gmat problem solving section

Recently viewed courses

Recently viewed.

Find Your Dream School

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

   COVID-19 Update: To help students through this crisis, The Princeton Review will continue our "Enroll with Confidence" refund policies. For full details, please click here.

4 Tips to Tackle GMAT Math Problem Solving Questions

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

GMAT Problem Solving the GMAC Way

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

The Quantitative section tests three broad content areas:

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

Read More: GMAT Practice Questions

Tips for GMAT Math Problems

1. remember what the gmat tests..

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

2. Practice working with different forms of numbers.

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

Read More: GMAT Sentence Correction Tips

3. Use the answer choices for help.

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

4. Study the wrong answers.

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

Practice for the GMAT Math Section

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

START A FREE PRACTICE TEST

• GMAT  
• Business School  

Find MBA Programs Matched to Your Interests

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

Top Online MBA Programs

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

Best Career Prospects

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

Top Schools for Entrepreneurship

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

Free MCAT Practice Test

I already know my score.

MCAT Self-Paced 14-Day Free Trial

Enrollment Advisor

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

1-877-LEARN-30

Mon-Fri 9AM-10PM ET

Sat-Sun 9AM-8PM ET

Student Support

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

Mon-Fri 9AM-9PM ET

Sat-Sun 8:30AM-5PM ET

Partnerships

• Teach or Tutor for Us

College Readiness

International

Advertising

Affiliate/Other

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

Register Book

Local Offices: Mon-Fri 9AM-6PM

• SAT Subject Tests

Academic Subjects

• Social Studies

Find the Right College

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

School & District Partnerships

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

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

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

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

• Skip to content

Free GMAT Test Questions

Welcome to our Question Bank!

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

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

All Questions

Quantitative reasoning - problem solving, quantitative reasoning - data sufficiency, verbal reasoning - critical reasoning, verbal reasoning - reading comprehension, verbal reasoning - sentence correction.

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

Getting the Most Out of Your Prep Class

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

Robo-Reader Report

Sentence Correction Secrets

• Exam Prep >
• Prepare for Business School >
• Business School & Careers >
• Explore Programs >
• Connect with Schools >
• How to Apply >
• Help Center >

Every journey needs a plan. Use our Career Guide to get where you want to be. 

Creating an account on mba.com will give you resources to take control of your graduate business degree journey and guide you through the steps needed to get into the best program for you.

• About the Exam
• Register for the Exam
• Plan for Exam Day
• Prep for the Exam
• About the Executive Assessment
• Register for the Executive Assessment
• Plan for Assessment Day
• Prepare for the Assessment
• NMAT by GMAC
• Shop GMAT Focus Official Prep
• About GMAT Focus Official Prep
• Prep Strategies
• Personalized Prep Plan
• GMAT Focus Mini Quiz
• Executive Assessment Exam Prep
• NMAT by GMAC Exam Prep

Prepare For Business School

• Business Fundamentals
• Skills Insight

Business School & Careers

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

Explore Programs

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

Connect with Schools

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

How to Apply

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

Help Center

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

GMAT Problem Solving: Flexibility is the Key

Chris Kane - Menlo Coaching

Chris Kane is a mba.com Featured Contributor.

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

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

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

Tip #1: Read Carefully! 

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

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

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

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

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

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

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

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

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

Tip #2: Be Flexible in Your Approach

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

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

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

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

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

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

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

Tip #3: Know What You Need to Know

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

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

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

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

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

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

GMAT Problem Solving Best Practices

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

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

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

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

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

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

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

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

Sample GMAT Problem

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

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

(A) $1,500 more

(B) $1,200 more

(C) $100 less

(D) $300 less

(E) $1,500 less 

Explanation:

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

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

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

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

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

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

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

Correct answer is thus D.

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

Final Thoughts

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

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

Chris Kane is an mba.com Featured Contributor.  

• Menlo Coaching
• Practice Questions
• Problem Solving

Are you ready for the GMAT Focus Edition? Save 10% on our GMAT Prep Course, starting March 16.

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

Book a GMAT Strategy Call with Hailey

Replies in 24 hours

[email protected]

✓ Get feedback on your profile as a test-taker

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

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

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

• Skip to content

GMAT Prep Courses & Tutoring

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.

GMAT Focus Intro: Quantitative Section

Next Lesson

GMAT Focus Intro: Verbal Section

Intro to the gmat focus.

GMAT Focus Intro: Test Day

GMAT Focus Intro: Data Insights Section

Computer Adaptive Testing

GMAT Focus Scores

Pacing, Skipping, and Guessing

Shorter GRE vs. GMAT Focus Content Differences

The Ultimate Guide to GMAT Quantitative Section

The GMAT Quantitative Section is a critical component that assesses your ability to analyze data and solve mathematical problems. Aspiring business school candidates often find this section challenging, but with the right strategies and preparation, success is within reach.

In this comprehensive guide, we will delve into the key aspects of the GMAT Quantitative Section, providing you with valuable insights, expert tips, and effective techniques to boost your confidence and maximize your score.

1: Understanding the GMAT Quantitative Section

A. overview of the gmat quantitative section.

Delving into the GMAT Quantitative Section, it’s crucial to understand its structure and format. This section, designed to assess your quantitative reasoning abilities, introduces two distinct question types: Problem Solving and Data Sufficiency. In the Problem-Solving segment, candidates encounter mathematical problems that require thoughtful solutions. On the other hand, the Data Sufficiency questions evaluate your ability to determine whether the given information is adequate to answer a problem. By familiarizing yourself with the format and nuances of these question types, you can enhance your preparation and approach the GMAT Quantitative Section with confidence.

b. Importance of the Quantitative Section

Understanding the significance of the Quantitative Section is crucial for prospective business school applicants. Business schools place a strong emphasis on quantitative skills due to their relevance in various aspects of management and decision-making. Your performance in the Quantitative Section significantly influences both your overall GMAT score and your chances of gaining admission to business school. A robust quantitative skill set is highly valued in the business world, and business schools use this section to assess your ability to analyze and interpret data, solve complex problems, and make informed decisions—a skill set vital for success in the challenging and dynamic business environment. Therefore, excelling in the Quantitative Section not only enhances your GMAT score but also strengthens your candidacy for admission to top-notch business programs.

2: GMAT Quantitative Question Types

A. problem solving.

Explore the GMAT Quantitative section, specifically delving into the Problem-Solving question type. This section offers a comprehensive breakdown of the Problem Solving questions, providing insights into diverse mathematical problems that you may encounter on the GMAT. Discover effective tips for approaching and solving these problems, gaining valuable strategies to enhance your performance in the Problem-Solving segment of the GMAT Quantitative section.

b. Data Sufficiency

Explore the various question types within the GMAT Quantitative section, starting with a detailed focus on Data Sufficiency. Delve into a comprehensive explanation of the intricacies behind Data Sufficiency questions, gaining a thorough understanding of the structure and expectations. Uncover valuable strategies designed to enhance your efficiency in evaluating the sufficiency of provided data. This insightful exploration goes beyond the surface, equipping you with the knowledge and skills needed to tackle GMAT Quantitative questions with confidence. Elevate your preparation with a nuanced understanding of Data Sufficiency, paving the way for success on exam day.

3: GMAT Quantitative Content Areas

GMAT Quantitative Content Areas encompass a range of essential mathematical concepts crucial for success on the exam. The Arithmetic section offers a thorough review of fundamental arithmetic concepts, accompanied by practice problems and detailed step-by-step solutions to reinforce understanding. In the Algebra segment, you’ll find comprehensive coverage of algebraic concepts, along with problem-solving techniques and helpful shortcuts designed to enhance your efficiency in tackling GMAT algebraic problems.

The Geometry section provides an overview of key geometry topics and formulas, equipping you with the knowledge needed to visualize and effectively solve geometry problems on the GMAT. Lastly, the Statistics and Probability content delves into the explanation of statistical and probability concepts, demonstrating their application in GMAT questions. This comprehensive coverage ensures that you are well-prepared for the quantitative challenges of the GMAT, with insights and strategies to approach each content area confidently.

4: Effective Preparation Strategies

4.1 creating a study plan.

Craft a study plan tailored to your journey. Uncover personalized strategies based on your strengths and weaknesses, ensuring a targeted approach to conquering the GMAT Quantitative Section. Learn the art of balancing your quantitative preparation with equal focus on other critical test sections.

4.2 Resources for GMAT Quantitative Preparation

Navigate the sea of study materials with confidence. Discover recommended books, online courses, and practice tests that will elevate your GMAT Quantitative preparation. Unearth the power of utilizing official GMAT materials to ensure effective and comprehensive readiness.

4.3 Time Management Tips

Master the clock and conquer the GMAT Quantitative Section. Explore proven strategies for efficient time management, with practice exercises designed to enhance both speed and accuracy. Transform time from a challenge into your greatest ally during the exam.

5: Advanced Tips and Tricks

5.1 shortcut techniques.

Unlock the secrets to time-saving success. Delve into shortcut techniques designed for solving complex quantitative problems swiftly and effectively. Learn the art of choosing the right shortcut at the right moment, empowering you to navigate the GMAT Quantitative Section with finesse.

5.2 Common Mistakes to Avoid

Navigate the pitfalls with wisdom. Identify and steer clear of common mistakes that lurk in the GMAT Quantitative Section. Arm yourself with tips for sidestepping errors during the exam, ensuring a smoother path to success.

5.3 Mock Tests and Analytics

Experience the real deal before the big day. Grasp the importance of taking full-length practice tests to simulate the GMAT environment. Learn to dissect your performance through analytics, gaining insights to refine and optimize your study plan for peak readiness.

Conclusion:

By understanding the question types, focusing on key content areas, and implementing effective study strategies , you can boost your confidence and enhance your performance on test day.

Remember, consistent practice, dedication, and a well-structured study plan are the keys to success in conquering the GMAT Quantitative Section and ultimately securing admission to your desired business school.

Frequently Asked Questions for The Ultimate Guide to GMAT Quantitative Section

Q1: what is the gmat quantitative section.

A1: The GMAT Quantitative Section is part of the Graduate Management Admission Test, assessing candidates’ mathematical and analytical skills. It consists of Problem Solving and Data Sufficiency questions, evaluating your ability to interpret data, solve quantitative problems, and make informed decisions.

Q2: How is the GMAT Quantitative Section structured?

A2: The Quantitative Section is structured into two types of questions: Problem Solving and Data Sufficiency. Problem Solving involves solving mathematical problems, while Data Sufficiency assesses your ability to determine if given information is sufficient to solve a problem.

Q3: Why is the GMAT Quantitative Section important for business school admissions?

A3: Business schools value quantitative skills as they are crucial for success in various MBA programs. Your performance on the GMAT Quantitative Section contributes to your overall GMAT score, which is often a significant factor in admissions decisions.

Q4: How can I prepare for the GMAT Quantitative Section?

A4: Effective preparation involves creating a personalized study plan, utilizing recommended resources, and practicing regularly. Focus on key content areas like arithmetic, algebra, geometry, statistics, and probability. Mock tests and time management strategies are also essential.

Q5: Are there specific resources you recommend for GMAT Quantitative preparation?

A5: Yes, consider using official GMAT materials, reputable GMAT prep books, and online courses. Practice tests provided by the official GMAT website are valuable for getting a feel for the exam format.

Q6: What are some time management tips for the GMAT Quantitative Section?

A6: Allocate specific time for each question, practice pacing during your study sessions, and be mindful of the clock during practice tests. Developing a time-conscious approach is crucial for success in this section.

Q7: Are there any shortcut techniques for solving GMAT Quantitative problems?

A7: Yes, this guide covers shortcut techniques for certain types of problems. While they can be time-saving, it’s important to use them judiciously and ensure accuracy. Practice with a variety of problems to determine when shortcuts are most effective.

Q8: How do mock tests contribute to GMAT Quantitative preparation?

A8: Mock tests simulate the actual GMAT experience, helping you familiarize yourself with the format, assess your strengths and weaknesses, and refine your time management skills. Regularly reviewing and analyzing mock test results is essential for improvement.

Q9: What common mistakes should I avoid in the GMAT Quantitative Section?

A9: This guide outlines common pitfalls, such as misinterpreting questions or overlooking key information. Being aware of these mistakes and practicing to avoid them will enhance your performance on test day.

Q10: Can success in the GMAT Quantitative Section improve my chances of admission to business school?

A10: Yes, a strong performance in the GMAT Quantitative Section can positively impact your overall GMAT score, strengthening your business school application. However, it’s important to balance performance across all sections for a well-rounded application.

Related Posts

Top gmat tips for time management.

GMAT Exam Day Essentials: What to Expect

Related Directories

Search for schools, colleges, universities, courses, coaching centers, and more..., start typing and press enter to search.

GMAT Prep Online Guides and Tips

Gmat quantitative: 10 tips to master the math section.

The GMAT quantitative section is probably the most notorious and daunting section of the exam. There are many myths surrounding the quant section of the GMAT, such as that it tests extremely advanced math concepts or that it’s impossible to achieve a perfect score. However, by building your understanding of the quant section through careful preparation, it’s more than possible to do well on this challenging part of the GMAT.

In this complete GMAT quantitative review, I’ll be giving you an in-depth look into the format of the section and what skills are tested on it. I’ll also take you through a detailed look at the two types of GMAT quant questions (data sufficiency and problem solving). Finally, I’ll give you tips that’ll help you achieve success in your test preparation and on test day.

GMAT Quantitative Overview

The GMAT quant section tests your ability to analyze data and draw conclusions using reasoning skills.   There are 31 multiple choice questions on this section that test your abilities in these areas, and you’ll have 62 minutes to complete the section. The quant section is the third section of the test, after the analytical writing assessment and integrated reasoning sections.

Like the two previous sections on the GMAT, you’ll take the quant section on a computer. However, unlike the integrated reasoning and analytical writing assessment, the quant section is adaptive. What that means is that the difficulty of the questions you get will be adjusted as you get questions right or wrong. If you’re struggling, you’ll receive easier questions. If you’re doing well, you’ll receive more difficult questions. Your score on the quant section is determined by three things: the number of questions you answer, the number of questions you answer correctly, and the difficulty of the questions you answer.

Quant scores technically range from 0 to 60, but the range in which people actually score is 6 to 51. Your quant score also contributes to your GMAT total score, which ranges from 200 to 800.

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

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

What’s Tested on the GMAT Quantitative Section?

The quant section tests your content and analytical knowledge of basic math concepts, such as arithmetic, algebra, and geometry. Contrary to popular belief, the GMAT quant section doesn’t test on advanced math concepts. In fact, you only need to know high-school-level math for the GMAT quant section. You’ll see the following concepts on the test:

• algebraic equations and inequalities
• percentages
• exponents and square roots
• geometry and coordinate geometry
• number lines
• variable operations

Rather than testing your knowledge of complex mathematical concepts, the GMAT wants to see how you apply your knowledge of basic math concepts on two types of questions: data sufficiency and problem solving.  While both question types will require you to do the same kinds of math, they’re testing very different skills. The problem solving questions test how well you can figure out the answers to different kinds of numerical problems, such as knowing how much commission to give on the sale of a good. The data sufficiency questions test your ability to determine whether information is adequate enough to solve problems. We’ll talk more about these two types of questions in the next section.

The 2 Types of GMAT Quant Questions

There are two types of GMAT quantitative questions: data sufficiency and problem solving. In this section, I’ll go into more detail about the format of each question type and give you an example problem and solution for each.

If you’d like to get more in-depth information about strategies for either of these sections, check out our detailed data sufficiency and problem solving guides (coming soon).

Data Sufficiency

Data sufficiency questions are multiple choice questions that come with two statements of data. Your job is to figure out whether or not the statements provide sufficient data to answer the question. Then, you’ll have to decide whether one or both statements, by themselves or together, give you enough information to answer the problem. You’ll have the same five answer choices for every data sufficiency question:

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

Let’s look at what a data sufficiency question looks like in practice.

Data Sufficiency Sample Question

Here’s an example of a data sufficiency sample question that’s retired from an actual GMAT.

First, let’s look at the features of this data sufficiency question. Notice how the question comes first (“Is the average (arithmetic mean) of x and y greater than 20?”). After that, the two statements are listed. Your job is to figure out whether each of those statements is enough to solve the question, either by themselves or together. Let’s look at the solution for that problem.

Data Sufficiency Sample Question Explanation

The first step for any question on the quant section is to understand what the question is asking you to find. This question is asking you to determine the mean of x and y. The mean (or average) can be expressed as the sum of both numbers divided by 2. So, you can express the mean of x and y in either of these equations:

(x + y)/2 > 20

x + y > 40

Now, you’ll want to turn your attention to each statement. Let’s look at statement 1 first. For this statement, you’ll need to express the statement as an equation and then simplify to solve for x + y. First, let’s figure out your equation. The statement says that the average of 2x and 2y is 48. That information yields this equation:

(2x + 2y)/2 = 48

Next, you can simplify to isolate x and y.

2x/2 + 2y/2 = 48

Think back to the first inequalities. We said that we can express the mean of x and y as either (x + y)/2 > 20 or x + y > 40. In the math we just did for statement 1, we simplified the equation to show that x + y = 48. 48 is greater than 40, which satisfies the requirement that x + y > 40. That means that the information is sufficient.

Now, let’s look at our second statement. Whenever you’re solving a data sufficiency question, you want to first solve the statements by themselves before considering them together. We solved statement 1 by itself, now we’re solving statement 2 by itself.

Statement 2 says that x = 3y. That means that we can substitute for x in our original inequality.

3y + y > 40

Remember, x = 3y. So, in my second equation I substituted in 3y for x. Now, I can combine like terms.

So, solving this inequality shows us that y is greater than 10. But let’s think back to what the question is asking us. The question is asking us if x + y > 40. From solving this inequality, we don’t have enough information about y or about x to see if x + y > 40.

You can also solve statement 2 by substituting values for x and y that satisfy the condition x = 3y. For instance:

If y = 7 and x = 21 then (x + y)/2 = 14, which is NOT greater than 20.

If y = 40 and x = 120, then (x + y)/2 = 80, which IS greater than 20.

Want to improve your GMAT score by 60 points?

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

Because there’s the possibility to get an answer greater than OR less than 20 for statement 2, we’ll need more information to solve the problem.

The correct answer to this sample question is, then, is A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Problem Solving

Problem solving questions are multiple-choice questions that test high school math skills. These questions are much more traditional and straight-forward than data sufficiency questions. For these questions, you’ll need to use basic math concepts from topics like arithmetic, algebra, and geometry to solve math problems. Let’s take a look at a problem solving sample equation.

Problem Solving Sample Question

Here’s an example of a problem solving sample question that’s retired from an actual GMAT.

Notice how the problem solving sample question looks much more like a question that you would see in your math class or on another standardized test. All problem solving questions have five multiple choice answers.

Problem Solving Sample Question Explanation

The first step to solving this problem is to figure out what it’s asking you and what it requires that you know. You’re trying to figure out the total cost of food for 7 adults on a 5-day trip. In order to do that, you need to figure out the cost of food per day for each adult. You can find that by looking at the costs of the 3-day trip.

In order to determine the food costs per person per day, divide the total food cost ($60) by the total number of adults (4), and then divide that by the number of days (3). Your equation should be: (60/4)/3 = x, when x is the food cost per person per day.

(60/4)/3 = x

The food cost per person per day is $5. Let’s plug that into an equation to determine the cost of food on the 7-day trip:  $5 (food cost per person per day) * 7 (number of adults) * 5 (number of days) = y (total cost of food on a 7-day trip)

5 * 7 * 5 = y

5 * 7 * 5 = 175

Total food cost per day on a 7-day trip is $175. So the correct answer is B.

10 Tips for Mastering the GMAT Quantitative Section

In this section, I’ll give you some tips that’ll help you as you practice and get ready to take the GMAT and some tips that’ll help you succeed on test day.

Overall GMAT Quant Study Tips

In your GMAT quantitative review, keep in mind these overall tips that’ll help you build your speed, accuracy, and confidence in solving data sufficiency and problem solving questions.

Master the Fundamentals

The GMAT quant section only tests high school math concepts. That means that you’ll have likely seen every skill you need to master the test. The key, then, lies in mastering these fundamentals. You won’t be able to use a calculator on the GMAT, so you’ll have to be fast with your basic calculations. Practice multiplying and dividing decimals and fractions. Memorize the exponent rules. Memorize common roots and higher powers. These simple tips will build your confidence and save you time on test day.

Use What You Know

GMAT quant questions are designed to look very complex and intimidating. However, 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 these questions by using what you know. If you break the problem down into small steps, beginning with what you know, you’ll be able to work towards an answer.

Plug-in Smart Numbers

Plugging-in numbers is a useful strategy for solving questions. If a question gives you only variables and doesn’t ask you to solve for a number, you can pick values for the variables to make them easier to work with or to test statements.

Want to Identify YOUR GMAT Strengths and Weaknesses?

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

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

However, you want to make sure you’re using smart numbers. -1, 1, and 2 are good numbers to plug in if you don’t have any confines, because they’re easy and manageable. If the question asks you to use a specific type of number (e.g., a multiple of 3), make sure you’re using one that’ll be easy to do basic calculations with (e.g., use 6 instead of 54).

Data Sufficiency Tips

The data sufficiency section is different than any other math test section you’ve seen before. Here are some tips to keep in mind as you’re preparing for and taking the GMAT.

Evaluate the Statements Individually First

Evaluating each statement individually will help you answer data sufficiency questions quickly and more easily. Evaluate statement 1 first, then evaluate statement 2 by itself. When you do evaluate statement 2, you’ll need to forget everything you did for statement 1. Pretend that they’re two different questions. Once you’ve determined whether each statement is sufficient on its own, you’ll be able to put them together. This strategy will also save you time. For instance, if neither statement is sufficient on its own, you’ll be able to eliminate answers A, B, and E. If both statements are sufficient on their own, you’ll be able to eliminate A, B, C, and E right away.

Memorize the Five Answer Choices

Every single data sufficiency questions has the same 5 possible answers:

The 12TEN mnemonic can help you remember those answers and save you time:

• 1: only statement 1
• 2: only statement 2
• T: both statements together
• E: either statement
• N: neither statement

Know the Two Types of Questions

There are two basic kinds of data sufficiency questions: value questions and yes/no questions. By learning to identify which type a given question is, you can be sure you understand what it’s asking and how to answer it.

Value questions ask you to find a numerical value (e.g., what’s the value of 5x?). For value questions, if you’re able to find a specific value using the information in either statement, then that statement is sufficient.

Yes/no questions ask you whether or not something is true (e.g., is y an even number?). For yes/no questions, a definitive yes or a definitive no answer are both considered sufficient. An answer that is sometimes yes or sometimes no is not sufficient.

Remember: a definitive answer is always sufficient. An answer that may or may not be correct is not sufficient.

GMAT Quantitative Test Day Tips

Here are some tips that’ll help you ace the quant section on test day.

Spend time reviewing the information in graphs, charts, and tables

There will be a number of questions on the GMAT quant section that require you to interpret charts, graphs, and tables. Try to spend at least 30 seconds reviewing the information on these. It’ s extremely important that you read the axis labels, the key, and the units of measurement so that you’re correctly interpreting the information contained in the graph, chart, or table and using the right information to make your calculations.

Read questions carefully

One of the most common mistakes you can make on the GMAT is to answer the wrong question. The people who write the GMAT will purposefully include questions that ask things like “Which of the following may not be true?” which can be commonly misread or misunderstood as “Which of the following may be true?” Make sure that you read every question carefully so you’re finding the correct answer to the correct question.

use your scrap paper

Even though the GMAT quant section test on high school math skills, use your scrap paper as much as possible. Writing down your calculations will help you see any mistakes and force you to make sure you’re thinking through every step of the question, especially since you can’t use a calculator on the GMAT quant section.

work backwards

If you’re not sure where to start on a question that asks you to solve for a specific value, remember that the test has already given you the right number — you just have to find it among the wrong ones. You can work backwards by plugging in the possible answers until you find one that works.

Moreover, the GMAT normally arranges answer choices in the ascending numerical value, so you can save time by starting with the middle answer. Then you can determine whether you need to go higher or lower with your answer and eliminate multiple incorrect answers at once.

GMAT Quantitative Review: What You Need to Know

The GMAT quant section can be daunting, but with careful preparation and attention-to-detail on test day, you’ll be able to master it. Spend time during your practice developing a deep familiarity with the two types of questions on the quant section (data sufficiency and problem solving) and mastering the basic math fundamentals tested on this section and you’ll be well on your way to achieving your goal score.

What’s Next?

If you think you’ve gotten a good handle on the quant section, check out our guide on mastering the three questions of the GMAT verbal section .

Still confused by data sufficiency? Check out our in-depth guide to learn more about this unique test question type .

Find out more about what makes up your  GMAT total score  and how business schools weight it against your quant score.

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

Share this:.

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

Author: 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

Save 10% on All AnalystPrep 2024 Study Packages with Coupon Code BLOG10 .

• Payment Plans
• Product List
• Partnerships

• Try Free Trial
• Study Packages
• Levels I, II & III Lifetime Package
• Video Lessons
• Study Notes
• Practice Questions
• Levels II & III Lifetime Package
• About the Exam
• About our Instructor
• Part I Study Packages
• Part I & Part II Lifetime Package
• Part II Study Packages
• About your Instructor
• Exams P & FM Lifetime Package
• Quantitative Questions
• Verbal Questions
• Data Insight Questions
• Live Tutoring
• EA Practice Questions
• Data Sufficiency Questions
• Integrated Reasoning Questions

GMAT Problem Solving: Technical Mathematics

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

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

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

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

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

Technical Mathematics Problem Solving Process

Word problem example.

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

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

Problem Solving process

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

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

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

This matches choice E.

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

Arithmetic Example

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

• \(3\sqrt{5}\)
• \(10\sqrt{3}\)

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

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

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

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

Geometric Example

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

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

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

Write down formulas and avoid drawing as much as possible

Area of rectangle = lw

 Diameter = diagonal = 10

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

                    Area of rectangle = lw

                     Diameter = diagonal = 10

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

                     Pythagorean integers = 6 : 8 : 10

                         l = 6, w = 8, d = 10

                       Area of rectangle = 6 × 8 = 48

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

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

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

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

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

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

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

Sample Problem Solving question

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

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

If \(\text{xy}≠0\)

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

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

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

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

The correct answer is 25, choice E.

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

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

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

Offered by AnalystPrep

GMAT Reading Comprehension: Exam Overview

Gmat quantitative reasoning section: number properties, gmat data sufficiency word problems.

Of the 31 questions you will come across in the quantitative reasoning section... Read More

How to Answer Challenging FRM® Exam Q ...

The FRM exam is challenging, and even the most prepared candidate will encounter... Read More

7 Tips to Advance Your Career as a Fin ...

A financial risk manager (FRM) is an individual in an organization who identifies... Read More

When is the New 2021 CFA® Exam Window ...

At the beginning of 2021, the CFA Institute offered February 2021 level I... Read More

GMAT Quant Section Breakdown

Last Updated on May 15, 2023

If you are new to studying for the GMAT and are already familiar with the overall format and structure of the exam , you may still be wondering what types of questions appear in the Quant section of the GMAT. This article provides a GMAT Quantitative section breakdown and discusses the concepts tested in the Quant section. It also discusses the specific Quant question types you can expect on the exam.

Here are the topics we’ll cover:

The quant section of the gmat, what quant topics does the gmat test, each major math topic has many subtopics.

• Don’t Try to Predict Which GMAT Quant Topics You’ll See

How Target Test Prep Does Topical Learning

The two types of gmat quant questions, problem solving question 1, problem solving question 2, value data sufficiency example, yes/no data sufficiency question example.

• GMAT Quant Summary

How Many Questions Are in the GMAT Quant Section?

How long is the gmat quant section, what are the topics in gmat quant, how hard is the gmat quant section, what’s next.

Let’s first discuss the general format of the Quant section of the GMAT.

The Quant section is just one of four sections on the GMAT : Quant, Verbal, Integrated Reasoning (IR), and the Analytical Writing Assessment (AWA). However, along with the Verbal section, Quant is recognized as one of the more critical sections of the GMAT. For one, Quant and Verbal are the only contributors to the all-important “0 to 800 score.” For another, many business schools place particular weight on the Quant score because it is a reliable predictor of how well you will perform in your business school classes.

The Quant section of the GMAT is one of the most important sections of the GMAT.

The Quant section consists of 31 questions and has a time limit of 62 minutes. Depending on the section order you select on test day, the Quant section can be the first, second, or third section on your GMAT.

Now that we are familiar with the general makeup of the GMAT Quant section, let’s discuss the Quant topics tested on the GMAT.

If you’ve ever spoken with anyone about GMAT Quant, you’ve likely heard that the GMAT tests “high school math.” Thus, regardless of what age you are when you begin your GMAT prep, at some point, you should start to lean on at least some of the things you learned in high school math as a foundation for GMAT Quant.

GMAT Quant comprises many math topics you learned in high school.

The 21 major math topics tested on the GMAT are as follows:

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

There are 21 major math topics tested on the GMAT.

You may say, wow, there are only 21 major Quant topics on the GMAT. However, that is not the whole story. Every major math topic has many associated subtopics.

For example, let’s look at the Quant topic of rates. Sure, we need to know that rate x time = distance. However, we also have to be familiar with many subtopics of rates. For example, you need to know topics such as average rates, converging rates, diverging rates, catch-up rates, catch-up and pass rates, round trip, etc. Thus, to truly master GMAT Quant, be ready to deal with the hundreds of subtopics that could show up in the GMAT Quant section.

Also, I have some bad news. There is no way to predict the exact Quant concepts you will see on your exam. Let’s discuss that now.

Although there are only 21 major Quant topics, there are hundreds of subtopics that you must learn to master GMAT Quant.

Don’t Try to Predict Which GMAT Quant Topics You’ll See 

While we can make some broad generalizations about which GMAT topics are most commonly tested, the GMAT is generally quite unpredictable. Test-takers see a random array of questions. Furthermore, this mix of questions differs from test to test. Also, you can’t assume that what you see on any official practice test will mimic what you see on test day.

If you don’t believe me, let’s use some basic logic. Do you think that the folks at GMAC (the developers of the GMAT) would allow students to study only the six official practice exams to determine what Quant topics will appear on test day? That scenario is quite unlikely, unless the plan is to have all test-takers knock the GMAT out of the park.

The test-makers know that part of the GMAT’s difficulty is that there are so few questions on the test, but those questions can span hundreds of topics. In other words, part of the test’s difficulty rests on the fact that we cannot accurately forecast what we will see from one GMAT to the next .

It’s impossible to predict the exact topics that will be covered on any given GMAT.

So, the conclusion is that all Quant topics are essential. In other words, don’t base what you study on the volume of specific topics in your practice exams or a past GMAT exam you took.

With that point in mind, let’s discuss the best way to study GMAT Quant.

The Best Way to Study GMAT Quant

We’ve established that you must learn a great number of concepts to succeed on GMAT Quant. A great way to learn so many concepts is to take a topical approach to your prep. Topical learning consists of learning just one topic at a time, and then practicing only that topic until you have achieved mastery.

If you use this topic-by-topic, linear approach to GMAT preparation, you’ll be employing the most effective strategy to guarantee that you fully comprehend each GMAT Quant topic. As a result, you won’t waste time attempting to understand complex topics before you fully grasp the fundamentals.

For example, do you think it would be helpful to jump from quadratic questions to ratio questions to geometry questions before fully grasping any of those topics? I think we can all agree that the answer is no.

If you randomly jump from topic to topic and do not give each topic the care and attention it deserves, it will be nearly impossible to develop your GMAT Quant skills. Rather than moving forward through your prep, you’ll just be treading water.

Topical learning allows you to learn each GMAT topic individually before progressing to the next.

To get a better idea of how topical learning works, let’s take a closer look at the TTP study plan.

At TTP, the foundation of our study plan is topical learning and practice. We ensure that students focus on just one Quant or Verbal topic at a time. Only once they master a topic do they move on to a new topic.

For example, mission 4 of the TTP study plan contains the Quant chapter on quadratic equations. So, the first task of any student who reaches mission 4 is to learn about linear and quadratic equations. They learn about single variable equations, equations with two or more variables, the substitution method of solving linear equations, factoring quadratic equations, foiling quadratic equations, the zero product property, quadratic identities, the difference of squares, factoring by grouping, etc.

Each subtopic makes up a lesson, and within each lesson, we present two to four example questions testing that specific concept. So, if you just learned about quadratic identities, for example, you would practice up to four example questions just on quadratic identities.

Also, after a chapter has been completed, several easy, medium, and hard chapter tests are presented. They test the student on the concepts just learned. A detailed summary of strengths and weaknesses is provided after each test.

While the TTP method of topical learning is just one example, it should give you a good picture of how to study GMAT Quant effectively.

A great way to learn GMAT Quant is to take a topical approach to your learning and practice.

So, now that we have a good approach for studying GMAT Quant, let’s discuss the types of questions you might see in the GMAT Quant section and provide some examples.

In the GMAT Quant section you will encounter two types of Quant questions:

• Problem Solving
• Data Sufficiency

Of the 31 questions in the Quant section, about two-thirds of them (roughly 20) are Problem Solving questions. Data Sufficiency questions account for the remaining 11 questions in the Quant section.

Of the 31 questions in the Quant section, Problem Solving questions represent 2/3 and Data Sufficiency questions make up 1/3.

Let’s discuss Problem Solving questions in a bit more detail.

GMAT Quant Problem Solving Questions

Problem Solving questions are multiple-choice questions. So, a Problem Solving question has five possible answer choices (A, B, C, D, and E), and only one of those answer choices is correct.

A Problem Solving question can test you on any of the 21 major Quant topics or the hundreds of subtopics. Let’s look at a few examples to get a feel for GMAT Problem Solving questions.

What is the units digit of 3^11?

The “major” topic here is number properties, and the main subtopic is units digit patterns.

To determine the units digit of 3^11, we must use the pattern of units digits when the base of three is raised to an integer exponent. So, let’s determine that pattern now, starting with 3^1. When listing our exponents below, we will show only the units digit of the result of the exponent, so we can easily spot the pattern.

So, we see that we have a repeating pattern of 4. In other words, the pattern when the base of three is raised to consecutive exponents is 3-9-7-1.

What is important about this pattern is that, since we have a repeating pattern of four , every 4th exponent has the same units digit. Thus, we can conclude that 3^4, 3^8, 3^12, … etc., all have the same units digit of 1.

Thus, the easiest way to determine the units digit of 3^11 is to find the exponent that is a multiple of 4 and also close to 11.

We see that, since 4^12 has a units digit of 1, 4^11 must have a units digit of 7.

Let’s try one more.

Harold is 30 years older than Paloma. If in 10 years Harold will be 3 times as old as Paloma, how old will Harold be in 3 years?

The major topic tested here is general word problems, and the subtopic is age problems.

Our first step to solve the problem is to create two variables:

H = Harold’s age today

P = Paloma’s age today

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

Since Harold is 30 years older than Paloma, we have:

Since in 10 years Harold will be 3 times as old as Paloma, we have:

H + 10 = 3(P + 10)

H + 10 = 3P + 30

H = 3P + 20

Next, we can substitute P + 30 for H in the second equation:

P + 30 = 3P + 20

Thus, Harold is currently 5 + 30 = 35 years old, so in 3 years, he will be 38 years old.

Now, let’s discuss Data Sufficiency problems.

GMAT Quant Data Sufficiency Questions

A Data Sufficiency question often starts with a question stem that includes a question and some optional information, followed by two statements (Statement One and Statement Two).

It is then up to you to decide whether you have enough information, from either or both of the statements, to answer the given question. Thus, the essence of a Data Sufficiency question (unlike Problem Solving) is to test your critical thinking and reasoning skills under a math umbrella.

While this type of analytical math may initially be a bit challenging or even intimidating, many students enjoy solving Data Sufficiency questions by the end of their GMAT prep.

Data Sufficiency questions test both your math and analytical reasoning skills.

To get a better understanding of Data Sufficiency questions, let’s look at the Data Sufficiency answer choices.

The Answer Choices in a GMAT Data Sufficiency Question

Like Problem Solving questions, Data Sufficiency questions have five answer choices. However, unlike Problem Solving questions, the Data Sufficiency answer choices are always the same. Thus, I advise that all of my students memorize the answer choices. They are as follows:

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 Data Sufficiency answer choices.

Let’s now discuss the two types of Data Sufficiency questions: (1) Value questions and (2) Yes/No questions.

Value Data Sufficiency Questions

A Value Data Sufficiency question is one in which we need to determine whether we have enough information to come up with a unique numerical answer. Below are some examples:

— What is the value of x?

— How old is Marcus?

— What is the price of the couch at store A?

— Liz’s investment earned how much interest?

— What is the value of xy?

In a Value question, we must obtain a single value as the answer to the question in order to determine sufficiency.

In a Value Data Sufficiency question, a statement is sufficient if we determine a unique value for what is being asked.

For example, let’s say we have a Data Sufficiency question in which we need to determine the value of x, and statement one is x^2 – x – 12 = 0. Well, factoring that quadratic equation, we have:

(x – 4)(x + 3) = 0

x = 4 or x = -3

Since we have determined two values for x, we see that statement one is not sufficient. However, had the statement been x^2 + 6x + 9 = 0, we would have:

(x + 3)(x + 3) = 0

In this case, since we have just one value for x, statement one is sufficient.

Let’s practice answering a Value Data Sufficiency question.

The ratio of the number of stamps owned by Nancy to the number of stamps owned by Diane to the number of stamps owned by Jill is 2 to 5 to 7. How many stamps does Nancy own?

1) The total number of stamps owned by Nancy, Diane, and Jill is 70.

2) Diane owns 10 fewer stamps than Jill.

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

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

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.

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

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

The major topic tested here is ratios, and the subtopic is general word translations.

To start, we create a ratio with the information provided in the problem stem.

We know that the ratio of the number of stamps owned by Nancy to the number of stamps owned by Diane to the number of stamps owned by Jill is 2 to 5 to 7. Thus, we can create the following ratio:

N : D : J = 2x : 5x : 7x

Our goal is to determine the number of stamps owned by Nancy.

Let’s now consider the statements:

Statement One Alone:

The total number of stamps owned by Nancy, Diane, and Jill is 70.

We can create the following equation:

2x + 5x + 7x = 70

Thus, Nancy owns 2 * 5 = 10 stamps.

Statement one is sufficient to answer the question.

Statement Two Alone:

Diane owns 10 fewer stamps than Jill.

5x = 7x – 10

Once again, we see that Nancy owns 2 * 5 = 10 stamps. Thus, each statement individually is sufficient.

Now, let’s discuss Yes/No Data Sufficiency questions.

Yes/No Data Sufficiency Questions

Unlike the Value question type, in Yes/No Data Sufficiency questions, we do not determine whether we have enough information to get a unique value. Rather, we determine whether we have enough information to get a definitive answer of YES or a definitive answer of NO.

In a Yes/No Data Sufficiency question, a statement is sufficient if we determine a definitive answer of yes or a definitive answer of no.

We must keep in mind that if we get an answer of yes AND an answer of no for any particular statement, then the statement is not sufficient.

For example, let’s say we have a Yes/No Data Sufficiency question in which we need to determine whether x is greater than zero.

If statement one says that x is greater than -2, that statement is insufficient because we could get a yes if x is 10 or a no answer if x is -1.

However, if the statement says that x is greater than 2, it would be sufficient because, regardless of which value we select for x, the value of x will always be greater than zero.

Let’s practice answering a Yes/No Data Sufficiency question.

Is x^2 > x?

1) x > 0

2) x > 1

The major topic tested here is inequalities, and the subtopic is exponents.

Since there is no given information, we can jump right into statement one.

We know that x is greater than zero, and since we should recognize that different types of numbers react differently to being raised to integer powers, let’s first test a positive proper fraction for x, and then test a positive integer value.

When x = 1/2, we have:

Is (1/2)^2 > 1/2?

Is 1/4 > 1/2?

NO, 1/4 is not greater than 1/2.

When x = 2, we have:

Is 2^2 > 2?

Is 4 > 2?

YES, 4 is greater than 2.

Since we have an answer of no for the first case and an answer of yes for the second case, statement one is not sufficient.

It’s important to see that we do not have to plug in values, as we did for statement one, because x is greater than one, which means it can’t be a proper fraction and can’t be equal to 1. Thus, regardless of which values we use for x, we see that x^2 will always be greater than x. Therefore, we will always have an answer of YES. So, statement two is sufficient to answer the question.

GMAT Quant Section Breakdown Summary

The GMAT Quant section consists of 31 questions, and you have 62 minutes to answer them. There are two question types: traditional Problem Solving questions, which have 5 answer choices, and Data Sufficiency questions, which are unique to the GMAT. About two-thirds of the Quant questions are of the Problem Solving type, and the remaining one-third are of the Data Sufficiency type.

Data Sufficiency questions present a stem with basic information, and they pose a question that the student must answer. There are two additional statements presented, called Statement One and Statement Two. The student must evaluate whether each statement leads to a definitive answer to the question posed.

Frequently Asked Questions (FAQ)

There are 31 Quant questions.

You are given 62 minutes to complete the GMAT Quant section.

The topics are generally those you have learned in high school math classes. They include:

Basic arithmetic, linear and quadratic equations, number properties, roots, exponents, inequalities, absolute values, general word problems, rates, work, unit conversions, ratios, percents, statistics, overlapping sets, combinations and permutations, probability, geometry, coordinate geometry, sequences, and functions.

GMAT Quant is not a walk in the park. However, if you give yourself plenty of time to study, use a great study resource, and keep your motivation level high, there is no reason why you can’t excel in GMAT Quant.

Now that you know about the structure of the GMAT Quant section and the types of questions asked, take a look at my article that provides expert tips to improve your Quant score .

You May Also Like...

About The Author

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

Leave a Reply Cancel Reply

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

• +91 630 323 9042
• support@gmatpoint.com

GMAT Point by Cracku

Smarter way to prepare

GMAT Problem Solving Questions With Answers

Problem Solving questions constitute a major chunk of the Quant section of the GMAT. Of the 31 questions that appear in this section, you can expect close to 50% of the questions from problem-solving. In this article, we will be looking into –

What are GMAT Quant Problem Solving Questions?

• 3 examples of GMAT Problem Solving Practice Questions
• 5 tips that can help you ace these questions.

Subscribe To GMAT Preparation Channel

Take Free GMAT Daily Targets

Problem Solving or PS questions are questions that have a question followed by five options. They are very similar to any MCQ question that we come across in our school or university examinations. You need to solve the question and arrive at the answer and mark the correct choice.

There is only one correct answer in Problem Solving Questions.

Problem Solving questions are considered easier than Data Sufficiency questions because they are straightforward. Having said that, a preparation without a proper plan might prove disastrous for these questions.

Let us now take a look at a few Problem-Solving questions to get you started.

Examples – GMAT Problem Solving Questions

Question 1:.

If a regular unbiased die is rolled twice, what is the probability of getting a sum greater than 10 in the two rolls?

In probability, the probability of an event E = The number of favourable outcomes / Total number of outcomes

The first step is to calculate all favourable outcomes.

Let {x,y} represent the two rolls.

For getting a sum greater than 10, we can get a sum of 11 it a sum of 12.

Now, for a sum of 11, we can have these cases – {5,6}, {6,5}

For a sum of 12, we can have these cases – {6,6}

Hence, there are three favourable outcomes.

Total number of outcomes = 6*6 = 36

Hence, probability = 3/36 = 1/12.

Question 2:

The length of the equal sides of an isosceles triangle is 6 cm. What is the maximum possible area of the triangle(in square centimetres)?

Let us assume that one of these 6 cm sides is the base and the angle that the other 6 cm side makes with the base is k degrees.

Now, we know that the area of a triangle whose 2 adjacent sides are known and the enclosed angle is known can be calculated as:

Area = (1/2)*a*b*sin(k)

a = First side

b = Second side

k is the angle enclosed.

Now, a and b are fixed as 6 cm each

If sin k is maximum = 1, the value will be maximum.

Hence, the maximum possible area = (1/2) x 6 x 6 = 18

Question 3:

If a set A has 16 distinct elements all of which are integers and set B necessarily has the square of all elements of set A, what can be the minimum number of elements in set B?

If all 16 elements in A are distinct, say 1, 2, 3, …., 16, then B also has 16 elements 1, 4, 9, ….., 256.

However, to reduce the number of elements of B, we need to have as many elements as possible in A that also has their negative counterpart in A. For example, if 2 is an element, -2 should be an element as well. As a result, if 4 (square of both 2 and -2) is present in B, it will account for 2 elements in A.

Hence, we can have 8 positive numbers in A and their corresponding negative numbers in A. In this way, we can say that B will have a minimum of 8 elements.

Hence, the minimum possible number of elements in B is 8.

Though these examples provide a good sense of what type of GMAT Problem Solving questions you can expect, in no way do they represent the exhaustive list of concepts required for the Quantitative section of GMAT.

Tips to keep in mind:

• Try to take some time out from easy Problem Solving questions so that you can use that time to solve tricky Data Sufficiency questions. Data sufficiency questions usually take more time to solve than Problem Solving questions.
• Do not get stuck in a question for long. If you find yourself trapped in a question for long, take a guess and move on.
• Read the units carefully.
• Look out for negation words. For example: Which of the following are NOT possible values of x?
• Some questions can be solved faster by the use of options. Make sure you don’t solve these questions in a conventional way.

You can check out the Free GMAT Daily Targets on our platform .

Also, check out the Free GMAT Verbal Tests and Quant Tests .

If you are starting your GMAT preparation from scratch, do check out GMATPOINT.

Join GMATPoint Telegram Channel

Hope this article was helpful. Wish you all the best for the GMAT.

Framework approach to problems

Gmat problem solving.

This section discusses solving GMAT problem-solving section, which is a part of quantitative reasoning. Most questions in this case can be solved using basic algebra. We quickly go through a set of 10 questions:

Disclaimer : These questions are sourced from the Official GMAT Guide for 2021 . I in no way claim to be the owner. The goal is to merely list some key questions and discuss the answer/approach to the problem.

The approach to solving the below questions is to define the variables and then writing down the equations based on the statements.

Representing Equations

• But can solved using by representing the first number as a variable n.
• The rest 4 can be represented as (n+1),(n+2), (n+3) and (n+4). The sum becomes 5n+10 .
• The average comes out to ( n+2 ). This is the same as the median of the 5 consecutive integers.
• The answer is (E)

• We have two variables. The 10 and 16 cent coins can be represented as X and Y.
• The first equation is X + Y = 16 while the second equation is 0.1*X + 0.25*Y = 2.35
• Solve this by replacing X in the second equation with the first one and we are good to go ahead.
• 1.6-0.1*Y + 0.25*Y = 2.35 which results in 0.15*Y = 0.75
• The answer is B

The 22nd question had two variables X & Y and two equations . We need as many equations as variables to be able to solve them and thereby being the trick behind lots of Data Sufficiency questions. We cannot solve for all variable values if the number of equations is lower than the variable count.

Units Standardisation

• The trick here is that the statements are represented as per dozen and per 3eggs. The units are different and need to be adjusted.
• Represent everything into dozen as a unit.
• Then later multiply the difference by 5 as required.

• I solved it by writing down all the 24 numbers but can be solved in a better way.
• And crossed all those divisible by 2,3 or 7.
• This comes out to be 17 thereby the answer being 17/24.

Using Dummy Values

• The circumference of a circle is 2*pi*r where r is the radius.
• r comes out to be 25/2
• One side of the square is 25 so the perimeter is 25*4 = 100.

• I assumed x, y, z to be 2,3 & 4 respectively.
• The options are between D & E since the multiplication of the two largest values.
• The option turns out to be 3(2+4) or 4(2+3).
• The second value is 20 > 16 and thereby E.

Approximation

• The first series can be assumed to be 1-8.
• The first set in Y goes from 5-12. Adding 4 to each number.
• The second set in Y goes from -3 to 4.
• We thereby have a complete overlap of the 8 elements.

• The numerator ~60 but greater than 60.
• The denominator is ~ 5. 4.86 + 5*0.03 = ~5
• Thereby we can quickly assume the value to be close to 12.
• The trick was representing 4.86 as 5 for the computation in the denominator with 0.03.

Confusing Statements

• Quickly represent the variables as PF, PNF and HNF.
• The first equation is PF + PNF + HNF = 140.
• The second equation being PNF = HNF + 20
• The third equation is PF = 2*PNF
• The final equation is 3*PNF + HNF = 140 or 4*HNF + 60 = 140
• Re-check this answer because you can get the translation wrong in this case.

• We subtract the values 3,15 and 32 from 72.
• The final value of N+1 = 22, N is thereby 21.
• Answer is C

All the questions are based on algebra and a basic understanding of the mathematical properties of circles, triangles, squares and other aspects of geometry. To quickly move through the questions

• Write equations where ever possible.
• Be careful when translating confusing statements.
• Ensure data units are the same.
• Any missing info can be derived from properties of geometry
• When approximating, get the computation of the large numbers correct and the small ones can be rounded off.

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

Featuring Bruce H.

Nail Overlapping Set Questions on the GMAT and GRE

Tuesday, april 30.

11:00 PM UTC · 45 minutes

Table of Contents

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.

Browse hundreds of expert coaches

Leland coaches have helped thousands of people achieve their goals. A dedicated mentor can make all the difference.

Browse Related Articles

May 24, 2023

How to Solve Data Sufficiency Questions in the GMAT Quantitative Section

Are you struggling with data sufficiency questions in the GMAT quantitative section? Look no further! Our comprehensive guide provides step-by-step strategies and tips to help you solve these tricky problems with ease.

January 24, 2024

Average GMAT Scores by Business School

Discover the average GMAT scores required for admission to top business schools.

March 13, 2024

The Ultimate MBA Application Guide (2024)

A step-by-step guide for every part of the MBA application, with tips and tricks from experts, additional free resources, essay and resume examples, and more.

How to Solve Critical Reasoning Questions in the GMAT Verbal Section

Learn how to tackle critical reasoning questions in the GMAT verbal section with our expert tips and strategies.

How to Solve Graphics Interpretation Questions in the GMAT Integrated Reasoning Section

Learn how to tackle Graphics Interpretation questions in the GMAT Integrated Reasoning section with our comprehensive guide.

How to Solve Table Analysis Questions in the GMAT Integrated Reasoning Section

Learn how to tackle table analysis questions in the GMAT Integrated Reasoning section with our comprehensive guide.

How to Solve Two-Part Analysis Questions in the GMAT Integrated Reasoning Section

Learn how to tackle two-part analysis questions in the GMAT Integrated Reasoning section with our comprehensive guide.

The GMAT Score Range: Test Results and Rankings

Discover the ins and outs of the GMAT score range and how it affects your test results and rankings.

Calculators on the GMAT/GRE: When You Can Use Them

Discover the ins and outs of using calculators on the GMAT/GRE with our comprehensive guide.

Decoding the GMAT: Essential Tips for First-Time Test Takers

If you're a first-time GMAT test taker, this article is a must-read! Discover essential tips and strategies to help you decode the GMAT and ace the exam.

April 9, 2024

GMAT vs. GRE for Business School—Which Should You Take (and How to Ace Both)

Applying to top MBA programs? Click here to determine if the GMAT or GRE is better for you—along with tips and tricks to ace both tests.

How to Improve Problem-Solving for a Higher GMAT Score

Looking to improve your GMAT score? Check out our latest article on how to enhance your problem-solving skills for a higher score.

• E-mail & Password
• Notification Settings
• Global Settings
• Applicant profile
• Update status
• My GMAT info
• --> My Education -->