LEARNING ASSISTANCE SERVICE

GRE Quantitative Reasoning

Study Guide

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Getting Started

Welcome to the University of Maryland College Park Learning Assistance Service GRE

Quantitative Reasoning Study Guide. In this guide, we will review some of the basic

information you will need to know in order to succeed in the math based portion of the new

GRE. This guide contains only limited sample practice problems and does not contain any

practice tests. You may want to supplement the information covered here by taking free practice

tests online. Please be sure that the tests you use are related to the new version of the GRE,

which was implemented in August 2011.

Free practice tests can be found at: www.ets.org/gre/revised_general/prepare/powerprep2

www.princetonreview.com/ChooseProducts.aspx?&testtype=TCA&producttype=FRE&productd

etail=OnlineFreePracticeTest

www.kaptest.com/GRE/Explore-the-GRE/gre-practice-test.html

www.4tests.com/exams/examdetail.asp?eid=11

www.majortests.com/gre/

www.greguide.com/gre-practice-tests.html/

You may want to begin your GRE preparation by taking a practice test to see what you do and do

not remember from earlier math instruction, as well as to determine what areas you will need to

focus most of your time and energy on. Please remember that most people who are not studying

a math-based field do not do particularly well on their first diagnostic test. Your score on this

test does not in any way indicate what your score on the actual GRE will be; it will just

help you determine what topics you will need to focus on! Do not let a low score discourage

you!

There are several different mathematical concepts that you will need to be familiar with in order

to succeed in the quantitative reasoning portion of the GRE. These are outlined in the subtopics

below. There are also several test taking strategies that you may want to learn in order to move

through the test as efficiently as possible. On average, you will have 90 seconds to complete

each problem in the quantitative reasoning portion of the GRE. It is important that you go

into the test comfortably proficient with each subtopic so that you are able to make the best

use of your time.

For a more comprehensive review of the mathematical concepts in the GRE, please visit:

www.ets.org/s/gre/pdf/gre_math_review.pdf . This document was prepared by the GRE testing

board and includes numerous definitions, properties and examples, as well as a set of exercises

and answers at the end of each review section. Please include this review early in your

preparation as it is rather long and goes into each concept with a considerable amount of detail.

For a review of the mathematical symbols and terminology used in the GRE, please also review:

www.ets.org/s/gre/pdf/gre_math_conventions.pdf . This document was also prepared by the

GRE testing board and contains information with which you will need to be familiar in order to

succeed in the Quantitative Reasoning portion of the GRE.

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Overview of Question Types

The GRE consists of two quantitative reasoning sections, two verbal reasoning sections and one

analytical writing section with two separately timed tasks. There are two main question types

that will appear in each quantitative reasoning section of the GRE. Since you will have 35

minutes to complete approximately 20 questions, you will need to become familiar with both

question types to ensure that you are able to answer within the allotted time frame. These

question types are quantitative comparisons and problem solving questions.

Quantitative comparisons: Expect to see between 7 and 8 questions of this type in each section.

Aim to spend around 1.5 minutes answering questions of this type.

Problem solving: Expect to see between 9 and 10 questions of per session of the standard

problem solving type. Standard problem solving questions require you to solve a mathematical

problem, and are generally multiple choice questions with five possible answers, only one of

which is correct. Aim to spend between 1.5 and 2 minutes solving questions of this type.

Data interpretation: These questions fall under the umbrella of problem solving questions;

however, you will need to interpret a graph or chart in order to determine the correct answer.

Expect to see 3 questions of this type per session, which will usually appear as one set based on

the same data array. Aim to spend around 2 minutes solving questions of this type.

Quantitative Comparisons

The most important thing to remember when faced with quantitative comparison questions is that

you are being asked to compare, not calculate. You may not be given information that will

allow you to solve for variables present, and that is fine. You are not being asked to determine

the value of a variable, but rather to determine the relationship between two quantities.

In the sample problem below, you are given several pieces of key information. Pay attention to

all information given, not just the two quantities you are being asked to compare.

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Notice that in addition to being shown two quantities, you are also told that the variable g is

greater than 1. This crucial detail lets you know that g has a positive value. This information

will help you to correctly make your comparison.

Once you have noted all information, observe the two quantities to determine what values they

share. Since you are being asked to compare the relative values of the two quantities, it is a good

idea to remove shared values by performing the same operation to each. In this example, you

will notice that both quantities contain the value -1. We can remove this value by adding +1 to

each.

You will also notice that both quantities have the value of g+3 in the denominator. Because the

centered information tells us that g has a positive value, we know that adding 3 to this

variable will also result in a positive value. To cancel out this positive denominator we

multiply each quantity by g+3. Note that if the denominator had been negative, rather than

positive, we would not have been able to follow this procedure. Remember to always consider

the meaning of all information you are given in a problem.

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This leaves us with a value of g for Quantity A and a value of 1 for Quantity B. As we have

been given the information that g is greater than 1, the answer to this problem is now clearly the

first option.

In quantitative comparison problems, you will always be given the same set of possible

answers from which to choose. Please be sure to solve several problems of this type prior to

taking the GRE so that you can recognize these questions quickly and answer as efficiently as

possible.

Problem Solving

For this type of question, you will be required to calculate a specific value. Answer choices

for problem solving questions will generally contain numbers. Always pay attention to the

form your answer choices take. This will be your greatest clue as to what you are being asked

to do in order to solve the question given.

The sample question below contains important information in both the form of the possible

answer choices and in the wording of the question itself.

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Because the answer options are all numerical values, we know that we are being asked to solve

for a numerical quantity alone, and not a value containing both a number and a variable. Note

that the question tells us both the value of the nth term in a sequence and that we are looking for

the 6th

value in this sequence. After carefully reading the question, we can see that in order to

find the answer to this question, we should replace the variable n with the number 6.

Once we have replaced the value of n with 6, we can easily solve this problem by following the

order of operations. First we solve the value within the parenthesis:

Then we square 5:

6

And finally, we solve the simple multiplication problem of 6 times 25 to reveal our answer:

Careful, strategic reading is often the most important part of solving these types of problems.

Once we were able to replace the variable with an integer value, the remainder of the solving

process required relatively simple mathematic procedures.

All That Apply Please note that not all questions will have only one, straightforward answer. Some questions

will ask you to select all that apply. In addition to directly stating that you will need to select

all that apply, these questions have square boxes in place of the usual ovals before possible

answer choices. To receive credit for these types of questions you must select all of the correct

answers and only the correct answers. There is no partial credit. Only certain types of

mathematical concepts will be tested using this type of format, as not all concepts lead to the

possibility that more than one answer may be correct.

In the sample below, note that the question relies upon a rule that gives a range of possible

correct answers rather than one definitive answer. This rule is the triangle inequality theorem

which states that any side of a triangle must be greater than the difference and less than the sum

of the other two sides.

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To help you visualize this problem, it is always a good idea to begin with a sketch.

Now use the theorem to determine the possible range of values that x may take.

Remember, the question is not asking for the possible values of this side, but rather the possible

values of the perimeter. This is the sum of the length of all three sides. From the information

given in the question, we know that the perimeter must be greater than the sum of the given two

sides alone, which allows us to eliminate one possible answer.

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Given that we know the range of values x can take and the sum of the other two sides, we can

determine the possible range of possible values of the perimeter by adding the sum of the first

two sides to the values that we know x must fall between.

It is important for us to remember that this theorem requires x to fall between the two values we

have found. These values themselves are not included in the possible range of values of x. As

such, we can eliminate answers that fall at these extremes and are left with two possible answers.

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Numeric Entry

Numeric entry problems require you to submit a numerical value based on your own

calculations into a blank textbox. For this type of question, there is one and only one correct

answer.

In the sample below, note that you are given a variable as well as numerical values. You will

need to either solve for the numerical value of this variable or find some other means of

removing it prior to inputting your answer.

As always, it is good to begin with a sketch indicating what exactly you are being asked to

determine. In this question, you are being asked to find the number of degrees in angle PRM.

As angle PRM makes up a portion of the straight line, angle QRM, we can use our knowledge

that there are 180 degrees in a straight line as the first step in determining the size of angle PRM.

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We can then begin to figure out the size of the angle whose value we are trying to determine.

Now that we have established this information, we can solve for the variable y, given our

knowledge that 12y = 180°:

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Since angle PRM is equal to 8y, we can now easily find the answer by multiplying the value of y,

15, by 8. We then write the answer into the box provided.

It is incredibly important to read the question carefully! Remember, the question is not asking

for the value of y, but rather the value of 8y. The important point in numeric entry questions is to

enter the correct response in numerical form. Please remember that only numbers are to be

typed into the textbox. A toggle function will be available on the computer based GRE exam

to include a negative sign. Always include only whole numbers or decimals unless you are

explicitly provided with two separate boxes positioned one on top of the other separated by a

line. This indicates that the response is to be provided in the form of a fraction. Please type the

numerator into the top box and the denominator into the bottom box if you are given an answer

box of this type.

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Test Taking Strategies

There are a number of different strategies that can help you complete the problem solving

questions more efficiently.

Picking numbers

This is a strategy that is best used when there is an unknown quantity or value that is integral to

the question asked. It is important to pick a number that will be easy to work with. There is no

one, magic number that will be useful for all types of problems; however, you should avoid

using 0, 1, or 2 as these numbers have unique properties that may affect the accuracy of your

answer.

In the example below, you must read carefully to discover what crucial information is missing in

order to form the equation that will help us determine the correct answer. The missing

information is the total number of employees. Without this number, it is much more complicated

to determine the fraction of the total number of employees who belong in neither of the two

categories listed.

In order to solve this problem, we need to select a number to represent the total number of

employees at this company. We can determine an appropriate number by looking at both the

form that possible answers take and common aspects of these possible answer choices. In the

example below, we see that all answer choices are fractions with a denominator of 80. As such,

it is a reasonable option for us to choose 80 as the number we substitute for the total number of

employees.

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Once we have designated a value for the total number of employees, we can determine how

many of these employees are technicians based on the information given in the question. As 2/5

of the total number of employees are technicians, we are able to determine that 32 of those 80 are

technicians, leaving 48 employees who fill other positions.

Since we are also given the information that 5/16 of this remaining number are accountants, we

can easily determine that out of the 48 non technicians employed in this company, 15 are

accountants.

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We can now easily determine how many of the original 80 employees are neither technicians nor

accountants by subtracting their sum from the selected total, 80. This leaves us with 33

employees, allowing us to determine that the ratio of 33/80 is the correct answer.

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Back solving

This is a strategy that can only be used when the answer choices available are all real numbers.

It involves selecting from the range of possible answer choices in order to determine which

correctly solves the problem set up in the question given.

Upon first glance at the example below, it looks like we’re going to have to write a complex

equation and solve for a variable in order to solve the question below. However, given that the

possible answers provided are all real numbers, we can substitute them for the variable we would

otherwise be looking for in order to determine which number of minutes gives us a difference of

$15.

In order to minimize the amount of time spent calculating, it is a good idea to first arrange values

in size order. In this example, possible answers are already arranged from smallest to largest.

Label your answer choices on your scrap paper and carefully note which value you are using in

your calculations as well.

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Always begin by substituting either the second largest or second smallest option provided. In

this example, we will begin with the second smallest option, 60. Since this leaves us with a

difference smaller than our target difference of 15, we now not only know that option B is

incorrect, but that all smaller values must also be incorrect as well.

We now can substitute the second largest value, 80, to determine which of the three remaining

possibilities is correct. If 80 leaves us with a difference of 15, then that is the answer. If 80

leads to a difference smaller than 15, we then know that the larger option, 81, is correct. If 80

leads to a difference larger than 15, we then know that the next smaller option provided, 77, is

correct. Since the difference between the two is 14.80, we know that the next largest option, 81,

is the correct answer to this problem.

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Stress Management and Study Tips

There are several things you will want to do to make sure that you study efficiently and go into

the GRE prepared and unstressed. The first, of course, is to make sure that you are both familiar

with and proficient in the math topics on which you will be tested. In addition to the links

provided in the “getting started” section, you may also want to visit:

www.ets.org/gre/revised_general/prepare

www.ets.org/gre/revised_general/about/content/quantitative_reasoning

hwww.ets.org/gre/revised_general/prepare/quantitative_reasoning

In order to become proficient in the math topics covered, you must practice! Start early and

continue regularly! Find a time of day that works for you several months before your

scheduled exam and dedicate at least 45 minutes to GRE math review. Make review a part of

your routine to be sure that you actually do the work required with enough regularity to learn.

You may also want to meet with the Math Learning Specialist or Math Learning Assistant a

month or so prior to taking the GRE to learn more math study tips or to discuss math anxiety

management. You can find more information on our math learning program at:

www.counseling.umd.edu/LAS/html/mlp.html

When you are studying, please remember that you will not be allowed to use a calculator for

many questions on the GRE. When you are provided with an on-screen calculator which will

look similar to the image below:

Make sure you practice without a calculator or with only a very basic calculator to prepare

you to solve problems unaided in the actual test!

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One of the best ways to minimize test anxiety is to practice taking the test under actual test

conditions. Once you feel you have adequate mastery of the concepts covered, take a practice

test online. Do not stop to take breaks between the sections or get up and walk around. Treat the

practice tests as though you are actually taking the official GRE. Since the GRE is computer

based, this will be very similar to the actual test-taking experience.

References

Educational Testing Service. (2012). Frequently Asked Questions About the GRE Revised

General Test. http://www.ets.org/gre/revised_general/faq/.

Kaplan Test Prep. (June 7, 2012). Math Session One, Lesson on Demand.

http://jasper.kaptest.com/apps/delivery/smartReportsHome.aspx

Best wishes to you on the GRE!