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Page 1: GRE

Manual for the

GRE®

Version 7.0

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Copyright © 2011 by The Princeton Review, Inc. All Rights Reserved.

Version 7.0

All rights reserved. No part of this manual may be reproduced for distribution to a third party in any form or by any means, electronic or mechanical, including photocopy, recording, or any information re-trieval system, without the prior express written consent of the publisher, The Princeton Review.

This manual is for the exclusive use of The Princeton Review course students, and is not legal for resale.

800-2Review

PrincetonReview.com

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AcknowledgmentsExtra special thanks to Joy Grieco, Neill Seltzer, Curtis Retherford, Peter Hanink, Brian Singer, and Neil Thornton.

Special thanks to the following for their many contributions to this manual:Andrew Brody, Heather Brady, Jennifer Downey, Kim Howie, Liz Rutzel, Meave Shelton, and the staff and students of The Princeton Review.

The Princeton Review would like to acknowledge the question authors and quality control experts without whose invaluable work this manual and course would not have been possible:

Question authors:Jennifer Amerkhanov, Stephanie Aylward, Brian Becker, Kevin Cook, Kirsten Frank, Mark Hellman, Jay Hilsenbeck, Beth Hollingsworth, Karen Hoover, Melissa Janae, Paul Kugelmass, Michael Levy, Aaron Lindh, Eliz Markowitz, Lisa Mayo, Amy Minster, Joshua Morris, Jerome J. O’Neill, Elizabeth Owens, Henry Price, Anthony Pumilia, Debbi Reynolds, Tim Ricchuiti, Lisa Rothstein, Audra Rouse, Janet Stolzer, Emily Swenson, Scott Thompson

Quality control specialists:Michael Chapian, Jennifer Downey, Karen Hoover, Rodi Steinig

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Table of Contents Introduction........................................................................... 1

Lesson1Math....................................................................... 15

Lesson2Math....................................................................... 35

Lesson2Verbal...................................................................... 49

Lesson3Math....................................................................... 59

Lesson3Verbal...................................................................... 77

Lesson4Math....................................................................... 95

Lesson4Verbal...................................................................... 127

Lesson5Math....................................................................... 139

Lesson5Verbal...................................................................... 159

Lesson6Math....................................................................... 177

Lesson6Verbal...................................................................... 201

Lesson7Math....................................................................... 217

Lesson7Verbal...................................................................... 237

Lesson8Math....................................................................... 243

Lesson8Essays..................................................................... 259

VerbalPractice....................................................................... 267

MathPractice........................................................................ 281

BetweenNowandTestDay...................................................... 297

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Introduction

I

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Do Your researchYou can’t look at a GRE score in a vacuum; your score is just a number. In order to know how much work you need to put in over the next several weeks, you need to know your starting score, your target score, and the role of the GRE in the admissions process at your target programs. Here are some questions you should be asking of your desired programs:

1. How important are scores? 2. What else is required for admissions? 3. What do you do with multiple scores? 4. Are you looking at all parts of the score? 5. Will scores be used for anything else? 6. How competitive is admissions? 7. What was the average GRE score for last year’s incoming class?

Admissions will ask you two questions that you should be asking yourself:

Why this program and why now?

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Just What Is the Gre?The GRE (Graduate Record Examination) is a standardized, multiple-choice test that is supposed to assess your ability in three general areas: math skills, verbal skills, and writing skills. The test is required by most university graduate programs. When considering you as a candidate, these programs weigh your GRE score in addition to your academic history, recommendations, and personal essays. Some programs also use the GRE as a determinant when awarding fellowships and grants.

hoW IMportant Is the Gre?Unfortunately, there’s no straightforward answer to this question. Some graduate programs consider the GRE very important; others consider it a mere formality. Still other programs do not use the GRE in the admissions process, though they use it when awarding financial aid. Also, different departments look at different parts of the test. For example, if you are considering enrolling in a graduate program in English literature, the quantitative portion of the GRE may not matter at all to your prospective schools. Similarly, a program in applied mathematics may consider the verbal portion immaterial. Some programs will not care how you performed on individual sections but will ask for a minimum composite score (made up of your performance on all parts of the GRE). If you’d like more specifics, contact the schools in which you’re interested. Speak directly with someone in your prospective graduate department. Department secretaries and officers can often tell you precisely how their department will use your GRE scores when considering your application.

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What Does the Gre test?Th e Analytical Writing Assessment (AWA) section probably comes the closest to measuring what it actually purports to measure—namely your ability to support an opinion and to critically evaluate arguments made by others.

Th e test author, Educational Testing Service (ETS), claims that the GRE measures “certain developed ver-bal, quantitative (math), and analytic abilities that are important in academic achievement.” Okay. But what does that actually mean?

If you’ve already taken the GRE, you know that it covers such basic math skills as algebra and geometry, such writing skills as formulating and critiquing arguments, and such verbal skills as reading comprehension and vocabulary. By testing your abilities in these areas, ETS argues that “the test necessarily refl ects the opportunities and eff orts that have contributed to those abilities.”

Of course, that’s what ETS would say. ETS has a vested interest in maintaining its monopoly on this and other standardized tests. Whatever the GRE purports to measure, it does not test the skills you developed in college, nor is it in any way an intelligence test. Most important of all and regardless of ETS’s claims, the GRE has nothing to do with aptitude for graduate study. In fact, it has never been demonstrated that there is any correlation between performance on the GRE and ability to tackle graduate work in any fi eld. Th e bottom line is quite simple:

The GRE tests how well you take the GRE.

Why, then, do you have to take the GRE, and why do schools use it when considering your candidacy? Th e answer is simple. Given our diff erent undergraduate backgrounds, schools like having a way to compare everyone by a single measure.

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Who Is ets?As you may already know, ETS—the same folks who ruined your high school years with the PSAT, SAT, and SAT Subject Tests—is responsible for the GRE.

ETS writes the other exams for graduate study, including the GRE Subject Tests, as well as exams for CIA agents, barbers, golf pros, and travel agents. ETS is a private, nonprofi t corporation (though it does have highly profi table for-profi t divisions). It is not supervised by the government. It is not supervised by anyone, at any level. What gives ETS the right to administer this test? Th e fact that it gives this test. To summarize:

ETS has the right to administer the GRE, which tests how well you take the GRE, because it administers the GRE.

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hoW Does ets WrIte the test?ETS—the Big Brother of standardized testing—knows how you think. Through extensive testing of indi-vidual problems, and by taking advantage of the ways in which we take standardized tests, ETS ensures that the GRE always produces the same results.

unpaid Guinea pigsOn nearly every test ETS administers there are experimental questions. These questions do not count toward your score. They are used by ETS to ensure that the questions that ultimately appear on real tests produce the results it desires. Any question that fails to do so is promptly rewritten or thrown out.

As unfair as it may be for ETS to have you pay it in order to do its research and development work, you don’t have any choice in the matter. The experimental questions are not optional. This is one way in which ETS guarantees that its tests produce perfect curves. Another way is by taking advantage of our test-taking tendencies.

setting trapsETS is remarkably good at setting traps for the average test taker. For example, the worst thing you can do on the GRE is spend too much time on hard questions and rush through easy ones. Yet ETS makes it seem as if the only way to do well on the test is by putting the same amount of time into every question.

Naturally, there’s more to the GRE than simply a series of traps. However, even when dealing with a problem that seems quite easy, you may unwittingly stumble into an ETS pitfall. Utilizing the strategic techniques and comprehensive review covered in this course, you’ll avoid the GRE’s many traps and beat ETS at its own game.

Now that you know a little about ETS, take a look at the GRE.

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ElEmEnts of thE tEst

section number of Questions time

Analytical WritingOne Issue essay and one

Argument essay

30 minutes per essay 1 hour total

No breaks between essaysVerbal Reasoning Two 20-question sections 30 minutes per section

Quantitative Reasoning Two 20-question sections 35 minutes per sectionExperimental One 20-question section 30/35 minutes

Research Varies Varies

The Verbal, Quantitative, and experimental sections can occur in any order. ETS says that it reserves the right to slightly alter the number of questions.

the EssaysThe first scored section of your test will be the two essay tasks. You will have a one-minute break after this section but no break between the essays.

Verbal and QuantitativeYou will have two Verbal and two Quantitative sections. They could come in any order. After the essays and the subsequent two multiple-choice sections, you will have a 10-minute break. There is a one-minute break after each of the other sections.

ExperimentalYou will actually see three Quantitative sections and two Verbal sections, or three Verbal and two Quanti-tative. The extra Quantitative or Verbal is experimental. The experimental section does not count towards your score. Other than knowing that it is Quantitative or Verbal, there is no way to figure out which section is experimental, so you will have to take each section seriously.

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how “adaptive by section” WorksThe GRE is adaptive by section. You will see at least two Quantitative and two Verbal sections. The more questions you get right on the first section, the harder the questions are that you will see on the second sec-tion. You have to do well on both sections to hit your target score.

eleMents of the course 1. Class—Classes will cover test skills, homework and drill questions, test review, and difficult

test content. 2. Tests—The course includes five full-length, online, GRE practice tests that simulate the actual

exam. 3. Test Review—A half hour before and after every class is reserved for one-on-one test review.

This is to be scheduled with your teacher and is available only to students who have completed all scheduled tests and drills.

4. Homework Drills—On your online student center you will find a series of drills designed to reinforce key GRE skills. The first portion of each class is reserved for homework review. Each drill question has a “Review in Class” button so that any and all of your content questions will get covered in class.

5. Online Lessons—Some GRE concepts will be introduced in online lessons. These concepts will be revisited and reinforced in class. Students who are already comfortable with a given concept can test out of a given lesson. Students who need more help with a concept will have access to extended practice drills and can also mark questions for review in class.

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score IMproVeMents

Score Improvement Expectations

Class Only

Class & Some Tests

Class & All Tests

Class, Tests, & Some Drills

Class, Tests & All Drills

results come in stagesTaking the GRE is a skill and, like any skill, it requires practice. You might understand how to play the piano the first time you sit down to play one, but that doesn’t mean you will be good at it. Mastering the piano requires long hours of practice. Mastering the GRE does too. The good news is that your score is entirely in your hands.

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MANUAL FOR THE GRE

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MANUAL FOR THE GRE

TECHNIQUESAll of the questions on the test can be divided into two categories:

Category 1: � e Questions You Are Supposed to Get Right. ese are the questions that involve math you are comfortable with or vocabulary words you know.

Category 2: � e Questions You Are NOT Supposed to Get Right. When the folks at ETS want you to get a question wrong, they will � nd a way. On the Verbal section, hard questions include arcane vocabulary words you’re not supposed to know; on the Math section, hard questions include wrong but tempting answer choices that you are supposed to pick.

The techniques do three jobs, all equally important.First, they ensure that you answer correctly the questions that you should get right. Second, they make hard questions easier.

Third, they help you manage your time more effi ciently.

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Global technique #1: take the Easy test FirstWithin a section, each question counts equally towards your score. However, some questions will be easy and others will be difficult. The beauty of the GRE is that you can answer questions in any order you like. A question you can nail in 25 seconds is worth just as much as a tough question. To maximize your score, leave the questions you don’t like for last. If you are going to run out of time (and, unless you are shooting for a 160 or higher, you should be running out of time), make sure the questions you end up bubbling in are the ones you didn’t want to work on anyway. We will practice this extensively throughout the course, but remember: Skip early and skip often.

Global technique #2: Scratch PaperOne of the genuinely helpful tools ETS gives you on the GRE is scratch paper. Over a four‐hour test, your brain is going to get tired. Keeping your hand moving is a way to stay focused on the task at hand. If your brain is communicating with your hand, then your brain is engaged rather than preoccupied with reading the question three times in a row, thinking about what you’re going to do when the test is over, or any other random things. You won’t outthink ETS, but you can out-process them.

For each different question type you will learn a graphic set-up to organize information and answer all questions as efficiently and accurately as possible.

Put your set-ups in theupper left corner.

Reserve the right side forscratch work.

Clearly number each problem so that you can �nd your work if you return to the problem.

When you’re done with eachproblem, draw a line underneath it, across the page, so that you have a clean space upon which to work the next problem.

Note how every answer choice has been checked and every problem has its own distinct space.

A a b c d B65 x = 1 y = 1 3434 x = 2 y = 1 6534 x = 2 y = 1 65

1.

2.

3.

4.

x = 4y = 6 56

322

64

8

xy

2

2

2 2

10

A 8 + 12 + 4B 8 + 12 + 16C 16 + 24 + 8D 16 + 24 + 8EE

3 • 2

80- 24

56

716248

48

322456

A B C D EE

1030 250 32

530 230 25 • 1 0 1 6 • 2 5 • 5 • 2 • 5 4 • 4 • 2 2 • 2 • 2 • 2 • 2=25

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Questions 1–7 are Text Completions.

1 Blanktext completions.

3 Blanktext completions.

2 Blanktext completions.

Note that this student has come up with her own words for theblank and has considered and marked everyanswer choice.

“Marked” questionsare clearly marked onscratch paper.

Questions 8–11/12 areReading Comprehension.Each passage has been mapped. Eachanswer choice has beenconsidered.

Questions 12–15 or 13–16 are Sentence Equivalence. Note that this student has come up with her own words for every blank and consid-ered every answer choice.

Every question is clearly numbered so that the student can easily return to the question if needed.

�ere is appropriate spacebetween each column of answerchoices to avoid crowding andto leave room for notes and marks.

1. A 2. A B B C C D D E E

3. A x x B x C x

falseref lects

6. A B x x x C x x x

7. A B C D E

8. A B C D E

12. A B C D E F

care common taciturn lying13. A B C D E F

14. A B C D E F

15. A B C D E F

9. A B C D E

10. A B C D E

11 A B C D E

m

fakes increased trend?

obvious wrong portraylatchonto

4. A x B x x C x

5. A x B x x C x

— —

Prob.1. Sediment: Climate Hist.2. Climate affects sediment3. “4. Cycle peaks at 1300 & 2400

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Global technique #3: the Mark ButtonReading or calculation errors on a four-hour test are unavoidable. The problem is that a misread question or a calculation error will completely change the way you see the problem, and once you see a question wrong, it is almost impossible to see it correctly. As long as you stay with a misread question, you will continue to see it wrong. Meanwhile, the clock is ticking and you’re not getting any closer to the answer. We call this

“Quicksand.” Once you’re in Quicksand, it is very difficult to get out.

On the flip side, once you’ve spotted the error, solving the problem correctly is often a straightforward process. A question that bedeviled you for minutes on end may appear to be appallingly obvious later. The trick is to change the way you see the question while you still have the opportunity to fix it.

Here are a few signs that you are in Quicksand:

• You’ve found an answer, but it is not one of the choices they’ve given you. • You have half a page of calculations but are no closer to an answer. • You’ve spent more than four minutes on a problem. • Your hand is not moving. • You’re down to two answer choices and both seem correct. • You’ve eliminated all of the answers. • There is smoke coming out of your ears. • You’re beginning to wonder if ETS made a mistake.

If you find yourself in any of these situations, you are in Quicksand. Stop what you’re doing and get out.

Step 1 Recognize you are in Quicksand.

Step 2 Mark and move.

Step 3 Distract your brain by doing two or three other questions.

Step 4 Return to the problem and take a second look.

Ways to see the problem with fresh eyes:

• Use your finger on the screen to force yourself to read the problem word for word. • Ask yourself if there are different ways to express the information. • Can you use the answer choices to help? • Can you paraphrase the answer choices? • If the path to the right answer is not clear on a second viewing, guess and walk away again.

Why stick with a problem you don’t know how to solve?

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Global technique #4: PacingSpeed kills on the GRE. The clock has a way of infecting your brain. Take a section untimed, and in addition to answering more questions, you’ll make fewer mistakes. The questions don’t get any harder when there is a clock, yet somehow most testers get more wrong. To make matters worse, the questions you get wrong are likely to have taken you far more time than the ones you got right.

The trick is to take each section as if there is no clock. As long as you are skipping the hard ones and skip-ping and coming back when you run into resistance on questions you’ve started, you should get very few questions in a section wrong.

Remember that it is not the number of questions that you answer that gives you your score, it is the number of questions you answer correctly. Accuracy is everything. Ignore the clock. Slow down and work for accuracy only. If you run into a brick wall, don’t continue to spend time on the problem; go do an easier one and come back. The minute you try to go faster, however, your accuracy will go down and your score along with it.

There is only one exception to this, and that is the last two minutes of a section. A skipped question and a wrong answer count the same. In other words, there is no penalty for “guessing” on a question you don’t know. When two minutes remain on your clock, stop what you’re doing and bubble in answers to any remaining unanswered questions. A few lucky guesses will pay off. If you don’t get any of them right, no harm done.

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Lesson 1Math

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1Question 1

c = 2

d = 5

Quantity A Quantity B (d – 4c)6 (d – 4 c)7

Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the

information given.

Question 2

32

2m

m=

Quantity A Quantity B m 8

Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the

information given.

Question 3

A B C

On line l, the length of BC is 1.5 times the length of AB. If the length of AC is 30, what is the length of BC ?

10 12 15 18 20

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scratch PaPer 1

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1Question 4

Four containers of flour are on the table:

The first contains 1

3 of a pound, the second

contains 1

6 of a pound, the third contains

1

9 of a

pound, and the fourth contains 1

18 of a pound. If

each container can hold one pound of flour, how

many additional pounds of flour are required to fill

all four containers?

2

9

2

3

11

9

25

9

10

3

Question 5

Machine Units Made per Hour Percentage of Defective Units

A 2,800 12%

B 1,500 7%

C 750 6%

What is the ratio of the number of defective units created in an hour by machine A to the number of defective units created in an hour by machine B?

Question 6

n x= + + + + + +2

7

1

3

4

9

2

3

5

9

5

7

In the equation above, if n is an integer, which of the following could be a possible value of x ?

Indicate all such values.

0

2

63 1

65

63 4

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scratch PaPer 1

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1

PluGGinG in

Question 1

Doug is 3 times as old as Neill and half as old as Liz. If Doug is d years old, what is the sum of their ages?

53

d

73

d

103

d

72

d

92

d

triG

Ger

Trigger: _______________________________________________________________

Question 2

If fg

= 3, where g is not equal to 0 and f is not equal

to 1, then which of the following is equal to g

f

−−

3

1?

g f g–f –f –g

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scratch PaPer 1

1. A B d = C n = D l = E

2. A B f = C g = D E

PluGGinG in

Question 1

Doug is 3 times as old as Neill and half as old as Liz. If Doug is d years old, what is the sum of their ages?

resPon

se

1. Recognize the opportunity: Plug In! 2. Set up your scratch paper. 3. Assign an easy number (e.g. 2, 5, 10, 100) to one variable.

4. Work through the problem. 5. Find the answer to the question. That’s your target number. Circle it. 6. Check all answer choices.

Question 2

If , where g is not equal to 0 and f is not equal

to 1, then which of the following is equal to ?

g f g–f –f –g

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1Question 3

If a factory produces 1,500 light bulbs in one minute, how many light bulbs will it produce in t seconds?

1,500t 25t 25

t

750

t

90 000,

t

Question 4

For y ≠ 0 and y ≠ 1, which of the following represents

the reciprocal of

1

1y

y−

?

y

y

2 1−

y

y

2 1+

y

y + 1

y

y2 1− y

y2 1+

Question 5

A group of 10 people decides to share equally in an apartment that costs r dollars to rent each month.If x people drop out of the group, how much more, in dollars, must each remaining person pay?

rx

x1010( )−

10r

x

r

x1010( )−

r

x10−

rx

x10−

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scratch PaPer 1

Check your work. For every problem, you should have terms labeled, a target number circled, and all answer choices checked.

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1

Quant comps

Question 6y≠ 0

Quantity A Quantity B –10y –y

Quantity A is greater.Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the

information given.

triG

Ger

Trigger: _______________________________________________________________

Need a weird number? Try FROZEN:

F – FractionsR – RepeatsO – OneZ – ZeroE – ExtremesN – Negative

Question 7x> y > 0

Quantity A Quantity B 6x 7y

Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the

information given.

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scratch PaPer 1

6. A a b c d B

y =

y =

y =

7. A a b c d B x = y =

x = y =

x = y =

Quant comps

Question 6y≠ 0

Quantity A Quantity B –10y –y

Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the

information given.

resPon

se

1. Recognize the Opportunity: PLUG IN!

2. Draw your set-up.

3. Plug in an easy number (according to the problem’s rules).

4. Cross off answer choices.

5. Repeat using FROZEN.

Question 7x> y > 0

Quantity A Quantity B 6x 7y

Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the

information given.

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1Question 8

3 < x < 6 < y < 10

Quantity A Quantity B The greatest possible 7 value of y – x

Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the

information given.

Question 9

a, b, and c are consecutive even integers such that a < b < c.

Quantity A Quantity B a + c 2b + 2

Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the

information given.

Question 10a ≠ 0

Quantity A Quantity B |a – 1| |a| – 1

Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the

information given.

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1

Must Be

Question 11

If a,b,and c are odd integers, which of the following must also be odd?

(a+b)c ac + b (a + b) – (b+c) abc (b–a) + (c–b)

triG

Ger

Trigger: _______________________________________________________________

Question 12

If p and q are integers, such that p < 0 < q, which of the following must be true?

Indicate all such statements.

2p < 2q p2 < q2

p + q = 0

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ABCDE

11.

a = a = a = b = b = b =c = c = c =

Must Be

Question 11

If a,b,and c are odd integers, which of the following must also be odd?

(a+b)c ac + b (a + b) – (b+c) abc (b–a) + (c–b)

resPon

se

1. Recognize the Opportunity: PLUG IN!

2. Draw your set-up.

3. Plug in an easy number (according to the problem’s rules).

4. Cross off answer choices.

5. Repeat using FROZEN.

Question 12

If p and q are integers, such that p < 0 < q, which of the following must be true?

Indicate all such statements.

2p < 2q p2 < q2

p + q = 0

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1

Drill

Question 1 of 7

Bill is twice as old as Heidi and six years younger than Mel. If Heidi is h years old, how old is Mel in terms of h?

h – 4 h + 4 2h – 4 2h 2h + 6

Question 2 of 7

Quantity A Quantity B 6 + x 6 – x

Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the

information given.

Question 3 of 7

0 < x < 10

0 < y < 1

Quantity A Quantity B x– y 9

Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the

information given.

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1Question 4 of 7

Eleven years ago, Lauren was half as old as Mike will be in 4 years. If Mike is m years old now, how old is Lauren now in terms of m?

4m – 11 1

24 11( )m + +

1

211( – )m

4m + 11

2 2m – 7

Question 5 of 7P < Q

Quantity A Quantity B

Q–P Q P–

3 Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the

information given.

Question 6 of 7

If the sum of three consecutive odd integers is k, then, in terms of k, what is the greatest of the three integers?

k − 6

3 k − 3

3 k

3 k + 3

3 k + 6

3

Question 7 of 7

Item F costs three times as much as item G, and item H costs $4 more than one-third the price of item G.

Quantity A Quantity B The cost of item F The cost of item H

Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the

information given.

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triG

Ger Variables in the answer

choices

resPon

se 1. List A,B,C,D,E on scratch paper.

2. Replace variable with number.

3. Work the problem.

4. Identify and circle target number.

5. Check all answer choices.

triG

Ger

Quant Comp with variables

resPon

se

1. Draw set-up.

2. Plug in an easy number.

3. Eliminate two answer choices.

4. Repeat using FROZEN.

triG

Ger

“Must be”

resPon

se

1. Draw set-up.

2. Plug in an easy number.

3. Eliminate answer choices.

4. Repeat using FROZEN.

02 GRE 7.0 Ch1 Class 1 Math.indd 34 3/28/11 7:05 PM