliminating meat and states that those people are not increasing their consumption of dairy, which is another instance of using animal products. Thus, these people are actually reducing the amount of animal products in their diets. Choice (C) addresses most food writers, who are irrelevant to this argument. Choice (D) addresses health lifestyles, which are irrelevant to this particular argument. Choice (E) addresses the reasons behind not eating animal products, which is irrelevant to the argument.

2. Studies reveal that a daily exercise regimen helps stroke survivors regain dexterity in their extremities. Being given an exercise routine and having a consultation with a doctor about the exercise routine have been shown to be effective mechanisms to get patients to exercise daily. From the above information, which of the following statements can be reasonably inferred? (A) A stroke survivor that is given a detailed exercise plan and consults her physician about the plan will regain full dexterity in her extremities. (B) If a stroke survivor is not given an exercise plan and does not consult with a doctor, she will not regain dexterity in her extremities. (C) Stroke survivors who are given an exercise routine and consult with a doctor about that routine will sometimes regain dexterity in their extremities. (D) Being given an exercise routine and having a consultation with a doctor about the routine is the best way to help a stroke survivor regain dexterity in their extremities. (E) Only being given an exercise routine is necessary to regenerate dexterity in the extremities of seniors who have suffered a stroke.

Answer: (C) This is an inference question, so evaluate the passage and then look for an answer choice that can be reasonably inferred from the information. The passage states that a daily exercise regimen helps stroke survivors regain dexterity in their extremities and that survivors who are given an exercise routine and who have a consultation with a doctor about the routine have been shown to be effective at getting patients to exercise daily . So it can be inferred that if a survivor is given a routine and consults with a doctor, they are more likely to exercise daily, which will help them regain dexterity. Choice (A) is an example of extreme language. The phrasing will regain full dexterity is not promised in the information in the passage, as the passage only states that a routine and consultations may help a survivor exercise more. Eliminate (A). Choice (B) is also an example of extreme language. There is no way to discern from the information provided that a strong survivor would not regain dexterity without an exercise routine and a consultation, so eliminate (B). Choice (C) is a reasonable inference to make from the information in the passage so keep (C). Choice (D) also contains the extreme language best way . The information does not compare this method with any other method so eliminate (D). Choice (E) is recycled language and does not address consulting with a doctor so eliminate (E). The correct answer is (C).

GMAT Reading Comprehension Questions

Although oft-maligned in modern culture, the pigeon once stood not only for speed and reliability but also for grace and beauty. Darwin himself became a pigeon fancier after beginning to work with the humble Columbia livia , discovering them to be more fascinating than he had formerly believed. During the Victorian age, in fact, raising show pigeons was a popular hobby, with new breeds continuously arising as amateur (and not-so-amateur) ornithologists crossed animals in the hopes of creating ever more fantastic creatures. One of the most sought-after varieties was known as the Almond Tumbler, a name presumably derived from the color of the birds combined with the distinctive flight style. Over the course of many generations, this bird was so manipulated as to have a beak so small as to prevent the adult birds from feeding their offspring. And yet, it was wildly popular, drawing high prices at auctions and high prizes at competitions. How then did an animal once so well-loved come to be so loathed? As recently as World War II, the military used pigeons to carry messages but today, many people would kick a pigeon before they would feed one. Perhaps it is just a problem of population density - a lack of esteem for that which is ubiquitous. Pigeons have become our constant urban companions and, as such, have been transformed from symbols of peace, plenty, and prosperity, to representatives of disease and decay.

1. The primary purpose of this passage is to (A) convince the reader of the nobility of the pigeon, based on its history as a symbol of virtue (B) dissuade the reader from mistreating a once-majestic animal that has fallen from favor (C) rebut claims that the pigeon carries disease any more frequently than do other domestic animals (D) promote a renewal of pigeon fancying and a resurgence of breeds such as the Almond Tumbler (E) suggest that there might be more to the story of some urban wildlife than is commonly known

Answer: (E) The passage gives a brief description of the pigeon's place in recent human history and then goes on to contrast that with modern perspectives of the birds. Choice (A) goes too far—the author doesn't give any indication of believing the pigeon to be noble. Choice (B) focuses too specifically on a side comment in the second paragraph. Choice (C) also focuses too specifically on a side comments—the passage is not primarily about disease. Choice (D) is too strong—the passage isn't really promoting any specific action. Choice (E) remains neutral and informational, as does the passage.

2. The case of the Almond Tumbler is most analogous to which of the following? (A) a strain of wheat that can be grown in plentiful quantities but loses much of its nutritional value in the process (B) Arabian horses that are able to run at phenomenal speeds due to centuries of careful breeding designed to enhance those physical attributes (C) vitamins that were purported to provide all of the necessary nutrients but have since been found not to be very effective (D) the dachshund, a popular breed of dog that is nonetheless prone to severe back problems, due to weaknesses exacerbated by targeted breeding (E) the wild rock doves that are most commonly found nesting in the faces of cliffs far from human habitation

Answer: (D) The Almond Tumbler is described as a breed of pigeon that was very popular during the Victorian era. The passage also mentions that the selective breeding used to create that particular kind of bird also led to tiny beaks that kept parent birds from feeding their babies. Therefore, the best analogy would be another animal that is popular even though it has problems due to its design. Choice (A) is incorrect because it leaves out the aspect of popularity. Choice (B) is only positive and you need something that's also negative. Choice (C) is not about something that has been bred for a specific purpose, nor does it deal with popularity. Choice (D) correctly refers to a popular animal with a common health problem. Choice (E) does not refer to pigeons that have been bred by humans.

3. The passage suggests that (A) pigeons were once known for flying with celerity (B) the Almond Tumbler was the most beautiful breed of pigeon (C) Darwin was infatuated with his fancy pigeons (D) modern pigeons are dirtier than the fancy pigeons of yore (E) only scientists should breed new kinds of animals

Answer: (A) For a question this open-ended, it's usually best to check each of the answers against the passage. Choice (A) appears to match the opening line of the passage, which states that the pigeon once stood not only for speed and reliability. Choice (B) goes too far—although many Victorians seems to have loved the Tumbler, there's no evidence that it was definitively the most beautiful. Choice (C) also goes too far—the passage mentions that Darwin was fascinated by his pigeons, not that he was infatuated. Choice (D) draws an incorrect assumption—the passage comments that the common opinion has changed, not the pigeon itself. Choice (E) is not supported by the passage, which states that amateurs, as well as trained individuals, bred pigeons.

Below you'll find GMAT sample questions covering the two question types you'll encounter on the Quantitative section: Problem Solving and Data Sufficiency.

Problem Solving Questions

1. A certain company sells tea in loose leaf and bagged form, and in five flavors: Darjeeling, earl grey, chamomile, peppermint, and orange pekoe. The company packages the tea in boxes that contain either 8 ounces of tea of the same flavor and the same form, or 8 ounces of tea of 4 different flavors and the same form. If the order in which the flavors are packed does not matter, how many different types of packages are possible? (A) 12 (B) 15 (C) 20 (D) 25 (E) 30

Answer: (C) Begin by figuring out how many different ways you can package the tea in boxes that contains 8 ounces of tea, all of the same flavor. There are five flavors, each flavor can come in either loose leaf or bagged form, so 5 flavors x 2 forms = 10 different ways to package the tea in boxes that contain only one flavor each. Now find the number of different ways to package 4 different flavors of the same form per box. In this case, you must choose 4 of 5 possible flavors, and order does not matter, so the formula is 5 x 4 x 3 x 2 ⁄ 4 x 3 x 2 x 1 = 5 different ways to combine the 4 flavors. Each combination can come in either loose leaf for bagged form, so you have 2 different forms x 5 different combinations = 10 total possible ways to combine the 4 flavors in either bagged or loose-leaf form. Thus, the total number of combinations is 10 + 10 = 20 total combinations. The answer is choice (C).

2. Karen sold her house at a loss of 25 percent of the price that she originally paid for the house, and then bought another house at a price of 30 percent less than the price she originally paid for her first house. If she sold the first house for $225,000, what was her net gain, in dollars, for the two transactions? (A) $15,000 (B) $25,000 (C) $60,000 (D) $75,000 (E) $90,000

Answer: (A) If Karen sold her first house for $225,000 and at a loss of 25 percent, then 25 percent of the original price equals $225,000. 75 ⁄ 100 x = 225,000, so x, or the price she originally paid, equals $300,000. Thus, Karen lost $75,000 on the sale of her first house. If she bought a second house for a price of 30 percent less than $300,000, then the second house cost $210,000, so she gained $90,0000. $90,000 - $75,000 = $15,000, so the answer is choice (A).

Sample Data Sufficiency Questions

1. In a certain company, at least 200 people own manual transmission vehicles. If 12 percent of the people who own manual transmission vehicles also own automatic transmission vehicles, do more people own automatic transmission vehicles than own manual transmission vehicles? (1) 5 percent of the people who own an automatic transmissions vehicle also own a manual transmission vehicle. (2) 15 people own both an automatic transmission vehicle and a manual transmission vehicle. (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. (D) EACH Statement ALONE is sufficient. (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Answer: (A) According to statement (1), 5 percent of the people who own an automatic transmission vehicle also own a manual transmission vehicle. The question also indicates that 12 percent of the people who own a manual transmission vehicle also own an automatic transmission vehicle. Both figures relate to the total number who own both, so that means that 5 percent of the automatic transmission owners = 12 percent of the manual transmission owners. The overlap in ownership makes up a smaller percent of those who own automatic transmission vehicles, so there must be more people who own automatic transmission vehicles. Statement (1) is sufficient, so you can eliminate choices (B), (C), and (E). Statement (2) indicates that 15 people own both an automatic transmission vehicle and a manual transmission vehicle, so you know that 12 percent of the people who own a manual transmission is equal to 15 people. 12 ⁄ 100 = 15, so x = 125. Thus, there are 125 people who own a manual transmission vehicle. However, you have no further information to allow you to calculate the number of people who own automatic transmission vehicles, so statement (2) is insufficient. The answer is choice (A).

2. What is the value of x ⁄ 2 ? (1) x is 1 ⁄ 5 less than 9 ⁄ 10 (2) x is between 2 ⁄ 5 and 4 ⁄ 5 (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. (D) EACH Statement ALONE is sufficient. (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Answer: (A) Statement (1) allows you to find the value of x, so you can answer the question. (If x is 1 ⁄ 5 less than 9 ⁄ 10 , then 9 ⁄ 10 - 1 ⁄ 5 = x. 1 ⁄ 5 = 2 ⁄ 10 , so x equals 9 ⁄ 10 - 2 ⁄ 10 = 7 ⁄ 10 . If x equals 7 ⁄ 10 , then x ⁄ 2 = 7 ⁄ 10 divided by 2, or 7 ⁄ 20 .) Statement (1) is sufficient, so eliminate choices (B), (C), and (E). According to statement (2), x is between 2 ⁄ 5 and 4 ⁄ 5 . That means that one possible value for x is 3 ⁄ 5 , but another possible value is 7 ⁄ 10 . Statement (2) is insufficient, so the answer is choice (A).

Below you'll find examples of how you'll be asked to use a chart, graph, or table to answer questions on the Integrated Reasoning section.

Sample Integrated Reasoning Questions

Item 1: Andre is buying gifts for his office staff. He wants to spend exactly $280 and he can buy either sweatshirts, which cost $22, or baseball caps, which cost $26. In the table below, choose the number of sweatshirts and the number of baseball caps that Andre should buy.

Answer: Sweatshirts, 8; Baseball caps 4 To solve this question, systematically test out the answer choices. The equation you need to solve is 22s + 26h = 280, in which both s and h are integers and s represents the number of sweatshirts and h represents the number of baseball caps. So, start with plugging in 4 for sweatshirts and see if the number of baseball caps is an integer. 22(4) +26h = 280 h = 7.38 Since the number of baseball caps is not an integer, Andre could not have bought 4 sweatshirts. Keep trying more sweatshirts one by one until you find an answer that will you an integer value for baseball caps. 8 sweatshirts will give you 4 baseball caps.

Question 2-1 The ratio of the U.S. population in 2000 to the U.S. population in 1900 is closest to __. (A) 1 to 4 (B) 2 to 7 (C) 2 to 1 (D) 3 to 1 (E) 11 to 3

Answer: (E, 11 to 3) According to the graph, the U.S. population in 2000 was a little bit more than 275 million, and the U.S. population in 1900 was a little over 75 million. Since the question asks what the ratio is "closest to," these numbers are good enough to approximate. 275 to 75 can be reduced by 5 to get 55 to 15, which can be reduced by 5 again to get 11 to 3. Alternatively, you could reduce 275 to 75 by 25 to get this same ratio.

Question 2-2 The U.S. population in 1950 was approximately __ of the U.S. population in 1850. (A) 800% (B) 600% (C) 200% (D) 85% (E) 15%

Answer: (B, 600%) The question asks what percent the U.S. population in 1950 is of the U.S. population in 1850. To get this you need to calculate population 1950 ⁄ population 1850 x 100. Since the U.S. population in 1950 is higher, you want something that is greater than 100%. Eliminate 85% and 15%. Since the sentence says "approximate" and also since the remaining answer choices are not close to each other, you can estimate the values. According to the chart, the population in 1950 was about 150 million and the population in 1850 was about 25 million. Therefore, you need to calculate 150 ⁄ 25 x 100 = 6 x 100 = 600%.

Question 2-3 The U.S. population increased by approximately __ from 1900 to 1950. (A) 25% (B) 33% (C) 50% (D) 100% (E) 200%

Answer: (D, 100%) To get percent increase, you need to use the formula difference ⁄ original x 100. The population in 1900 was about 75 million, and the population in 1950 was about 150 million. The difference between the two figures is 75 million. Therefore, the percent increase is 75 ⁄ 75 x 100 = 100%.

Below you'll find a sample Analytical Writing Assessment (AWA) question. On the GMAT you'll have 30 minutes to write a critique of the argument.

Analysis of an Argument

The following appeared as part of a medical advertisement in a magazine.

A new medical test that allows the early detection of a particular disease will prevent the deaths of people all over the world who would otherwise die from the disease. The test has been extremely effective in allowing doctors to diagnose the disease six months to a year before it would have been spotted by conventional means.

Discuss how logically convincing you find this argument. In explaining your point of view, be sure to evaluate the line of reasoning and the use of evidence in the argument. For example, it may be necessary to consider what questionable assumptions underlie the thinking and what other explanations or counterexamples might weaken the arguments conclusion. You can also discuss what kind of evidence would strengthen or refute the argument, what changes in the argument would make it more logically persuasive, and what, if anything, would enable you to better evaluate its conclusion.

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Quantitative Section - GMAT Problem Solving

Gmat problem solving questions.

Problem solving (PS) questions may not be new to you. You must have seen these types of questions in your high school or college days; they are essentially multiple-choice questions. The format is as follows: There is a question stem and is followed by five options, out of which, only one option is correct or is the best option that answers the question correctly. PS questions measure your skill to solve numerical problems, interpret graphical data, and assess information. These questions present to you five options, and no option is phrased as "None of these". Mostly the numeric options, unlike algebraic expressions, are presented in ascending order from option A through E, occasionally in descending order until there is a specific purpose not to do so.

Sample Problem Solving Question

A typical Problem Solving question look like the following:

If a 12 a is a four-digit number with the digit a in both the thousands and units places, what is the value of a if the number is divisible by 6 ?

As stated earlier, this question format is generally comfortable since most of us have attempted many similar multiple-choice questions in our secondary school and university experience.

There can be more than one approach to solve a PS question. Though for many, these types of problems are approached with traditional methods, it is not necessary that you would do the same for every the GMAT PS question. Traditional approaches are certainly one possible option to solving any GMAT Problem Solving question. The key is to apply optimum approach to a question.

Note that the GMAT is not a test on your mathematical proficiency; rather, it tests your ability to efficiently handle mathematical data to make decisions. The GMAT does not test mathematical concepts beyond the high-school level.

Let's solve this question with three approaches. Note that none of the approaches may be the best one; it depends on you which of them clicks for you on the test day.

Approach 1:

A number is divisible by '6' implies that it is divisible by both of its two prime factors: '2' and '3'.

Since a 12 a is divisible by '2', the digit in the units place, i.e., a must be even. Thus, the possible values of a are: 2, 4, 6 or 8 ( a cannot be '0' since the digit in the thousands place of a four-digit number cannot be '0').

Again, since the number is divisible by '3,' too, the sum of its digits must be divisible by '3,' too.

Sum of the digits of the number a 12 a = a + 1 + 2 + a = 2 a + 3 .

Thus, ( 2 a + 3 ) must be divisible by '3'. Since the constant 3 in ( 2 a + 3 ) is divisible by 3, 2 a must also be divisible by 3, i.e., a is divisible by 3.

Thus, checking with the possible values of a , i.e., 2, 4, 6 or 8, we see than only a = 6 satisfies the above condition.

Hence, we have a = 6 .

The correct answer is Option D.

In this approach, we applied the concept of divisibility rules of '2' and '3' for the given number.

Let's see another approach.

Approach 2:

Note that if a number is divisible by an even number, here 6, the number must be even. Thus, ( 2 a + 3 ) must be even; however, this does not help us much as we are able to eliminate only one choice: Option B = 3, an odd number.

Let's apply the plug-in value approach.

We start with Option A: a = 2

Thus, a 12 a = 2122 . Diving 2,122 by 6 leaves a remainder of 4. Thus, 2,122 + 4 = 2,126 is divisible by 6; however, here the thousands digit and the units digit are not same. So, let's add 4 to our original answer, 2, and make the thousands digit equal to 6. We can then see whether 6,126 is divisible by 6. We see that it is divisible by 6; thus, a = 6 .

In this approach, we applied the traditional method of division and at the second stage, we made a logical conclusion.

Approach 3:

We can rewrite a 12 a as a × 1000 + 1 × 100 + 2 × 10 + a × 1 = a 000 + 100 + 20 + a

Let's divide a 000 + 100 + 20 + a by 6 . We get ( a 000 ) 6 + 100 6 + 20 6 + a 6 .

Looking at a 6 , we see that if a = 6 , it is divisible, so is ( a 000 ) 6 ; however, 100 6 and 20 6 are not. With a little thinking, you would observe that if we add 100 and 20, we get 120, which is divisible by 6 . So, ( a 000 + 120 + a ) is divisible by 6 if a = 6 .

In this approach, we applied the concept of place value and at the second stage, we made a logical conclusion.

How to Solve Problem-Solving Questions in the GMAT Quantitative Section

Learn how to tackle problem-solving questions in the GMAT Quantitative section with ease.

Posted May 24, 2023

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Sequential Numbers Made Fast and Easy for the GMAT and GRE

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If you are planning to take the GMAT, then you are likely aware of the difficulty that comes with the Quantitative Section. This section assesses your math skills and your ability to apply them to real-life business scenarios. One of the question types that test takers encounter in GMAT Quantitative Section is the Problem-Solving question. In this article, we will be discussing ways of solving problem-solving questions in the GMAT Quantitative section.

Understanding the Structure of GMAT Quantitative Section

Before we dive into solving problem-solving questions, let's have a quick overview of the GMAT Quantitative section's structure. You will have 62 minutes to answer 31 multiple-choice questions. The questions are divided into two categories: Problem-Solving and Data Sufficiency. The Problem-Solving questions present a real-life scenario and ask you to solve a problem using your math skills.

The Data Sufficiency questions, on the other hand, present a scenario and ask you to determine whether the given information is sufficient to answer the question or not. These questions are designed to test your ability to analyze and interpret data, rather than just solving problems. It is important to note that both types of questions carry equal weightage in the GMAT Quantitative section, so it is essential to prepare for both types of questions equally.

Tips and Tricks for Tackling GMAT Quantitative Questions

One of the keys to success in the GMAT Quantitative section is to have a solid understanding of the math concepts tested on the exam. This includes integers, algebra, geometry, probability, and statistics. You can find a comprehensive list of concepts tested in this section in the GMAT Official Guide. Additionally, it's essential to practice solving questions, so you get comfortable using the concepts in a timed setting.

Another important tip for tackling GMAT Quantitative questions is to read the questions carefully and identify what is being asked. Many questions are designed to test your ability to interpret data and apply mathematical concepts to real-world scenarios. Therefore, it's crucial to understand the context of the question and identify the relevant information before attempting to solve it.

Finally, it's essential to manage your time effectively during the GMAT Quantitative section. The section consists of 31 multiple-choice questions that you must complete in 62 minutes. This means you have an average of two minutes per question. Therefore, it's crucial to pace yourself and not spend too much time on any one question. If you're unsure about a question, make an educated guess and move on to the next one. You can always come back to it later if you have time.

Identifying Common Mistakes in GMAT Quantitative Section

One common mistake test-takers make is to overcomplicate the questions given poor time management skills. The GMAT does not test complex math concepts, but rather it checks if you can apply simple math skills to solve business problems. Another mistake that GMAT test-takers make is to rush through the questions. You should avoid this mistake by reading the question carefully and understanding what is being asked before rushing to answer.

Another common mistake that GMAT test-takers make is to rely too heavily on calculators. While calculators are allowed on the GMAT, they should only be used for basic calculations. Relying too much on calculators can slow you down and lead to errors. It is important to practice mental math skills to improve your speed and accuracy.

Additionally, some test-takers make the mistake of not reviewing their work. It is important to double-check your answers and make sure you have not made any careless mistakes. This can be done by going back through the questions and checking your calculations or by plugging your answer back into the original problem to ensure it is correct.

Developing a Strategy for Solving Problem-Solving Questions in GMAT

Developing a strategy for solving problem-solving questions is crucial to perform well in the GMAT Quantitative section. A good strategy includes identifying the question type, breaking down the question into steps, and using the process of elimination to arrive at the correct answer. Additionally, an efficient approach entails solving the easier questions first and allocating more time to challenging questions.

Another important aspect of developing a strategy for solving problem-solving questions in GMAT is to practice regularly. Practicing regularly helps in identifying the areas where you need improvement and also helps in building speed and accuracy. It is recommended to solve a variety of questions from different sources to get a better understanding of the question types and to be prepared for any surprises on the test day. Moreover, taking timed practice tests can help in simulating the actual test environment and in managing time effectively during the test.

Importance of Time Management in GMAT Quantitative Section

Effective time management in the GMAT Quantitative section is necessary as you have 62 minutes to answer 31 questions. Ensure that you allocate more time to the challenging questions and leave the easy ones for the last. If a question seems too time-consuming, skip it and come back to it later. Remember, a wrong answer costs you more points than leaving a question unanswered.

Another important aspect of time management in the GMAT Quantitative section is to practice with timed mock tests. This will help you get accustomed to the time pressure and develop a strategy to tackle the questions within the given time frame. Additionally, it is essential to stay calm and composed during the exam and not panic if you feel you are running out of time. This can lead to mistakes and negatively impact your score.

Furthermore, time management is not just about answering questions quickly but also about using your time efficiently. Make sure to read the questions carefully and understand what is being asked before attempting to solve them. This will help you avoid making careless mistakes and save time in the long run. Also, avoid spending too much time on one question and move on to the next if you are unsure about the answer.

Enhancing Problem-Solving Skills through Practice Tests

The best way to increase your problem-solving skills in the GMAT Quantitative section is through practice tests. There are several GMAT practice tests and prep materials available online that you can use to simulate the actual test experience. Practice tests also give you an idea of your strengths and weaknesses, allowing you to work on areas that need improvement.

Utilizing Online Resources to Ace GMAT Quantitative Questions

Online resources are an excellent way to supplement your GMAT preparation. You can find several websites, blogs, and forums that provide tips and tricks for solving GMAT Quantitative questions. Also, there are online calculators that can help speed up your calculations, allowing you to solve the problems even faster.

Improving Speed and Accuracy in Solving GMAT Quantitative Questions

In GMAT Quantitative, it's essential to strike a balance between speed and accuracy. To improve your speed, practice solving questions under timed conditions. To increase accuracy, review your answers and look for consistent mistakes. Additionally, you should eliminate common answer choices like zero, one, negative numbers, and decimals since they are often incorrect.

Analyzing and Interpreting Data in GMAT Quantitative Section

Problem-Solving questions in the GMAT Quantitative section often require you to analyze and interpret data. It's essential to read the question carefully and understand what is being asked. If there is a graph or chart that accompanies the question, study it and use it to arrive at the correct answer.

Understanding the Different Question Types in GMAT Quantitative

There are different types of questions in the GMAT Quantitative section, ranging from arithmetic to statistics. You should familiarize yourself with the different types of questions and learn the best approach to solving them. This way, you will know what to expect on test day and be adequately prepared.

Effective Approaches for Solving Challenging GMAT Quantitative Questions

Sometimes, you will encounter challenging questions that require more time and effort to solve. In such cases, breaking down the problem into smaller steps can be helpful. Also, consider using the process of elimination, and look for patterns or shortcuts that can speed up your calculations.

Importance of Confidence and Calmness During the Exam

Finally, it's crucial to stay calm and confident during the exam. Remember that the GMAT tests your ability to apply basic math skills to solve business problems. Trust your preparation and take the time to read and understand the questions before answering. If you encounter challenging questions, take a deep breath and move on to the next question.

Reviewing the Basics: Essential Math Concepts for the GMAT Quantitative Section

It's essential to review the basics of math concepts tested on the GMAT Quantitative section. These include integers, algebra, geometry, probability, and statistics. Understanding the fundamental concepts and their application in real-life situations can help you solve the questions faster and with more accuracy.

Tips for Overcoming Anxiety and Stress During the Exam

Lastly, test anxiety is a common problem that many test-takers face. To overcome anxiety, ensure that you get adequate sleep and rest before the test day. Take deep breaths to calm your nerves and avoid rushing through the questions. Remember, the GMAT is just one part of the overall evaluation process. Determine your desired score and approach the exam with a positive and confident mindset.

In conclusion, solving problem-solving questions in the GMAT Quantitative section requires practice, strategy, and time management. Utilize online resources, practice tests, and review the basics of math concepts tested on the exam. With the right preparation, mindset, and confidence, you can ace the GMAT Quantitative section and achieve your desired score.

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It is composed of 20 questions that ask candidates to assess how multiple sources and types of information – including graphic, numeric, and verbal – relate to one another and can be leveraged to make informed decisions. Questions may require math, data analysis, verbal reasoning, or all three. Candidates can use an on-screen calculator while working on this section. 

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