Introduction - Math Workout for the GMAT

Math Workout for the GMAT

Part I Introduction


So you’ve just purchased this book to help boost your math skills. You want to get an MBA and you know that you need a good GMAT score to get into your top-choice business school. It may be that your math skills are a bit rusty. For example, you may not have taken many (or even any) math classes in college. These days, you probably use a calculator or computer to balance your checkbook, to crunch numbers at work, and to handle any other calculations that come your way. The result is that you haven’t really used your math muscles for several years or more. Or maybe you are comfortable with your math skills. Maybe you were the kid everyone cheated off in math class. However, you lack that edge necessary to push you over the top. You need a strong system you can use to reach that elite score. That’s the bad news.

In either case, at least at some point, you did learn the math that’s tested on the GMAT. None of the concepts is more advanced than high school algebra and geometry. No trigonometry, no calculus, and no multi-variable regression analysis (whatever that is). Even the most challenging problems don’t require you to learn a lot of new stuff; you just need to refresh your memory.

In the following chapters, you’ll cover the math you need to know for the GMAT—and only that. If it’s not on the test, it’s not in this book. You’ll also learn some test-taking strategies specific to the GMAT. This stuff probably won’t help you in your first-year statistics course, but it will help you to get there in the first place. In addition, this book includes an introduction to the new Integrated Reasoning section of the GMAT.


You already know that you have to take the GMAT to get into business school, but there may be a number of other things you’re not so sure about. How important is the GMAT? What’s a good score? What other things do schools consider?

The importance of the GMAT depends on several factors. One is how long you’ve been out of school. If you graduated a long time ago, say more than five years, then MBA programs will place more weight on your GMAT score than they would if you graduated a year or two ago. That’s because they will de-emphasize your college GPA in considering your application, thereby making your GMAT score more important in the mix.

Another factor in the importance of your GMAT score is the particular GMAT score in question. In addition to the overall score (200−800 range), you will receive a separate Math score, Verbal score, Integrated Reasoning score, and AWA (Analytical Writing Assessment) essay score. With the introduction of the new Integrated Reasoning section (as part of the Next Generation GMAT), the scoring breakdown has changed. The Integrated Reasoning section is scored separately from the rest of the test. This section is a blend of math and verbal skills and it is scored on a scale of 1-8 in whole point increments. As far as scoring goes, most schools concentrate on the overall score and the Math score in their admissions decisions. They look at the overall score because it’s a broad measure of your ability. They look at the Math score because many MBA courses require significant use of quantitative skills, and the schools want to ensure that entering students have the necessary mathematical ability.

A good GMAT score is one that will make you competitive with other applicants to the programs of your choice. Check with the programs you’re considering to find out the average GMAT score and GPA for the latest entering class. That GMAT score gives you a good target. If your GPA is below the average, you should shoot for a higher GMAT score to compensate.

Business schools consider many factors in the application process, with GMAT scores, undergraduate GPA, and work experience making up the “big three.” GPA is fairly self-explanatory, and GMAT scores are discussed above. The work experience factor includes both the length of your full-time experience and its nature. Several years of experience are virtually mandatory for the top programs. Schools like to see leadership roles and increasing responsibility in your career to date.

MBA programs will also look at several other factors, including letters of recommendation and your application essays. Although these elements are not counted as heavily as the three factors discussed above, they are still important. If your “big three” qualifications are average for a given program, strong essays and recommendations can help you stand out from the pack.

A full discussion of the various criteria in MBA admissions is beyond the scope of this book; it is, after all, a GMAT math review. However, it is important to give due consideration to all of the elements in your application, not just your GMAT scores.


The GMAT lasts approximately four hours. The test is administered by computer.

The test starts with the AWA essay. You will have 30 minutes to write one essay that’s an Analysis of an Argument. The section after the essay is the new Integrated Reasoning section. You will have 30 minutes to answer 12 questions, which sounds like a piece of cake, right? Most of those questions have multiple parts, though. So you’ll need all of that time to tackle these multi-part questions.

Then you’ll come to the Quantitative section (what we call the Math section), which is the first computer-adaptive section of the GMAT. We’ll explain computer-adaptive tests more in a moment. For now, know that all of the math questions are multiple-choice and you may not use a calculator on this section.

In the Math section, you will have 75 minutes to answer 37 questions, which come in two formats: problem solving and data sufficiency. The problem solving questions are the more familiar format. For these questions, you work the problem, come up with an answer, and choose the answer choice that matches. The data sufficiency format, which is totally unfamiliar to most test takers, is discussed in detail in Part III.

After the Math section, you will have an optional break before the Verbal section, in which you will have 75 minutes to answer 41 questions. The questions come in three formats: sentence correction, critical reasoning, and reading comprehension. Sentence correction questions involve grammar and other issues of sentence construction. Critical reasoning questions require you to analyze the logic of short arguments. Reading comprehension questions require you to find information in long passages.

Approximately one-fourth of the questions will be experimental questions. These questions are not labeled in any way, so you will not know whether a question is experimental. Unlike the others, experimental questions do not affect your score in any way. These questions are being tested for future use, and you are essentially serving as a guinea pig, providing statistical information on the difficulty of the questions through your performance on them relative to the scored questions. Additionally, the difficulty of these questions does not track your performance, as does the difficulty of the scored questions. Therefore, some questions that seem much easier or more difficult than those in the rest of the section may be experimental.


CAT is an acronym for “computer adaptive test.” The test is adaptive because it tries to match the difficulty of the questions to your performance. The better you do, the harder the questions get. The Math and Verbal sections of the GMAT are computer-adaptive tests. The Integrated Reasoning and Essay sections are not.

In the Verbal and Math sections, each section starts with a question of medium difficulty and initially assigns you a medium score. When you answer a question correctly, the computer raises your score and gives you a harder question. When you choose a wrong answer, the computer lowers your score and gives you an easier question.

At the beginning of a section, the computer knows very little about you, so each answer, right or wrong, can change your score a lot. By the end of the section, in contrast, the computer already has a very strong idea of your performance, so your answers to the last few questions won’t change its mind much at all.

Do you really need to know all this? Well, you don’t need to be an expert in computer adaptive testing, but it’s good for you to know a little so that you don’t freak out when the test gets harder and harder and harder. In Part II, you’ll examine some of the implications for pacing and the best way to attack the Math section.

For now, you should realize that you cannot skip questions, because the computer can’t determine which question to give you next until it sees your performance on the current one. You also cannot go back to change an answer to a previous question. Therefore, you will sometimes have to move ahead without knowing how to work a particular question, and strong guessing skills will be an important factor in doing your best on the GMAT.


Each chapter in this book reviews one particular area of math or one type of problem. The chapters are arranged sequentially so that later chapters assume familiarity with the material covered in earlier chapters. Spaced throughout each chapter are quizzes that will test your knowledge of the material in each subsection. At the end of each chapter is a set of problems that covers all of the material in that chapter. Explanations are provided for all the problems in the drills.

Ideally, you’ll work through the book from front to back, taking the time to review each subject area thoroughly, work all of the drills, and check all of the explanations. You should give yourself several weeks (at least!) for this plan, so that you have plenty of time to review the drills and learn from your mistakes.

Of course, we don’t live in an ideal world, and you may not have the time to review each subject, work every problem, and read every explanation. If this is your situation, you should skip over the topics with which you’re familiar. Try a few of the problems. If you are comfortable with them, move on to something else that gives you more trouble. If you’re not comfortable with them, review that topic more thoroughly and do most or all of the problems.

In general, the more time you spend preparing for the test, the better you’ll do. Give yourself plenty of time and set up a disciplined practice schedule.

As you use this book, you should do all of your calculations and other work on separate scratch paper. This practice simulates the situation during the test, when you can’t write on the computer screen. (The testing sites get a bit touchy about that.) Get used to copying key information and diagrams from the problem to your scratch paper. Watch out for mistakes in your copying. Also, writing A, B, C, D, E will help you keep track of answers as you eliminate them. Physically crossing off answer choices not only provides enjoyment but also prevents careless mistakes.

In addition to working problems from this book, you should take some practice tests on the computer to help you get comfortable with the format and also work on pacing strategies. You can take an online practice test on The Princeton Review’s website. Go and click on the link to take a free practice test, complete with adaptive question selection and a full range of question types. In addition to the practice GMAT, you’ll also find lots of useful information on the site about preparing for the test and applying to business school.

Another source for practice tests is GMAC. Their GMATPrep software is available for free download at their website, Another helpful GMAT tool is GMAC’s GMAT preparation book, The Official Guide for GMAT Review.


Although the GMAT tests knowledge of concepts and problem analysis more than calculation skills, you’re going to do a significant amount of number-crunching during the test. You want to make sure that your number manipulation skills are sharp so that you won’t make careless mistakes or waste precious time struggling with the calculations.

Chances are good that you do most of your calculations with the aid of a calculator or a computer spreadsheet. When was the last time you did long division by hand? Hmm, that’s what we thought.

Starting today, do all your day-to-day math by hand: Balance your checkbook, figure out a 15-percent tip, calculate your softball batting average, and so forth. You can check your results with a calculator, but force yourself to exercise those math muscles.


On the real GMAT, the answer choices are not labeled by the letters A, B, C, D, and E. In all of the examples in this book, the answer choices are marked by bubbles similar to those you’ll see on the test. In the explanations for the questions in the in-chapter drills and comprehensive drills, however, this book uses the letters to identify the answer choices. We refer to the first answer choice as (A), the second as (B), and so forth. This notation is simply less cumbersome than referring to “the first answer,” “the second answer,” and so on.


The Princeton Review is one of the leaders in helping people prepare for standardized tests such as the GMAT. We started by offering courses and tutoring for the SAT in 1981. Now we offer courses, books, and software to an audience of more than two million people each year.

The Princeton Review’s central philosophy is that the tests are beatable. Standardized tests measure test-taking skills more than they do fundamental knowledge or intelligence. We are dedicated to teaching people the test-taking skills they need to perform their best and beat the standardized tests.