Revised_GRE_Manual_7.pdf

Manual for theGRE ® Version 7.0 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 retrieval 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 Acknowledgments Extra 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 Table of Contents Introduction .......................................................................... 1 Lesson 1 Math ...................................................................... 15 Lesson 2 Math ...................................................................... 35 Lesson 2 Verbal ..................................................................... 49 Lesson 3 Math ...................................................................... 59 Lesson 3 Verbal ..................................................................... 77 Lesson 4 Math ...................................................................... 95 Lesson 4 Verbal ..................................................................... 127 Lesson 5 Math ...................................................................... 139 Lesson 5 Verbal ..................................................................... 159 Lesson 6 Math ...................................................................... 177 Lesson 6 Verbal ..................................................................... 201 Lesson 7 Math ...................................................................... 217 Lesson 7 Verbal ..................................................................... 237 Lesson 8 Math ...................................................................... 243 Lesson 8 Essays .................................................................... 259 Verbal Practice ...................................................................... 267 Math Practice ....................................................................... 281 Between Now and Test Day ..................................................... 297 Introduction I . 3.MANUAL FOR THE GRE DO YOUR RESEARCH You can’t look at a GRE score in a vacuum. you need to know your starting score. Here are some questions you should be asking of your desired programs: 1. 4. . In order to know how much work you need to put in over the next several weeks. your score is just a number. your target score. How important are scores? What else is required for admissions? What do you do with multiple scores? Are you looking at all parts of the score? Will scores be used for anything else? How competitive is admissions? 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? 2 | © The Princeton Review. 5. 7. 6. and the role of the GRE in the admissions process at your target programs. Inc. 2. others consider it a mere formality. | 3 . Speak directly with someone in your prospective graduate department. If you’d like more specifics. if you are considering enrolling in a graduate program in English literature. though they use it when awarding financial aid. verbal skills. For example. different departments look at different parts of the test.INTRODUCTION JUST WHAT IS THE GRE? The GRE (Graduate Record Examination) is a standardized. contact the schools in which you’re interested. Also. 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). © The Princeton Review. Some programs also use the GRE as a determinant when awarding fellowships and grants. the quantitative portion of the GRE may not matter at all to your prospective schools. Department secretaries and officers can often tell you precisely how their department will use your GRE scores when considering your application. multiple-choice test that is supposed to assess your ability in three general areas: math skills. recommendations. Still other programs do not use the GRE in the admissions process. and writing skills. a program in applied mathematics may consider the verbal portion immaterial. When considering you as a candidate. The test is required by most university graduate programs. these programs weigh your GRE score in addition to your academic history. there’s no straightforward answer to this question. Some graduate programs consider the GRE very important. Similarly. Inc. and personal essays. HOW IMPORTANT IS THE GRE? Unfortunately. Most important of all and regardless of ETS’s claims. nor is it in any way an intelligence test. quantitative (math). it has never been demonstrated that there is any correlation between performance on the GRE and ability to tackle graduate work in any field. In fact. 4 | © The Princeton Review.MANUAL FOR THE GRE WHAT DOES THE GRE TEST? The 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. Why. The bottom line is quite simple: The GRE tests how well you take the GRE. and such verbal skills as reading comprehension and vocabulary. . By testing your abilities in these areas.” Of course. But what does that actually mean? If you’ve already taken the GRE. schools like having a way to compare everyone by a single measure. the GRE has nothing to do with aptitude for graduate study. ETS argues that “the test necessarily reflects the opportunities and efforts that have contributed to those abilities. and why do schools use it when considering your candidacy? The answer is simple. and analytic abilities that are important in academic achievement. that’s what ETS would say. The test author. do you have to take the GRE. Educational Testing Service (ETS). then. you know that it covers such basic math skills as algebra and geometry.” Okay. Whatever the GRE purports to measure. ETS has a vested interest in maintaining its monopoly on this and other standardized tests. it does not test the skills you developed in college. Inc. such writing skills as formulating and critiquing arguments. claims that the GRE measures “certain developed verbal. Given our different undergraduate backgrounds. INTRODUCTION WHO IS ETS? As you may already know. ETS is a private. and SAT Subject Tests—is responsible for the GRE. SAT. © The Princeton Review. because it administers the GRE. barbers. What gives ETS the right to administer this test? The fact that it gives this test. including the GRE Subject Tests. at any level. nonprofit corporation (though it does have highly profitable for-profit divisions). ETS—the same folks who ruined your high school years with the PSAT. It is not supervised by anyone. and travel agents. It is not supervised by the government. To summarize: ETS has the right to administer the GRE. which tests how well you take the GRE. | 5 . Inc. as well as exams for CIA agents. ETS writes the other exams for graduate study. golf pros. For example. 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. you may unwittingly stumble into an ETS pitfall. As unfair as it may be for ETS to have you pay it in order to do its research and development work. Through extensive testing of individual problems. you don’t have any choice in the matter. These questions do not count toward your score. 6 | © The Princeton Review. Another way is by taking advantage of our test-taking tendencies. Setting Traps ETS is remarkably good at setting traps for the average test taker. However.MANUAL FOR THE GRE HOW DOES ETS WRITE THE TEST? ETS—the Big Brother of standardized testing—knows how you think. and by taking advantage of the ways in which we take standardized tests. This is one way in which ETS guarantees that its tests produce perfect curves. The experimental questions are not optional. even when dealing with a problem that seems quite easy. Inc. Unpaid Guinea Pigs On nearly every test ETS administers there are experimental questions. . Utilizing the strategic techniques and comprehensive review covered in this course. the worst thing you can do on the GRE is spend too much time on hard questions and rush through easy ones. take a look at the GRE. you’ll avoid the GRE’s many traps and beat ETS at its own game. Naturally. 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. Now that you know a little about ETS. there’s more to the GRE than simply a series of traps. ETS ensures that the GRE always produces the same results. You will have a one-minute break after this section but no break between the essays. There is a one-minute break after each of the other sections. After the essays and the subsequent two multiple-choice sections. The Essays The first scored section of your test will be the two essay tasks. They could come in any order. | 7 . Experimental You will actually see three Quantitative sections and two Verbal sections. there is no way to figure out which section is experimental. Other than knowing that it is Quantitative or Verbal. © The Princeton Review.INTRODUCTION ELEMENTS OF THE TEST Section Number of Questions Time Analytical Writing One Issue essay and one Argument essay 30 minutes per essay 1 hour total No breaks between essays Verbal Reasoning Two 20-question sections 30 minutes per section Quantitative Reasoning Two 20-question sections 35 minutes per section Experimental One 20-question section 30/35 minutes Research Varies Varies The Verbal. The extra Quantitative or Verbal is experimental. you will have a 10-minute break. Inc. so you will have to take each section seriously. The experimental section does not count towards your score. or three Verbal and two Quantitative. Verbal and Quantitative You will have two Verbal and two Quantitative sections. ETS says that it reserves the right to slightly alter the number of questions. Quantitative. and experimental sections can occur in any order. homework and drill questions. Students who need more help with a concept will have access to extended practice drills and can also mark questions for review in class. Inc. Each drill question has a “Review in Class” button so that any and all of your content questions will get covered in class. 4. These concepts will be revisited and reinforced in class. The more questions you get right on the first section. Online Lessons—Some GRE concepts will be introduced in online lessons. 3. test review. . The first portion of each class is reserved for homework review. and difficult test content. 2. You will see at least two Quantitative and two Verbal sections. 5. This is to be scheduled with your teacher and is available only to students who have completed all scheduled tests and drills. Test Review—A half hour before and after every class is reserved for one-on-one test review. Tests—The course includes five full-length. GRE practice tests that simulate the actual exam.MANUAL FOR THE GRE How “Adaptive by Section” Works The GRE is adaptive by section. Homework Drills—On your online student center you will find a series of drills designed to reinforce key GRE skills. online. 8 | Class—Classes will cover test skills. Students who are already comfortable with a given concept can test out of a given lesson. ELEMENTS OF THE COURSE 1. © The Princeton Review. the harder the questions are that you will see on the second section. You have to do well on both sections to hit your target score. it requires practice. Inc. Mastering the piano requires long hours of practice. but that doesn’t mean you will be good at it.INTRODUCTION SCORE IMPROVEMENTS Score Improvement Expectations Class Only Class & Some Tests Class & All Tests Class. Mastering the GRE does too. & Some Drills Class. | 9 . You might understand how to play the piano the first time you sit down to play one. © The Princeton Review. The good news is that your score is entirely in your hands. Tests & All Drills Results Come in Stages Taking the GRE is a skill and. like any skill. Tests. 10 | © The Princeton Review. First. On the Verbal section. The techniques do three jobs.MANUAL FOR THE GRE TECHNIQUES All of the questions on the test can be divided into two categories: Category 1: The Questions You Are Supposed to Get Right. on the Math section. When the folks at ETS want you to get a question wrong. hard questions include wrong but tempting answer choices that you are supposed to pick. Category 2: The Questions You Are NOT Supposed to Get Right. Inc. they will find a way. hard questions include arcane vocabulary words you’re not supposed to know. all equally important. Second. they ensure that you answer correctly the questions that you should get right. Third. . they make hard questions easier. These are the questions that involve math you are comfortable with or vocabulary words you know. they help you manage your time more efficiently. make sure the questions you end up bubbling in are the ones you didn’t want to work on anyway. A a b c d B 65 x = 1 y = 1 34 34 x = 2 y = 1 65 34 x = 2 y = 1 65 8 2. draw a line underneath it. or any other random things. you should be running out of time). Clearly number each problem so that you can find your work if you return to the problem. but you can out-process them. © The Princeton Review. Put your set-ups in the upper left corner. You won’t outthink ETS. your brain is going to get tired. unless you are shooting for a 160 or higher. 1. Inc. To maximize your score. Keeping your hand moving is a way to stay focused on the task at hand.INTRODUCTION Global Technique #1: Take the Easy Test First Within a section. but remember: Skip early and skip often. A B C D EE 10 32 2 64 x=4 y=6 56 7 80 . However.24 56 1030 5 3•2 30 2 A B C D EE 8 + 12 + 4 8 + 12 + 16 16 + 24 + 8 16 + 24 + 8 250 30 16 24 8 48 32 24 56 32 25 • 10 16 • 2 5•5• 2• 5 4•4•2 2 • 2 • 2 • 2 • 2=2 5 4. If your brain is communicating with your hand. Over a four‐hour test. 2 2 2 x y 2 3. each question counts equally towards your score. If you are going to run out of time (and. Note how every answer choice has been checked and every problem has its own distinct space. 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. then your brain is engaged rather than preoccupied with reading the question three times in a row. Reserve the right side for scratch work. some questions will be easy and others will be difficult. leave the questions you don’t like for last. Global Technique #2: Scratch Paper One of the genuinely helpful tools ETS gives you on the GRE is scratch paper. The beauty of the GRE is that you can answer questions in any order you like. When you’re done with each problem. A question you can nail in 25 seconds is worth just as much as a tough question. | 11 . so that you have a clean space upon which to work the next problem. across the page. We will practice this extensively throughout the course. thinking about what you’re going to do when the test is over. A B C x x x x 7. Sediment: Climate Hist. A B C D E 9.MANUAL FOR THE GRE Questions 1–7 are Text Completions. A x B x x C x fakes increased trend? 6. A B C D E F taciturn 14. A B C D E wrong x x | © The Princeton Review. A B C D E F Every question is clearly numbered so that the student can easily return to the question if needed. 12 4. reflects 1. Note that this student has come up with her own words for the blank and has considered and marked every answer choice. A B C — x x There is appropriate space between each column of answer choices to avoid crowding and to leave room for notes and marks. A B C D E 10. “ 4. Climate affects sediment 3. A x B C x false 2. Each answer choice has been considered. Inc. obvious 3. A B C D E F 8. A B C D E x x Prob. Questions 8–11/12 are Reading Comprehension. 1 Blank text completions. “Marked” questions are clearly marked on scratch paper. Questions 12–15 or 13–16 are Sentence Equivalence. 1. A B C D E m 11 A B C D E lying 15. Note that this student has come up with her own words for every blank and considered every answer choice. A B C D E F common 13. Cycle peaks at 1300 & 2400 care 12. . Each passage has been mapped. A B C D E 3 Blank text completions. 2 Blank text completions. — x x latch portray onto 5. 2. As long as you stay with a misread question. but it is not one of the choices they’ve given you. you will continue to see it wrong.” Once you’re in Quicksand. You’ve spent more than four minutes on a problem. Why stick with a problem you don’t know how to solve? © The Princeton Review. The problem is that a misread question or a calculation error will completely change the way you see the problem. Ask yourself if there are different ways to express the information. Step 1 Recognize you are in Quicksand. guess and walk away again. Your hand is not moving. Stop what you’re doing and get out. Here are a few signs that you are in Quicksand: • • • • • • • • You’ve found an answer. you are in Quicksand. Meanwhile. | 13 . Step 2 Mark and move. There is smoke coming out of your ears. You’re beginning to wonder if ETS made a mistake. it is very difficult to get out. once you’ve spotted the error. 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. the clock is ticking and you’re not getting any closer to the answer. The trick is to change the way you see the question while you still have the opportunity to fix it. Inc. If you find yourself in any of these situations. Step 4 Return to the problem and take a second look. You’re down to two answer choices and both seem correct.INTRODUCTION Global Technique #3: The Mark Button Reading or calculation errors on a four-hour test are unavoidable. it is almost impossible to see it correctly. and once you see a question wrong. On the flip side. A question that bedeviled you for minutes on end may appear to be appallingly obvious later. You have half a page of calculations but are no closer to an answer. We call this “Quicksand. You’ve eliminated all of the answers. solving the problem correctly is often a straightforward process. Ways to see the problem with fresh eyes: • • • • • Use your finger on the screen to force yourself to read the problem word for word. Step 3 Distract your brain by doing two or three other questions. A skipped question and a wrong answer count the same. If you don’t get any of them right. The clock has a way of infecting your brain. Ignore the clock. If you run into a brick wall. Slow down and work for accuracy only. Inc. your accuracy will go down and your score along with it. it is the number of questions you answer correctly. There is only one exception to this. don’t continue to spend time on the problem. The questions don’t get any harder when there is a clock. Take a section untimed. As long as you are skipping the hard ones and skipping and coming back when you run into resistance on questions you’ve started. A few lucky guesses will pay off. no harm done.MANUAL FOR THE GRE Global Technique #4: Pacing Speed kills on the GRE. Accuracy is everything. To make matters worse. you’ll make fewer mistakes. The minute you try to go faster. 14 | © The Princeton Review. you should get very few questions in a section wrong. The trick is to take each section as if there is no clock. and that is the last two minutes of a section. there is no penalty for “guessing” on a question you don’t know. In other words. When two minutes remain on your clock. stop what you’re doing and bubble in answers to any remaining unanswered questions. and in addition to answering more questions. go do an easier one and come back. . however. Remember that it is not the number of questions that you answer that gives you your score. the questions you get wrong are likely to have taken you far more time than the ones you got right. yet somehow most testers get more wrong. Lesson 1 Math . The two quantities are equal. The relationship cannot be determined from the information given. what is the length of BC ? 10 16 | © The Princeton Review. 12 15 18 20 . Question 3 A B C C On line C. The two quantities are equal. Inc. Quantity B is greater. Quantity B is greater.MANUAL FOR THE GRE 1 Question 1 c=2 d=5 Quantity A (d – 4c)6 Quantity B (d – 4c)7 Quantity A is greater.5 times the length of AB. The relationship cannot be determined from the information given. Question 2 32 m Quantity A m = m 2 Quantity B 8 Quantity A is greater. the length of BC is 1. If the length of AC is 30. LESSON 1 MATH SCRATCH PAPER 1 © The Princeton Review. | 17 . Inc. the third contains of a 6 9 1 pound. how many additional pounds of flour are required to fill all four containers? 2 2 11 25 10 9 3 9 9 3 Question 5 Machine Units Made per Hour Percentage of Defective Units A 2. the second 3 1 1 contains of a pound. which of the following could be a possible value of x ? Indicate all such values. if n is an integer.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= 2 7 + 1 3 + 4 9 + 2 3 + 5 9 + 5 7 + x In the equation above. . and the fourth contains of a pound. 4 18 | © The Princeton Review. 1 . If 18 each container can hold one pound of flour. Inc.800 12% B 1.MANUAL FOR THE GRE 1 Question 4 Four containers of flour are on the table: 1 The first contains of a pound. . 0 . 65 63 . 2 63 . | 19 .LESSON 1 MATH SCRATCH PAPER 1 © The Princeton Review. Inc. then which of the following is equal to ? f −1 g 20 | © The Princeton Review.MANUAL FOR THE GRE 1 PLUGGING IN Question 1 Doug is 3 times as old as Neill and half as old as Liz. what is the sum of their ages? ⎛ d⎞ 5⎜ ⎟ ⎝ 3⎠ ⎛ d⎞ 7⎜ ⎟ ⎝ 3⎠ ⎛ d⎞ 10 ⎜ ⎟ ⎝ 3⎠ ⎛ d⎞ 7⎜ ⎟ ⎝ 2⎠ TRIGGER ⎛ d⎞ 9⎜ ⎟ ⎝ 2⎠ Trigger: _______________________________________________________________ Question 2 If f = 3 . where g is not equal to 0 and f is not equal g g−3 to 1. Inc. f g–f –f –g . If Doug is d years old. LESSON 1 MATH SCRATCH PAPER 1 1. A B C D E d= n= l = 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. RESPONSE 1. Recognize the opportunity: PLUG IN! 2. A B C D E f= g= © The Princeton Review, Inc. | 21 MANUAL FOR THE GRE 1 Question 3 If a factory produces 1,500 light bulbs in one minute, how many light bulbs will it produce in t seconds? 1,500t 25 25t t 750 90,000 t t Question 4 For y ≠ 0 and y ≠ 1, which of the following represents 1 the reciprocal of y− 1? y y −1 y2 + 1 y y y y +1 2 y y y −1 y +1 2 2 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 10(10 − x) 10r x r 10(10 − x) r 10 − x rx 10 − x 22 | © The Princeton Review, Inc. LESSON 1 MATH SCRATCH PAPER 1 Check your work. For every problem, you should have terms labeled, a target number circled, and all answer choices checked. © The Princeton Review, Inc. | 23 MANUAL FOR THE GRE 1 Quant Comps Question 6 y≠0 Quantity A –10y Quantity B –y Quantity A is greater. Quantity B is greater. The two quantities are equal.  The relationship cannot be determined from the TRIGGER information given. Trigger: _______________________________________________________________ Need a weird number? Try FROZEN: F – Fractions R – Repeats O – One Z – Zero E – Extremes N – Negative Question 7 x>y>0 Quantity A 6x     24 | © The Princeton Review, Inc. Quantity B 7y Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information given. LESSON 1 MATH SCRATCH PAPER 6. A a b c d 1 B y= y= y= 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. 7. A a b x= c d y= x= y= x= y= RESPONSE 1. Recognize the Opportunity: PLUG IN! B © The Princeton Review, Inc. | 25 MANUAL FOR THE GRE 1 Question 8 3 < x < 6 < y < 10 Quantity A The greatest possible value of y – x     Quantity B 7 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 a+c     Quantity B 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 10 a≠0 Quantity A |a – 1|     26 | © The Princeton Review, Inc. Quantity B |a| – 1 Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information given. LESSON 1 MATH SCRATCH PAPER 1 © The Princeton Review. | 27 . Inc. Inc. which of the following must also be odd? TRIGGER (a + b)c ac + b (a + b) – (b + c) abc (b – a) + (c – b) Trigger: _______________________________________________________________ Question 12 If p and q are integers. . 28 | © The Princeton Review. .MANUAL FOR THE GRE 1 Must Be Question 11 If a. 2p < 2q p2 < q2 p+q=0 . b. which of the following must be true? Indicate all such statements. such that p < 0 < q. and c are odd integers. . Recognize the Opportunity: PLUG IN! © The Princeton Review. 4. Draw your set-up.LESSON 1 MATH SCRATCH PAPER 1 11. | 29 . Repeat using FROZEN. 5. 3. Inc. a= b= c= a= b= c= a= b= c= A B C D E 2. Plug in an easy number (according to the problem’s rules). Cross off answer choices. RESPONSE 1. The two quantities are equal. Quantity B 9 Quantity A is greater. The relationship cannot be determined from the information given. The two quantities are equal.MANUAL FOR THE GRE 1 DRILL Question 1 of 7 Bill is twice as old as Heidi and six years younger than Mel. Quantity B is greater. . Question 3 of 7 0 < x < 10 0<y<1 Quantity A x–y     30 | © The Princeton Review. The relationship cannot be determined from the information given. 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 6+x     Quantity B 6–x Quantity A is greater. Quantity B is greater. Inc. Inc.LESSON 1 MATH SCRATCH PAPER 1 © The Princeton Review. | 31 . MANUAL FOR THE GRE 1 Question 4 of 7 Eleven years ago. The relationship cannot be determined from the information given. in terms of k. The two quantities are equal. 11 Quantity B The cost of item H Quantity A is greater. and item H costs $4 more than one-third the price of item G. The two quantities are equal. how old is Lauren now in terms of m ? 4m – 11 1 2 1 (m + 4) + 11 (m – 11) 2 4m + 2 Question 5 of 7 P<Q Quantity A Quantity B Q–P Q– P     3 Quantity A is greater. If Mike is m years old now. then. Quantity B is greater. Quantity A The cost of item F     32 | © The Princeton Review. Question 6 of 7 If the sum of three consecutive odd integers is k. Lauren was half as old as Mike will be in 4 years. Inc. Quantity B is greater. The relationship cannot be determined from the information given. what is the greatest of the three integers? k−6 k−3 k k+3 k+6 3 3 3 3 3 Question 7 of 7 Item F costs three times as much as item G. 2m – 7 . Inc.LESSON 1 MATH SCRATCH PAPER 1 © The Princeton Review. | 33 . Check all answer choices. Draw set-up. Repeat using FROZEN. Draw set-up. Work the problem. 3. 4. “Must be” 2.B. 4. Identify and circle target number. RESPONSE TRIGGER 5. Eliminate two answer choices. Plug in an easy number.E on scratch paper. 1. 4.C. RESPONSE TRIGGER 1. List A. Plug in an easy number. Variables in the answer choices 3. 3. RESPONSE 34 1. Repeat using FROZEN. Quant Comp with variables 2. Replace variable with number.MANUAL FOR THE GRE 2. . Eliminate answer choices.D. TRIGGER | © The Princeton Review. Inc. Lesson 2 Math . Inc.MANUAL FOR THE GRE 2 EXPONENTS & ROOTS Question 1 12 20 × 3 = 5 9 25 3 21 5 20 1 3 5 3 3 TRIGGER 5 5 Trigger: _______________________________________________________________ Question 2 x5 + x3 x 4 + x2 = –4x2 36 | © The Princeton Review. –x2 2x x x2 . LESSON 2 MATH SCRATCH PAPER 2 Convert large bases to their prime factors. RESPONSE Find and cancel common factors. Inc. | 37 . © The Princeton Review. .MANUAL FOR THE GRE 2 Question 3 Quantity A Quantity B 4 −4 12 11 48 643     Quantity A is greater. What is the value of a + b ? Question 5 Which of the following statements must be true? Indicate all such statements. ( x )3 = x −1 (x2) = ( x)2 x-2 < x2 . . Inc. The relationship cannot be determined from the information given. Question 4 126 = 3a2b. Quantity B is greater. . 38 | © The Princeton Review. The two quantities are equal. Inc. | 39 .LESSON 2 MATH SCRATCH PAPER 2 © The Princeton Review. 14% 15% 30% 40% . for student loans. and of the 8 8 5 remainder for rent. If at the end of each month Sarah puts 1 of her remaining income into a CD 2 account. what portion of Sarah’s monthly income TRIGGER does she put into the account? 1 1 7 1 1 8 10 80 16 20 Trigger: _______________________________________________________________ Question 2 In a certain apartment building.MANUAL FOR THE GRE 2 HIDDEN PLUG INS Question 1 1 of her monthly income for food. Inc. 40 percent of the units have one bedroom. If 20 percent of the onebedrooms and 10 percent of the two-bedrooms are vacant. and the remaining units have two bedrooms. Sarah pays 8 1 1 4 for utilities. what percent of the units in the building are vacant? 10% 40 | © The Princeton Review. Inc. © The Princeton Review. | 41 .LESSON 2 MATH SCRATCH PAPER 2 RESPONSE Plug In for the unknown value or amount. 840 $4.000 $4. and Adam went to buy a $90 radio.250 Question 3 Gerald is three times as old as his cousin Lucy and 14 years older than his parrot Polly. Roger. and if the cost of the car and the paint job combined was $4.MANUAL FOR THE GRE 2 PITA Question 1 Vicken. How old is Gerald? 24 42 | © The Princeton Review. then what was the purchase price of the car? $800 $960 $3. In 4 years Lucy will be half as old as Polly will be then.800. If the cost of the paint job was one-fifth of the purchase price of the car. Inc. If Roger agrees to pay twice as much as Adam. 36 45 54 60 . how much must Roger pay? TRIGGER $10 $20 $30 $45 $65 Trigger: _______________________________________________________________ Question 2 Mike bought a used car and had it repainted. and Vicken agrees to pay three times as much as Roger. LESSON 2 MATH SCRATCH PAPER 2 1. POE. RESPONSE 1. Recognize the Opportunity: Plug In the Answers (PITA)! © The Princeton Review. Work the problem in bite-sized pieces. 4. 6. 3. 5. A B C D E R 10 20 30 45 65 A V 2. Inc. List answer choices on your scratch paper. | 43 . Label the first column. making a new column for each new step. Plug In (C). and the remainder are seniors. onethird are sophomores. Quantity B is greater. Quantity B is greater. Quantity A The number of juniors in the band     44 | © The Princeton Review. The relationship cannot be determined from the information given.MANUAL FOR THE GRE 2 Plugging In Drill Question 1 of 5 One-half the members of a team are juniors. which of the following has the greatest value? −1 x3 x x 1 1+x x Question 3 of 5 In a high school pep band that consists of forty students. the number of seniors is five fewer than twice the number of juniors. Question 2 of 5 If –1 < x < 0. The two quantities are equal. Quantity A The number of juniors on the team     Quantity B The number of seniors on the team Quantity A is greater. and 30% of the students in the band are neither juniors nor seniors. The two quantities are equal. . The relationship cannot be determined from the information given. Quantity B 11 Quantity A is greater. Inc. | 45 .LESSON 2 MATH SCRATCH PAPER 2 © The Princeton Review. Inc. which of the following is the first term in the sequence? 2 3 8 9 1 5 3 2 Question 5 of 5 If 20 percent of the trees in a certain park are evergreens. . s2. Inc. and there are 75 percent as many oak trees as maple trees in the park. and 40 percent of the non-evergreens are maple trees. If s5 – s3 = 28.MANUAL FOR THE GRE 2 Question 4 of 5 S is a sequence s1. what fraction of the trees in the park are not maples. oaks. or evergreens? 1 10 3 25 1 5 6 25 1 4 46 | © The Princeton Review. s3…sn in which every term after the first is one less than three times the previous term. LESSON 2 MATH SCRATCH PAPER 2 © The Princeton Review. Inc. | 47 . Inc. Label the first column. List answers on your scratch paper. RESPONSE TRIGGER | 1. 5. If percentages. Assume (C) to be correct. plug in 100 for total. If fractions. 2. An urge to write your own algebraic formula 4. Use (C) to work the problem. plug in common denominator. RESPONSE TRIGGER SUMMARY Numbers too big to calculate Convert large bases to their prime numbers.” “how many. Plug In for the unknown value or amount: Answer choices expressed as fractions or percentages © The Princeton Review. or 3.” “what is the value of” RESPONSE TRIGGER 2 . RESPONSE 48 The phrases “how much. POE.MANUAL FOR THE GRE TRIGGER Exponents Find and cancel common factors. Lesson 2 Verbal . As your brain gets tired. Text Completion 1 2 3 4 5 Text Completion 6 7 8 9 Sent. Inc. and the ability to change the order in which the questions are answered. no matter how many times you reread it. Section B Although the Math sections test the same rules over and over again. Click the Mark button and move on.MANUAL FOR THE GRE 2 Section A Reading Comp. Equivalence Reading Comp. 10 11 12 13 14 15 16 17 18 19 20 Reading Comp. you will continue to misinterpret it in the exact same way. as important as they are on the Math sections. Four NOs = a YES: • Find the wrong answers. . The time required to complete verbal problems can also vary much more than the time required for math problems. When taking the GRE. you are more likely to misread questions or passages. • • Don’t sacrifice accuracy for speed: • Get more efficient at Text Completions and Sentence Equivalence so that you have more time for Reading Comprehension. Once this happens. proper pacing and POE are paramount on the Verbal sections. the inexperienced test taker will take the the test in the order in which it is given. So. and return after several questions. the Verbal sections have passages from many different disciplines and an incredible variety of vocab. Using the Mark Button The Mark button is particularly important on the verbal side of the test. ignoring the level of difficulty. 50 | © The Princeton Review. Sent. the number of questions. Equivalence Reading Comp. for Reading Comprehension questions. | 51 . C. you’ll write out A. Inc. It looks like this: Proper pacing and efficient use of POE require effective use of one’s scratch paper.LESSON 2 VERBAL 2 SCRATCH PAPER All Verbal scratch paper looks the same. your scratch paper will look something like this: © The Princeton Review. B. 2) Take your second pass through the remaining choices using the strategies you’ll learn in the upcoming lessons. For instance. so you can mark each answer choice. Use these symbols: When you are done. and E on your scratch paper for each problem. Use a two-pass approach to POE so that you do not get bogged down on any one answer choice: 1) Eliminate the answer choices that are clearly wrong. D. For most of this century. An assertion is made and a general supporting example is given. If it was the industrial revolution that spawned the era of massive industrialized companies. big companies dominated an American business scene that seemed to thrive on its own grandness of scale. centralized companies is now being challenged as some of the giants of American business are being outperformed by a new generation of smaller. corporate ideology in the United States has held that bigger is better. semi-independent divisions capable of making their way into the twenty-first century. Question 1 The primary purpose of the passage is to present evidence that resolves a contradiction in business theory discuss reasons an accepted business pattern is changing describe a theoretical model and a method whereby that model can be tested argue that a traditional ideology deserves new attention resolve two conflicting explanations for a phenomenon Question 2 Which of the following best describes the organization of the passage? A conventional model is described and an alternative is introduced and evaluated. A historical overview is given to explain a phenomenon. streamlined businesses. the growth of the railroad and steel industries. which lack huge overhead and inventory. . Small companies. then perhaps it is the information revolution of the 1990s that is spawning the era of the small company. an almost limitless supply of cheap raw materials. plus a population boom that provided an ever-increasing demand for new products (although not a cheap source of labor) all coincided to encourage the growth of large companies. can respond quickly to a technologically advanced age in which new products and technologies can become outmoded within a year of their being brought to market. This traditional view of the primacy of big.MANUAL FOR THE GRE 2 Line 5 10 15 20 25 30 35 52 | Until recently. Two contradictory points of view are presented and evaluated. An organizational trend is described and then criticized. Inc. To avoid this trap. successful emerging small companies face a potential dilemma in that their very success will tend to turn them into copies of the large corporate dinosaurs they are now supplanting. Of course. © The Princeton Review. But rapid developments in the marketplace have begun to change the accepted rules of business and have underscored the need for fast reaction times. small companies may look to the example of several CEOs of large corporations who have broken down their sprawling organizations into small. The expansion westward. Inc. | 53 .LESSON 2 VERBAL SCRATCH PAPER Genre (What) • Problem • Question • Conflict • Paradox • Change • Innovation • Discovery Purpose (Why) • • • • • Predict Recommend Inform/Explain Correct Evaluate Structure (How) • • • • • 2 Cause/Effect Chronology Classification Comparison/Contrast Steps/Stages © The Princeton Review. Proponents of evolutionary psychology believe that psychology must be rooted in biology. ranging from language-acquisition modules to cheater-detection modules. For example. nervous. skeptics argue. such behaviors as monogamy can perpetuate genes. Admittedly. reproductive. evolutionary psychology as it is applied to human psychology is quite contentious. so too must the seemingly inherent psychological mechanisms be the result of evolution. can lead to contradictory conclusions.MANUAL FOR THE GRE 2 Line 5 10 15 20 25 30 35 40 54 | Though application of evolutionary theory to the psychology of animals is generally done without controversy. . Additionally. Survivability and sexual selection determine which modules are passed on. skeletal. Question 1 The primary purpose of the passage is to explain the origins of evolutionary psychology resolve a dispute regarding acceptable forms of evidence reconcile the differences between two methods seeking to explain the same phenomenon describe a field of research and caution against its dismissal argue the importance of a debate between scientists regarding the application of one methodology to another Question 2 It can be inferred from the passage that the author believes which of the following? Evolutionary psychology has some merit but has failed to bridge the divide between the social sciences and the natural sciences. nevertheless. These psychologists believe that natural selection has engendered many cognitive modules in the brain. some critics accuse evolutionary psychology of ethnocentrism since many traits once considered universal have turned out to be culturally dependent. many detractors confess their inexperience and lack of firsthand knowledge with the discipline. the quality of work in this field has been uneven. Evolutionary psychology should not be uniformly rejected. This. Inc. muscular. but so too can infidelity. Some critics offer several objections to extending this application to humans. endocrine. immune. as Edouard Machery stated. The debate between proponents of evolutionary psychology and its detractors is intractable.” Evolutionary psychology should be restricted to non-human animals. humans evolved during a period—the Pleistocene—about which very little essential demographic information on humans is known. but. Though evolutionary psychology remains controversial. and urinary systems are evolved adaptations resulting from natural selection or sexual selection. Just as the body’s circulatory. some accuse evolutionary psychologists of proffering “just-so stories”—internally consistent hypotheses that. digestive. “the heuristics and the strategies of confirmation used by evolutionary psychologists are on a firm grounding.“ © The Princeton Review. Evolutionary psychologists should be admonished for failing to justify their hypotheses with more than “just-so stories. respiratory. lymphatic. have no other supporting evidence. Lastly. For instance. LESSON 2 VERBAL SCRATCH PAPER Genre (What) • Problem • Question • Conflict • Paradox • Change • Innovation • Discovery Purpose (Why) • • • • • Predict Recommend Inform/Explain Correct Evaluate Structure (How) • • • • • 2 Cause/Effect Chronology Classification Comparison/Contrast Steps/Stages © The Princeton Review. | 55 . Inc. A phenomenon is explained. government policy makers need not consider removing the corn subsidies that make HFCS a cheaper alternative to sucrose for food manufactures but instead should consider limiting the sale of all foods with high concentrations of sucrose to children. However. In the last 20 years. that explanation is defended and forms the basis for a policy recommendation. Increases in consumption of HFCS have been accompanied by a huge spike in obesity rates among children and adolescents. in an effort to promote public health. other studies do show that increased consumption of sugar in general is a leading cause for the spike in obesity among children. especially among our youth. An explanation is put forth. Thus. commonly known as table sugar. . a reason for its rejection is offered. Given the analyses. whether it be table sugar or HFCS. has increased from 26 pounds per person per year to 135 pounds per person per year. When oligosaccharides. sugar consumption in the U. © The Princeton Review. and further studies are recommended.S. Accordingly. An incomplete explanation is revised and a recommendation based on that revision is proffered. studies by the American Medical Association reveal that absorption by the body of HFCS is not relevantly dissimilar to the body’s absorption of sucrose. are broken down into simple sugar glucose by glucoamylase and are then converted into 42% fructose and 50-52% glucose by mixing some other sugars along with xylose isomerase. it is very likely that these increases are significantly responsible for the rise in childhood obesity.MANUAL FOR THE GRE 2 Line 5 10 15 20 25 30 35 40 56 | Some have attributed the dramatic increase in childhood obesity that has occurred in the United States from the 1990s throughout the 2000s to increased consumption of high fructose corn syrup—also called maize syrup or glucose-fructose syrup—by members of this demographic. which are produced by treating cornstarch with alphaamylase. Question 1 The primary purpose of the passage is to argue against a failed policy recommend a change in HFCS consumption correct a faulty methodology consider the implications of a study advocate for the amelioration of children’s health Question 2 Which of the following best describes the organization of the passage? An explanation is provided. a possible objection is raised and then dismissed. children should be discouraged from consuming in large quantities any type of refined sugar. While further epidemiological studies are needed to test the long-term effects of such sweeteners. A point of view is defended against critique but then dismissed in favor of a more effective policy. HFCS—high fructose corn syrup—is created. which suggest that substantial increases in sucrose consumption may have negative effects on metabolic control. Inc. LESSON 2 VERBAL SCRATCH PAPER Genre (What) • Problem • Question • Conflict • Paradox • Change • Innovation • Discovery Purpose (Why) • • • • • Predict Recommend Inform/Explain Correct Evaluate Structure (How) • • • • • 2 Cause/Effect Chronology Classification Comparison/Contrast Steps/Stages © The Princeton Review. | 57 . Inc. . Lesson 3 Math . MANUAL FOR THE GRE PERCENT CHANGE 3 Question 1 A dress that originally sold for $120 now sells for $96. The new price is what percent less than the original price ? 8% 12% 20% 24% 1 TRIGGER 33 3 % Trigger: _______________________________________________________________ Question 2 If x is the percent increase from 3 to 4. y is the percent . . decrease from 4 to 3 y is the percent decrease from 12 to 8 y is the percent increase from 6 to 8 . 60 | © The Princeton Review. Inc. for which of the following does x = y ? Indicate all such answers. . | 61 .LESSON 3 MATH SCRATCH PAPER 3 RESPONSE Write the percentage change formula: Percent change = difference ×100 original © The Princeton Review. Inc. MANUAL FOR THE GRE RATIOS 3 Question 3 A can of nuts has almonds and cashews in a ratio of x : y. Inc. Quantity A 12 Quantity B The number of nickels in the jar Question 5 The ratio of a to b is 3 to 4. respectively. 62 | © The Princeton Review. If there are z almonds in the can. After three pennies are removed. the ratio of pennies to nickels is 3 : 2. Quantity A Quantity B a+1 4 b+1 5 . which of the following represents the number of cashews? TRIGGER y(x + z) y(z − y) xy yz x z x yz Trigger: _______________________________________________________________ Question 4 A certain jar contains pennies and nickels in a ratio of 7 : 4. © The Princeton Review.LESSON 3 MATH SCRATCH PAPER 3 RESPONSE Draw a ratio box on your scratch paper. | 63 . Inc. 000  $27.000. If the average (arithmetic mean) score for all of the students was 78. Inc. what was the average score for the remaining students? 52 58 64 70 78 64 | © The Princeton Review.000. what is the average salary of the other 4 employees? TRIGGER  $25.000 Trigger: _______________________________________________________________ Question 7 The average score for half of the students in a class on a certain test was 90. The average score for another fourth of the students was 80.000  $27. .MANUAL FOR THE GRE AVERAGES 3 Question 6 The average salary of 12 employees at a certain firm is $35.500  $28.000  $30. If the average salary of 8 of the employees is $40. LESSON 3 MATH SCRATCH PAPER 3 RESPONSE Draw an Average Pie every time the word average appears in the question. | 65 . © The Princeton Review. Inc. y} The mode of set A. Inc. 3. If x > y. and x and y are both integers. 1. . above. 4. What is the median number of hours of text messaging per teenager? TRIGGER 9 10 11 12 13 Trigger: _______________________________________________________________ Question 9 Set A = {5. what is the greatest possible value of y ? 66 | © The Princeton Review. 5. 4. x. 6. is 5 and the median is 4.MANUAL FOR THE GRE Question 8 Hours Spent Text Messaging 3 Hours per teenager Number of teenagers 6 1 8 2 10 3 12 3 14 4 The table above shows the number of hours spent text messaging in a week by a group of 13 teenagers. LESSON 3 MATH SCRATCH PAPER 3 RESPONSE Identify the list and put the numbers in order. © The Princeton Review. | 67 . Inc. Machine B produces x donuts in 6 hours. they both start driving at 9:00 a. Trigger: _______________________________________________________________ Question 11 68 2:30 p. 3:40 p. 1:00 p. .MANUAL FOR THE GRE RATES 3 Question 10 Rob and David live 200 miles apart. Working at a constant rate.m. Deciding to have a picnic.. Rob and David drive at an average speed of 30 and 50 miles per hour. respectively. Inc. traveling in a straight line towards each other.m. Machine A produces x donuts in 12 hours.m.m. Working at a constant rate.m. Quantity A The number of hours it Quantity B The number of hours it will take both machines will take Machine B to x produce donuts 3 working together to prox duce donuts 2 | © The Princeton Review.m. 1:30 p. At what time do they meet for their picnic? TRIGGER 11:30 a. | 69 . © The Princeton Review.LESSON 3 MATH SCRATCH PAPER 3 RESPONSE Write down D = R × T on your scratch paper. Inc. MANUAL FOR THE GRE DRILL 3 Question 1 of 8 Q is a set of consecutive odd integers. how many workers are there at the factory? 300 240 168 48 24 Question 3 of 8 The average age of the members of club K is 22 years. Quantity A The number of members in club K     70 | © The Princeton Review. Quantity B is greater. The relationship cannot be determined from the information given. Quantity A The average of set Q     Quantity B The median of set Q Quantity A is greater. If 120 workers drive to work. Quantity B is greater. The average age of the members of both clubs combined is 27 years. Inc. each worker either drives to work or takes the bus. The average age of the members of club Q is 29 years. Question 2 of 8 At a certain factory. The two quantities are equal. The two quantities are equal. The relationship cannot be determined from the information given. Quantity B The number of members in club Q Quantity A is greater. The ratio of workers who take the bus to work to those who drive to work is 2 : 5. . Inc.LESSON 3 MATH SCRATCH PAPER 3 © The Princeton Review. | 71 . in miles per hour. when he drove from his job to the restaurant?      30 40 45 50 60 Question 5 of 8 November October September August July June May Depth of Water (in inches) Depth of Smith Pond During a drought. he would have decreased the time it took him to drive from his job to a certain restaurant by 25%. . Each unit on the vertical axis represents 1 inch.MANUAL FOR THE GRE Question 4 of 8 3 If Dan had increased his average speed by 20 miles per hour. If the depth of the lake decreased 20 percent from July to August. What was Dan’s actual average speed. what was the depth of the lake in August?  5 inches  20 inches  25 inches  30 inches  40 inches 72 | © The Princeton Review. Inc. the depth of a pond was measured each month from May through October. | 73 .LESSON 3 MATH SCRATCH PAPER 3 © The Princeton Review. Inc. which of the following is y in terms of x and z ? x+ z 2 x+ z 3 2z − x z 3 − x 2 3z − 2x Question 8 of 8 Earthquake Fault Zones Average Annual Frequency of Earthquakes 1986-1993 Zone One Zone Two Zone Three Zone Four Zone Five x 8. Ollie drives at an average speed of 50 miles per hour from Town C to Town B.7 5.3 5.0.0 . a distance of 150 miles.5 7. If the average of x and y is z. then how much less than the mean of the five annual earthquake frequencies is the mode of the five annual earthquake frequencies? 1.3 5. Quantity A Amount of time Stan spends driving Quantity B Amount of time Ollie spends driving Question 7 of 8 The average of 2 numbers is x.MANUAL FOR THE GRE Question 6 of 8 3 Stan drives at an average speed of 60 miles per hour from Town A to Town B.7 74 | © The Princeton Review.7 y In the chart above. 5. if the mean frequency of earthquakes in Zones One. and Three is 8.0 8. a distance of 120 miles. Two.5. Inc. and the mean frequency of earthquakes in Zones Four and Five is 5. | 75 . Inc.LESSON 3 MATH SCRATCH PAPER 3 © The Princeton Review. Write formula: D = R × T RESPONSE “…average…” Percent change = RESPONSE “…ratio…” TRIGGER “…percent increase/more…” Write formula: RESPONSE | “…percent decrease/less…” RESPONSE 76 “…percent change…” RESPONSE 3 .MANUAL FOR THE GRE SUMMARY TRIGGER TRIGGER TRIGGER TRIGGER © The Princeton Review. “…median…” “…speed…” “…rate…” difference ×100 original Draw ratio box on scratch paper. Inc. Identify the list and put the numbers in order. Draw an Average Pie every time the word average appears in the question. Lesson 3 Verbal . Come up with your own word or phrase for the blank. .MANUAL FOR THE GRE Question 1 3 Bob is well known for being _________ because he frequently gives money to charities. Inc. 78 | Find the Story. Check each answer choice and use your scratch paper: ✓ an answer that sort of matches your word × an answer that does not at all match your word ? any word you don’t know for a maybe © The Princeton Review. Don’t plug the words into the sentence. SCRATCH PAPER Your word/phrase: critical stingy cunning munificent famous Ignore the answer choices. 3. . . 2. Write that word or phrase down on your scratch paper. . . Steps for Sentence Equivalence Questions 1. . which were written in the early years after the founding of the United States of America and are frequently the subject of contextual analysis by historians. forbidding tone.LESSON 3 VERBAL GET A CLUE Who or what is the blank talking about? What information does the sentence give you about that person or thing? 3 The clue is the word or phrase in the sentence that indicates what word or idea must go in the blank. Art critics have characterized Jackson’s latest work as a _________ of different ideas. The _________ professor was so talkative that his rambling lectures would continue long after the students had left the lecture hall. Van Vliet was a sculpting _________ . His greatest talent was his _________ : his ability to lie to anyone. Acclaimed by several important artists as a prodigy. © The Princeton Review. Suddenly he _________ . Inc. all thrown together with little thought of any unifying theme. and no one could tell where he had disappeared to. are noted for their dark. The _________ stories in Brown’s novels. Tamson was so gifted a singer that her colleagues were often dazzled by her _________ and failed to appreciate her other talents. | 79 . and many others must work together to produce a movie.MANUAL FOR THE GRE Question 2 3 Filmmaking is a _________ effort. . . 80 | prosperous stalwart dismayed prescient steadfast naïve © The Princeton Review. . . cinematographer. . writer. Mr. . . Inc. editor. he remained calm and resolute even during times of immense volatility in the market at large. . . . . creative lucrative collaborative joint concentrated glamorous Question 3 As CEO. since the director. . Bluvband distinguished himself primarily because he was more _________ than his peers. SCRATCH PAPER Your word/phrase: . I really like you. and ______________________________________________. . His early work was boring. . . : since consequently She used to be poor. . but also insofar because and . now she’s ______________________________________. . . but ______________________________________________.LESSON 3 VERBAL Question 4 SCRATCH PAPER Although most species of fish off the southwest coast of Africa have died off due to the oxygen-poor and jellyfish-rich waters. Inc. © The Princeton Review. the bearded goby is actually _________ . . | 81 . Your word/phrase: 3 thriving destructive withering transitory flourishing picturesque I really like you. Contrasts Agrees although though despite however nonetheless nevertheless instead rather whereas while but yet thus therefore not only . so it’s refreshing to see that his latest piece is ______ _______________________________________________________________. . MANUAL FOR THE GRE Question 5 3 Some pundits postulate that the end of the Cold War _________ one of the major political parties. . . . . . . Inc. . . . . fragmented bolstered encouraged engendered vitiated attenuated Question 6 As soon as Brett stepped off stage. he slipped out of his brash and outspoken stage persona and returned to his usual _________ self. . SCRATCH PAPER Your word/phrase: . 82 | timorous heady diffident florid fastidious blunt © The Princeton Review. many voters had previously viewed that party as vital because of its role in the fight against Communism. .  . Inc. but only a small fraction of these colors are actually available. . . only to find themselves stunned and devastated by his confession on the final day of the proceedings. . . . . SCRATCH PAPER 3 Your word/phrase: fixed infinite innumerable realistic limited essential Question 2 of 5 James’s _________ work associates were among the many who trusted his financial savvy and testified on his behalf in the hearing.LESSON 3 VERBAL DRILL Question 1 of 5 The stunning array of colors present in our natural world would suggest a seemingly _________ palette for paint manufacturers to draw on for inspiration. . . | 83 . cynical unwavering petty recent steadfast capricious © The Princeton Review. . . . MANUAL FOR THE GRE Question 3 of 5 3 Colbert’s pompous character is crafted with such _________ that some critics mistake his satire for mere bombast. . . . . . . insouciance guile originality cunning literacy refulgence Question 4 of 5 Unfortunately, Jackson’s public disavowal of the group was _________ by his ongoing support of the group’s leaders. . . . . . . undermined fortified reviewed braced subverted retained Question 5 of 5 The studio head, naturally _________ , lets his underlings speak for him during most meetings, remaining silent until absolutely necessary. . . . . . . 84 | taciturn laconic solicitous impertinent loquacious blithe © The Princeton Review, Inc. SCRATCH PAPER Your word/phrase: LESSON 3 VERBAL STEPS FOR SENTENCE EQUIVALENCE QUESTIONS 1. Find the Story. 2. Come up with your own word or phrase for the blank. Write it down on your scratch paper. 3. Check each answer choice: ✓ an answer that sort of matches your word × an answer that does not at all match your word ? any word you don’t know for a maybe © The Princeton Review, Inc. | 85 MANUAL FOR THE GRE 3 5 10 15 20 25 30 35 40 45 86 | Because democracies allow their citizens to elect leaders and sometimes—through referendum—vote on particular laws, it may seem that the primary result of political democratization is the increase in freedom for the country’s citizens. But in spite of the fact that democracies ostensibly allow citizens to place limits on the power exercised by their leaders, the 20th century saw the rise of what Fareed Zakaria termed “illiberal democracies”—governments elected through democratic elections but nonetheless tyrannical—which deprive their citizens of rights and freedoms. This phenomenon can be seen in various regions of the globe ranging from Peru to Sierra Leone to Slovakia to Pakistan. A particularly infamous example is Adolf Hitler, who became chancellor of Germany through free election. One unexpected result is that tyrannical regimes can be far more tolerant than their liberal counterparts. This incongruity is not mere irony or accident, but rather the result of the absence of one essential component for a free society. Giovanni Sartori notes how most Third World countries that—while still impoverished—proclaimed themselves democracies became dictatorships within a decade. In contrast, autocratic regimes that cultivated economic freedom, even if only for elites, inevitably became democracies by the mid-20th century. Consider the democratic evolution of Great Britain, Denmark, Belgium, and the Netherlands, in contrast with the democratic evolution of France, Austria, and Germany. The evolutions of the former were far more peaceful compared to those of the latter. History has shown that in even the most undemocratic regimes, once the seeds of an economically independent middle class have been planted, the change to a free, democratic society is inevitable. The bestconsolidated democracies in Latin America and East Asia were all ruled by military juntas. But by opening their economies—however slowly— the process made the government more liberal and the economically prosperous citizenry more demanding of limits of power; enfranchisement became inevitable. It is no coincidence, then, that an economically independent middle class is glaringly absent in failed democracies that degenerated into dictatorships. © The Princeton Review, Inc. Question 1 All of the following are stated by the author as possible characteristics of countries with democratically elected regimes EXCEPT enfranchised populaces limits on powers of leaders  despotism  freedom of religion  economic independence for its middle class Question 2 Consider each of the choices separately and select all that apply. The author suggests which of the following about democracies? . They may be more resilient when buttressed by a strong middle class. . They are not sufficient for securing certain . freedoms for their citizens. During the 20th century, they usually devolved into tyrannical regimes. LESSON 3 VERBAL SCRATCH PAPER Answering the Questions 3 1. Translate the question. 2. Find proof in the passage. 3. Answer the question in your own words. 4. POE. Look to ELIMINATE. Wrong answers • contradict the passage • don’t answer the question • are NOT found in the text © The Princeton Review, Inc. | 87 MANUAL FOR THE GRE 3 Question 3 Question 4 In the context in which it appears, “incongruity” (line 21) refers to The primary purpose of the passage is to the fact that some democracies only confer rights to the elite and not to the masses  the fact that democracies inevitably devolve into despotic regimes  the fact that some despotic regimes have certain liberal characteristics that some democracies lack  the fact that the middle class is largely absent from failed democracies  the fact that some countries have yet to evolve into democratic regimes 88 | © The Princeton Review, Inc. compare two outcomes that result from implementing a particular system of government  contrast two forms of government  explain why one form of government is superior to another  discuss why democracies are not always capitalistic  explain why an apparent contradiction occurs LESSON 3 VERBAL SCRATCH PAPER Genre (What) • Problem • Question • Conflict • Paradox • Change • Innovation • Discovery Purpose (Why) • • • • • Predict Recommend Inform/Explain Correct Evaluate Structure (How) • • • • • Cause/Effect Chronology Classification Comparison/Contrast Steps/Stages 3 © The Princeton Review, Inc. | 89 the author would most likely agree with which of the following?  The cause of the Permian mass extinction is not controversial. then oceanic sediments from the Permian period will yield chemical evidence of a rise in hydrogen sulfide consuming bacteria. Some hypothesize that the impact of a massive asteroid caused the sudden eradication of most species. Question 1 The primary purpose of the passage is to  consider several hypotheses concerning the cause of the Permian mass extinctions  discuss the strengths and weaknesses of the asteroid hypothesis concerning the cause of the Permian mass extinctions  propose that theories regarding the cause of the Permian mass extinctions be tested  argue the Permian mass extinctions could not have been caused by a volcanic explosion  describe one reason that a rise in hydrogen sulfide would cause massive marine extinctions Question 2 Select the sentence that best illustrates the reason one theory may be superior to the other theories mentioned in the passage. Fortunately. this theory is testable.  There is no conclusive explanation for the Permian mass extinction.  The Earth experienced a series of successive meteor strikes that destroyed plant life. However. . leading to intense global warming. If this theory is true. Question 3 According to the passage. To produce such a pattern would require a succession of asteroid strikes thousands of years apart.  The Permian mass extinction was caused by depleted oxygen that accompanied increases in toxic hydrogen sulfide in the oceans. Other theorists have proposed that volcanic explosions raised the CO2 levels. a look at the carbon-isotopic record suggests that existing plant communities were decimated and revived several times. A new theory proposes that the combination of rising concentrations of toxic hydrogen sulfide in the world’s oceans and gradual oxygen depletions in the surface waters caused the extinctions. One problem with this theory is that it cannot explain the mass marine extinctions at the end of the Permian period. Inc.  Marine life must have survived the Permian mass extinction.MANUAL FOR THE GRE 3 5 10 15 20 Theorists are divided about the cause of the Permian mass extinction. 90 | © The Princeton Review. LESSON 3 VERBAL SCRATCH PAPER 3 © The Princeton Review. Inc. | 91 . particularly those interested in educational reform. 92 | © The Princeton Review. Question 3 In the first paragraph. despite their merits. Question 1 Which of the following statements best summarizes the main point of the passage?  Assessments of charter schools’ performance have reinforced the position that rigid rules and regulations are stifling academic achievement. the prior achievement of the students. and statutes that govern them will have a revolutionary effect on academic achievement. regulations. or some other factor. Metrics for educational accountability have changed considerably in the past decade. Thus. Educators. select the sentence that best illustrates an example of a hypothetical benefit.  It qualifies the author’s agreement with those academics who question the degree to which charter schools have made an impact. it has been suggested that such schools could develop more effective teaching methods that could then be replicated in other schools. answerability to multiple stakeholders. the challenging conditions under which schools operate. Inc. while public opinion differed concerning the social desirability of charter schools. For instance.  Freeing schools from some regulations has caused a positive change in education. charter schools are less likely to meet state performance standards than traditional public schools. fail to overcome the long-standing problems in public education. . Charter schools.  It draws a conclusion concerning the challenges that schools face that goes beyond the information in the previous paragraphs. impossible to know whether this is because of the performance of the schools. In 1991. however. They conclude that freedom from many of the policies and regulations affecting traditional public schools and the concomitant control over decisions that guide the day-to-day affairs of the school have not resulted in equally dramatic changes in students’ academic abilities.  It qualifies the author’s rejection of those academics who question the degree to which charter schools have made an impact. performance on state-mandated tests is increasingly used as a measure of student performance. all agreed that there would likely be a pronounced effect. It is. and the difficulty of meeting the educational requirements of children with special needs all persist. many critics warned of the deleterious effects that such free-wheeling schools could have on the academic achievement of students. Fundamentally. have changed little: the struggle for resources. be they traditional or charter schools. now seriously question the degree to which charter schools have made an impact.  Freeing schools from rules and regulations has not had the deleterious effect that some critics had feared.  Charter schools. In many states.  It restates the point concerning the successes that schools have achieved. public schools that operate under a contract (or “charter”).  Charter schools have engendered a whole new approach to educating children. low pay for teachers. were given just such an opportunity.MANUAL FOR THE GRE 3 5 10 15 20 25 30 35 40 It is frequently assumed that freeing schools from the rigid rules. Question 2 Which of the following best describes the function of the concluding paragraph of the passage?  It sums up the general points concerning charter schools made in the entire passage. when Minnesota passed the first charter school law. Inc. | 93 .LESSON 3 VERBAL SCRATCH PAPER 3 © The Princeton Review. 2.MANUAL FOR THE GRE SUMMARY Answering the Questions 1. Answer the question in your own words. Look to ELIMINATE. 3. • contradict the passage • don’t answer the question • are NOT found in the text . Find proof in the passage. 4. Inc. Wrong answers 94 | © The Princeton Review. POE. Translate the question. Lesson 4 Math . Inc. .MANUAL FOR THE GRE SCRATCH PAPER GEOMETRY BASIC STEPS 4 96 | 1. Draw It. Label Everything! Write out Formulas. 2. © The Princeton Review. 3. LESSON 4 MATH SCRATCH PAPER 4 © The Princeton Review. Inc. | 97 . Quantity B 8 . Inc.MANUAL FOR THE GRE TRIANGLES Question 1 B 4 C 8 A D ABCD is a square. Quantity A The area of XYZ 98 | © The Princeton Review. TRIGGER Quantity A The length of diagonal AC Quantity B 12 Trigger: _______________________________________________________________ Question 2 Y 4 X Z Triangle XYZ is an equilateral triangle. | 99 .LESSON 4 MATH SCRATCH PAPER 4 Identify your triangles and label the sides! a a √2 30° 2a a √3 45° a a RESPONSE 45° 60° © The Princeton Review. Inc. Inc. 2 a+a . if BC = 4 2 .MANUAL FOR THE GRE Question 3 B 30º 4 60º A a C What is the perimeter of triangle ABC in terms of a ? 2a + 3 a(3 + 3 ) 3a + a 2 2a 3 Question 4 B A C Triangle ABC is an isosceles triangle and AB = 6 Quantity A The perimeter of triangle ABC Quantity B The area of triangle ABC Question 5 B 105 A 30 C In the triangle above. then AB = 6 4 3 8 4 6 10 100 | © The Princeton Review. LESSON 4 MATH SCRATCH PAPER 4 © The Princeton Review. | 101 . Inc. What is the area of the shaded region? 3π 102 | © The Princeton Review. Inc. If the measure of angle AOC is 60°. Trigger: _______________________________________________________________ Question 2 B 4 O 225º A O is the center of the circle shown above. 4π 6π 8π 16π .MANUAL FOR THE GRE CIRCLES Question 1 A 4 B C O O is the center of the circle shown above. then the length of arc ABC is what fraction of the circumference? TRIGGER Enter your answer as a fraction. LESSON 4 MATH SCRATCH PAPER 4 RESPONSE Central Angle sector arc = = 360º circumference area © The Princeton Review. Inc. | 103 . If the length of arc ABC is equal to one-sixth of the circumference of the circle. . If arc ABC has a length of 5π. what is the measure of angle AOC ? 60° 90° 100° 110° 120° Question 4 B A C Note: Figure not drawn to scale.MANUAL FOR THE GRE Question 3 B A C 4 9 O O is the center of the circle above. what is the area of the circle? 6π 12π 24π 36π 48π 104 | © The Princeton Review. In the circle above. Inc. chord AC has a length of 6. LESSON 4 MATH SCRATCH PAPER 4 © The Princeton Review. Inc. | 105 . what is the area of the shaded region? TRIGGER 8 12 3 16 3 24 3 64 Trigger: _______________________________________________________________ Question 2 2m In the figure above. 6m2 15m2 18m2 60m2 . respectively. then what is the area of the figure? 6m 106 | © The Princeton Review. Inc. if each short segment has length 2m. AC = CE = AE = 8. If B and D are the midpoints of AC and CE. and all segments intersect at right angles.MANUAL FOR THE GRE SHADED REGIONS AND STRANGE-LOOKING SHAPES Question 1 C 4 B D A E In the figure above. | 107 . etc.). © The Princeton Review. If all else fails. draw radii & drop heights. connect. play with the figures! RESPONSE Find familiar shapes. Inc.LESSON 4 MATH SCRATCH PAPER 4 Shaded = Total – Unshaded Draw lines (split. then what is the area of the shaded region? 4−π 8 − 2π 16 − 4π 4 + 2π 8+π 108 | © The Princeton Review. Inc.MANUAL FOR THE GRE Question 3 G 10 F 4 10 8 E H 6 What is the area of quadrilateral EFGH shown above? 24 + 25 3 24 + 50 3 48 + 50 3 72 It cannot be determined from the information given. side XY of square WXYZ is equal to 2. . Question 4 W Z X Y In the figure above. If Z is the center of the circle. | 109 .LESSON 4 MATH SCRATCH PAPER 4 © The Princeton Review. Inc. MANUAL FOR THE GRE OVERLAPPING SHAPES Question 1 4 B C A D Note: Figure not drawn to scale Rectangle ABCD has length 6 and width 8. Trigger: _______________________________________________________________ . What is the area of the circle? TRIGGER 10π 20π 25π 64π 100π 110 | © The Princeton Review. Inc. Inc.LESSON 4 MATH SCRATCH PAPER 4 RESPONSE Figure out what the two shapes have in common. | 111 . © The Princeton Review. if A and C are the centers of the two circles. The two quantities are equal. Quantity B The area of triangle BCD Quantity A is greater.MANUAL FOR THE GRE Question 2 B x° 4 A C D In the figure above. then x = 30 40 45 60 90 Question 3 B A C D AD || BC Quantity A The area of triangle ABC     112 | © The Princeton Review. Quantity B is greater. Inc. . The relationship cannot be determined from the information given. | 113 . Inc.LESSON 4 MATH SCRATCH PAPER 4 © The Princeton Review. TRIGGER Quantity A The length of the third side Quantity B 5 Trigger: _______________________________________________________________ Question 2 c° d° a° b° e° f° g° h° Note: Not drawn to scale. . . . In the figure above. a=f b=f c=h .MANUAL FOR THE GRE DRAW & REDRAW Question 1 4 A triangle has sides of lengths 3 and 4. if a = e. Inc. then which of the following must be true? Indicate all such statements. 114 | © The Princeton Review. Inc.LESSON 4 MATH SCRATCH PAPER 4 RESPONSE Draw it twice. © The Princeton Review. | 115 . Exaggerate the differences. Question 2 Two quilts are equal in area. each of which has an area of y square inches. Quantity B 45 . Inc.1 f 6. The first quilt is made up of 25 patches. Quantity A x Quantity B y Question 3 (x. stretch and squash.1 6.1 6. The second quilt is made up of 14 patches.0 g 6. Exaggerate the differences.1 Quantity A f Quantity B g When redrawing your shape.MANUAL FOR THE GRE STRETCH & SQUASH Question 1 4 6. each of which has an area of x square inches. y) a° x<y Quantity A a 116 | © The Princeton Review.1 6. Inc. | 117 .LESSON 4 MATH SCRATCH PAPER 4 © The Princeton Review. What is the value of x ? 60 75 105 115 140 Question 2 of 10 E B 120° C A x° D In the figure above. and ∠BCE = 120°.MANUAL FOR THE GRE GEOMETRY TIMED DRILL Question 1 of 10 4 N M x° l1 40° 65° l2 In the figure above. C is the midpoint of both segment AE and segment BD. four lines intersect as shown. Inc. . l1 || l2. 240 300 420 It cannot be determined from the information given. If n = 60. If AE = BD. then x = 30 45 50 60 75 Question 3 of 10 q° p° r° n° In the figure above. what is the value of p + q + r ? 180 118 | © The Princeton Review. LESSON 4 MATH SCRATCH PAPER 4 © The Princeton Review. Inc. | 119 . Quantity B The perimeter of a square with a side of length 8 . Inc. The sum of QR 3 PQ + QR + RS is what percent of the perimeter of the rectangle? 55 5 % 9 2 66 % 3 70% 75% 5 85 % 7 Question 6 of 10 Quantity A The perimeter of a rectangle with a side of length 15 120 | © The Princeton Review. PQ = 2 .MANUAL FOR THE GRE 4 7 a+ b+ 5 Question 4 of 10 x° x° Quantity A a Quantity B b Question 5 of 10 P S Q R In rectangle PQRS above. LESSON 4 MATH SCRATCH PAPER 4 © The Princeton Review. | 121 . Inc. Quantity B is greater. The relationship cannot be determined from the information given. In the figure above. then. Inc. . in terms of x. Quantity A One-half the area of the circle with center Q     Quantity B The shaded region Quantity A is greater. The two quantities are equal. Question 8 of 10 Note: Figure not drawn to scale. the area of the larger circular region is twice the area of the smaller circular region. If the diameter of the larger circular region is x.MANUAL FOR THE GRE Question 7 of 10 4 Q S The two circles with centers at Q and S both have radius r. what is the area of the smaller circular region? π x2 2 π x2 4 π x2 8 πx 2 πx 4 122 | © The Princeton Review. Inc. | 123 .LESSON 4 MATH SCRATCH PAPER 4 © The Princeton Review. Inc. and JK = 3. Quantity B is greater.MANUAL FOR THE GRE Question 9 of 10 G H 4 K I J In the rectangular solid depicted above. IJ = 12. Quantity A The area of rectangle HGKJ     Quantity B 39 Quantity A is greater. Quantity B is greater. The two quantities are equal. Quantity B The volume of a cylinder that has a circular base with a radius of 4 inches and a height of 3 inches Quantity A is greater. The two quantities are equal. The relationship cannot be determined from the information given. Question 10 of 10 Quantity A The volume of a cylinder that has a circular base with a radius of 3 inches and a height of 5 inches     124 | © The Princeton Review. . The relationship cannot be determined from the information given. HI = 5. | 125 . Inc.LESSON 4 MATH SCRATCH PAPER 4 © The Princeton Review. = circumference area circle TRIGGER TRIGGER Overlapping shapes Find the elements the two shapes have in common. . drop heights. or otherwise play with the shape). RESPONSE | Shaded regions or strange-looking shapes RESPONSE 126 RESPONSE Find familiar shapes. a big side that is twice the small side. sector. Shaded = Total – Unshaded. 3 . draw radii. Write your formula: RESPONSE Right triangle with 30º. 60º. or the height of an equilateral triangle 2 RESPONSE Right triangle with 45° or or diagonal of a square RESPONSE 4 TRIGGER SUMMARY angle F 360 = arc area sector . Find the 30°-60°-90° triangle (you know it’s in there somewhere). Inc. © The Princeton Review. TRIGGER Geometry on Quant Comp or Must Be questions Draw the shape twice. Draw lines (split. Exaggerate the differences. or a fraction of a circle Find the 45°-45°-90° triangle (you know it’s in there somewhere). connect.MANUAL FOR THE GRE TRIGGER TRIGGER Arc. Lesson 4 Verbal . What the passage states. Remember: Half Bad = All Bad. . Common Wrong Answer Types 1. or WHAT would be similar to the passage. superlatives. 3. always. 2. Question about a specific part of the passage or the passage overall. Read all five answers in full. 128 | Doesn’t answer the question • Too broad or too narrow • Wrong location (peripheral or wrong paragraph) Contradicts the passage • Contradicts a fact in the passage • Goes against the main point or purpose • Contradicts the structure/chronology in the passage Not in the text • Might be true but not supported • Contains information from outside the passage (predictions or judgments) • Extreme language—absolutes. Inc. Use a two-pass approach through the answer choices. not to justify. Translate the Question Proof: Find proof in the passage Predict: Answer the question in your own words POE: Look to eliminate How GRE Constructs a Typical Reading Comp Question 1. 4. WHY the passage states something. 2. Look to eliminate. and extreme words (must. Words from the wrong part of the passage (doesn’t answer the question) Words from the passage made too extreme (not in the text) Words combined with something NOT from the passage (not in the text) Correct information paraphrased and disguised Patchwork of words and phrases taken directly from the passage How to Avoid Falling Into Traps • • • • Predict what the answer will do before looking at the answer choices. etc…. 3. all) that go beyond the passage © The Princeton Review. HOW the author feels about something.MANUAL FOR THE GRE ATTACKING THE QUESTIONS 4 1. you cannot pick it. Inc. or sentence that proves your answer choice.LESSON 4 VERBAL Down to 2? 1) 2) Compare the remaining answers to each other. and come back to it after two questions. Which answer choice most agrees with the main idea? Still struggling? Just mark it. 4 If you can’t put your finger on a single word. | 129 . move on. phrase. © The Princeton Review. What’s the same? What’s different? Go back to the passage. It’s wrong. As anyone will attest. and lateral displacements. vertical. and the saccule. In essence. A mass of particulate material presses down on membranes. the inner ear signals just the opposite. One of several frames of reference utilized by living creatures in the effort at orientation is the direction of gravity. the utricle. . In human beings. Another instance of the system’s failure is motion sickness. this orientation is provided by the vestibular system of the inner ear. the result is motion sickness. we manage to maintain a sound sense of orientation despite the fact that our heads are seldom perfectly perpendicular to the plane of gravitational pull. The brain is flooded with contradictory signals: while the eye indicates that the body is at rest. By utilizing this system of mental signals. Inc. watching television while lying sideways is taxing on the brain. allowing the eye to match the information contributed by the vestibular system. these canals form a system of Cartesian coordinate axes along which the brain maps the body’s horizontal. Yet this complex system has its imperfections. The simple cure for this is to restore both systems of signals to synchrony. The three semicircular canals are oriented perpendicularly to one another and provide the locus of balance. When signals from the retina’s frame and signals from the inner ear’s frame fail to coincide. This is accomplished by redirecting the gaze to the exterior of the moving vehicle. further allowing the mind to register linear motion and the direction of gravity. a labyrinth of chambers comprising the semicircular canals.MANUAL FOR THE GRE Line 4 5 10 15 20 25 30 35 130 | © The Princeton Review. while reading at the same inclination is all but impossible (without tilting the book to match the angle of sight). LESSON 4 VERBAL SCRATCH PAPER 4 © The Princeton Review, Inc. | 131 MANUAL FOR THE GRE 4 Question 1 Question 4 According to the passage, motion sickness is induced by The main function of the passage as a whole is to delayed compensation of the vestibular system asynchronous pairing of information from two systems the non-perpendicular orientation of the head with respect to the body a failure to register linear motion and the direction of gravity disorientation caused by pressure in the inner ear Question 2 Question 5 Consider each of the choices separately and select all that apply. Which of the following best describes the organization of the passage? According to the passage, the vestibular system of the inner ear allows humans to accomplish the following: . Track forward movement . Pinpoint the origin of a sound . Maintain spatial orientation Question 3 It can be inferred from the passage that the utricle and the saccule are solely responsible for the maintenance of balance correct for gravitational orientation provide axes of spatial orientation are integral with the semicircular canals function only in tandem with visual signals 132 | account for the failure of the vestibular system of the inner ear reconcile discordant theories about spatial orientation investigate the impact of stresses on the vestibular system of the inner ear consider the limitations of one bodily system describe the various frames of reference used to orient the body © The Princeton Review, Inc. A system is described, details are provided, and possible alternative explanations are considered. A system is described, and its imperfections are explained and contrasted with another system’s. A system is described, its components are enumerated, and an explanation for its purpose is introduced. A system is described, and examples suggesting that the system is inadequate are considered. A system is described and weaknesses of that system are then exposed. LESSON 4 VERBAL SCRATCH PAPER 4 © The Princeton Review, Inc. | 133 MANUAL FOR THE GRE Line 4 5 10 15 20 25 30 35 134 | © The Princeton Review, Inc. The wealth of morphological, phonetic, and word similarities among certain languages has led linguists to recognize the unity of the welldefined family of languages called the Aryan or Indo-European family. Yet even this latter term is largely a misnomer. This group of languages spreads over an enormous range virtually without interruption, reaching from Central Asia to the fringes of westernmost Europe. The westernmost terminus of the family is Celtic, while its easternmost representatives were the Tokharian languages, a pair of tongues once spoken by the residents of the Tarim River Basin in Western China and unearthed in documents written more than a thousand years ago. So remarkable and definite are the similarities among these languages that linguists are convinced they all derived from an earlier language spoken by some community in the prehistoric past. While we know that Latin began as a rustic dialect in the province of Latium, no one knows where proto-Aryan was first spoken. Some speculate that it was first used in Southern Russia, while still others point to the Iranian plateau as a potential cradle. Though some philologists believe that the Old Indic and Persian of the Avesta contain the most archaic features of Aryan found to date, this does not necessarily fix the habitat of these early Aryan-speaking peoples closer to Asia than to Europe. Consider Icelandic. Though this language has strayed far from its birthplace, it preserves many of the characteristics discarded by those who remained behind. From the existing evidence, only one thing seems certain. By the time of the Vedic hymns, the first recorded instance of Aryan, those tribes speaking this early language had already begun their widespread dispersal. LESSON 4 VERBAL SCRATCH PAPER 4 © The Princeton Review, Inc. | 135 MANUAL FOR THE GRE 4 Question 1 Question 3 The main purpose of this passage is to The author mentions the Tokharian languages primarily in order to account for a difference illustrate a difficulty advocate a change refute a hypothesis define similarities date them to a far earlier period than Celtic suggest that they possess many of the same features as did the Old Indic and Persian of the Avesta prove that they were once spoken over a far greater range than they are today undermine the accuracy of the name “Indo-European” for their particular family of languages explain the remarkable similarities among the languages spoken by residents of the Tarim River Basin Question 2 Which of the following situations is most nearly analogous to the history and unique characteristics of Icelandic as described in the passage? A nomadic tribe which resides primarily in one part of the Sahara is known to sing songs from a distant part of the Sahara. Two communities of people develop similar styles of pictographic writing despite never having had contact with one another. Descendants of the French explorers who first settled an Atlantic island routinely use words, phrases, and forms of address longabandoned in contemporary France. One group of South American Indians speaks a language that is a unique assimilation of several distinct modern languages. Modern inhabitants of a city speak a dialect which retains many of the words abandoned by speakers of a different dialect in a distant city. 136 | © The Princeton Review, Inc. Question 4 Consider each of the choices separately and select all that apply. According to the passage, Indo-European languages are characterized by . similarities in the structures of words and . . in the sounds employed widespread recorded instances in prehistoric literature preservation of characteristics discarded by earlier speakers | 137 .LESSON 4 VERBAL SCRATCH PAPER 4 © The Princeton Review. Inc. Inc. • Don’t answer the question • Are not found in the text . Wrong answers: • Contradict the passage 138 | © The Princeton Review.MANUAL FOR THE GRE SUMMARY 1) Translate the Question / Make it a question: What info do they want? 2) Proof: Where is this info? Map or Passage? Which paragraph? 3) Predict: What should the correct answer do or say? 4) POE: Look to eliminate. not to justify. Lesson 5 Math . 000 $48.000 $2.000.000.000 $121.000.000 $624.000 . Inc.6 billion Summary of Community Services Expenditures by Category in City T Children’s Services Retirement Homes Hostels Housing Libraries Public Health Social Development Social Services Total 140 | © The Princeton Review. 1998 5 Community Services 44% Public Transit 14% Urban Planning and Development 1% Corporate Services 4% Other 12% Culture and Tourism 6% Police 8% Public Works 11% 100% = $5.000 $176.000 $117. 1997 $211.000.000.000 $9.000.000 $1.000 $89.000.MANUAL FOR THE GRE THE CHART TOTAL EXPENDITURES AND SUMMARY OF COMMUNITY SERVICE EXPENDITURES FOR CITY T Total Expenditures in City T.000.000.000.000.000.000.000.000.458.000 $62.000 1998 $228.000 $8.000.000 $96.829.000 $264.153.000 $181.000 $1.000 $906.000.000. Use rounding. 2. • • • Scroll down to find all the charts.LESSON 5 MATH GET YOUR BEARINGS Before you start the questions. 4. Which chart is the question about? Go back to the chart to locate information specific to the question. 5 WORKING THE QUESTIONS 1. 3. Estimate before you calculate. Inc. Use your scratch paper as a ruler if necessary. Read the question carefully. estimation. © The Princeton Review. | 141 . Check units. Label all numbers and the results of EVERY step. spend a few seconds looking the charts. Stay organized. and common percent-to-fraction conversions to arrive at a rough answer. Read titles and legends. more was spent on Social Services than on any other area. . In 1998. Community Service expenditures in City T exceeded expenditures for the next four most highly funded areas combined.MANUAL FOR THE GRE Question 1 Which one of the following Community Service programs had the greatest percent increase in expenditure from the 1997 budget to the 1998 budget in City T ? Children’s Services Hostels Public Health Social Development Social Services 5 Question 2 The amount by which City T’s Community Service expenditures in 1998 exceeded Public Works expenditures in 1998 was what percent of the expenditures for Public Works in 1998 ? Disregard the percent sign when entering your answer. Question 3 Which of the following can be inferred from the graph or table? Indicate all such statements. Inc. 142 | © The Princeton Review. . . In 1998. . In both 1987 and 1998. Libraries received greater funding than did Public Health. Inc.LESSON 5 MATH SCRATCH PAPER 5 © The Princeton Review. | 143 . 7 5 Percent 5. if a total of 1. West Pacific . what was the overall population of people 16 years or older in the United States that year.7 Northeast 3.1 4 3.MANUAL FOR THE GRE UNITED STATES UNEMPLOYMENT RATES AS A PERCENT OF THE POPULATION 16 YEARS AND OLDER BY REGION 1998 1999 6 5.4 4.9 5 4.2 million people were unemployed in the Northeast region.4 5.6 Midwest South West Pacific Region Question 4 Which region had the smallest decrease in its unemployment rate? Northeast Midwest South Question 5 In 1999.2 4. in millions? million Question 6 Which of the following regions had the greatest percent decrease in unemployment rate from 1998 to 1999 ?  Northeast  Midwest  South  West Pacific 144 | © The Princeton Review. Inc.4 4.7 4. Inc. | 145 .LESSON 5 MATH SCRATCH PAPER 5 © The Princeton Review. Students who receive a score of 66 or lower on the exam will fail the course. the 400 students taking statistics received an average score of 76 on the final exam. 102 . 11 5.MANUAL FOR THE GRE 5 TRIGGER STANDARD DEVIATION Trigger: _______________________________________________________________ Question 1 Which of the following lists of data has the greatest standard deviation? 10. Quantity A The standard deviation of Set A Quantity B The standard deviation of Set B Question 3 At Rocktown College. each of which is between 0 and 100. Inc.10. 19 100. each of which is between 100 and 200. 15 Question 2 Set A is a set of 10 integers. How many of the students will fail the course? 146 | © The Princeton Review. and the scores had a normal distribution. 10. Set B is a set of 10 integers. 10.10 9. 101. 1. and only 8 students earned a score of 96 or higher. 10. LESSON 5 MATH SCRATCH PAPER Draw a bell curve! RESPONSE 5 © The Princeton Review. | 147 . Inc. Inc. regroup. try to cancel out common factors.” or “percent decrease” TRIGGER TRIGGER REVIEW © The Princeton Review. RESPONSE Urge to set up equation and do algebra The words “how much. Set up your scratch paper and Plug In using FROZEN. . RESPONSE TRIGGER “Must be” Plug In more than once. RESPONSE | Exponents or numbers too big to calculate RESPONSE 148 Write the percentage change formula: difference Percent change = ×100 original RESPONSE 5 Question asks for “percent change.C. target number circled.” “percent increase.MANUAL FOR THE GRE TRIGGER TRIGGER Factor. TRIGGER Variables in the answer choices List A. Plug In (terms labeled. all answer choices checked).” or “what is the value of” List answer choices in a column on your scratch paper.B. Write answers choices down the left side of scratch paper and variables across the top. Label the first column and PITA.E on scratch paper. RESPONSE TRIGGER Quant Comp with variables Plug In more than once. Plug in a simple number. then use FROZEN.” “how many.D. RESPONSE RESPONSE “Median” TRIGGER 5 perpendicular to the base. RESPONSE 1 Write down A = bh and park information 2 underneath. RESPONSE TRIGGER LESSON 5 MATH TRIGGER Find a bunch of numbers and list them in order on your scratch paper. rectangle.) © The Princeton Review. or square problem containing the word “area” Write down the area formula and park information directly underneath. RESPONSE “Parallel lines” or ( Label all big angles and small angles. and add the sides together. | 149 . RESPONSE TRIGGER “Ratio” Draw a ratio box on your scratch paper. Inc. (The height will always be TRIGGER Triangle question contains the word “area” TRIGGER Parallelogram. label the sides.“Average” Draw an Average Pie for every time the word average appears in the question. RESPONSE TRIGGER “Perimeter” Draw the shape. or 3 . You know it’s in there somewhere. Inc. a hypotenuse that is twice the smallest leg. RESPONSE TRIGGER Right triangle with 45° or 2. circumference. RESPONSE TRIGGER Right triangle with 30°. You know it’s in there somewhere. 60°. RESPONSE TRIGGER “Arc” or “sector” Central Angle sector arc = = 360º circumference area RESPONSE TRIGGER MANUAL FOR THE GRE Group problem with overlap or “both” Write down group formula: Total = [Group 1] + [Group 2] – [Both] + [Neither] RESPONSE 5 150 | © The Princeton Review. or diagonal of a square 45°-45°-90° triangle. diameter. and area. Find radius.TRIGGER Circle Write “r d C A” vertically on scratch paper. Group question in which elements are in either one group or other (no overlap) Group X Group Y Total Group A Group B Total RESPONSE TRIGGER Draw Group Grid: . or height of equilateral triangle Find the 30°-60°-90° triangle. | 151 .LESSON 5 MATH SCRATCH PAPER 5 © The Princeton Review. Inc. Question 2 of 15 A cell phone company offers two different calling plans to its customers. If the perimeter of the triangle is 12. Question 5 of 15 Y X Z Triangle XYZ in the figure above is an equilateral triangle. of a call. it would have cost each person $1 less. what is its area? 2 3 4 3 8 5 6 10 12 15 Quantity B 12 8 3 .35 for the first 5 minutes and 7 cents for each additional minute.MANUAL FOR THE GRE DRILL Question 1 of 15 Question 4 of 15 Quantity A Quantity B 512 – 510 (23)510 5 Quantity A is greater. 1 1 x Quantity A is greater. Quantity B is greater. With plan C. in minutes. If there had been one more person in the group. the customer is charged $1. Quantity B is greater. With plan D. The relationship cannot be determined from the information given. If x represents the length. the customer is charged a flat rate of 15 cents per minute. The two quantities are equal. How many people were in the group originally? x>0 Quantity A 2 2+ 152 | © The Princeton Review. The relationship cannot be determined from the information given. what is the greatest integer value of x for which a customer can save money by using plan D rather than plan C? 8 9 10 11 12 Question 3 of 15 Several people rented a car for $30. Inc. The two quantities are equal. | 153 . Inc.LESSON 5 MATH SCRATCH PAPER 5 © The Princeton Review. how many customers order both hamburgers and french fries? 15 10 7. Inc. If 22 customers order neither hamburgers nor french fries. 0. –4. M 2 . 7. What is the ratio of alcohol to water in the mixture? 5:1 4:1 12 : 5 6:5 5:6 Question 8 of 15 List A: 3.MANUAL FOR THE GRE 5 Question 6 of 15 Question 9 of 15 On a geography quiz. how many more points did Julie earn than Emily ? Of 110 customers at a restaurant.5 8 30 31 46 88 Question 7 of 15 In a mixture of alcohol and water there is 1 more Question 10 of 15 N 5 alcohol than water. 20. 63 order hamburgers and 71 order french fries. If Katherine and Julia scored an average of 85 points. Emily and Katherine scored an average of 80 points. 7. then the area of the . 8. 8.5 5 2. if MN = circle with the center O is π 4 π 2 π 2π 4π 154 | © The Princeton Review. 0 How much greater is the median of the numbers is list B than the median of the numbers in list A ? O In the figure above. –10 List B: 5. Inc. | 155 .LESSON 5 MATH SCRATCH PAPER 5 © The Princeton Review. MANUAL FOR THE GRE Question 11 of 15 Question 13 of 15 B A 5 C D What is the perimeter of the isosceles triangle ABC shown above if the measure of ∠ ABC is 120°. and 24 of the female employees are blue-collar. and threefifths of Bobbie’s books are signed by the authors. 75 are white-collar and the rest are blue-collar. if BC ( EF ( DG and ED = EA. Inc. If 58 employees are male. If Fred and Bobbie combine their collections. if the area of the larger circular region is twice the area of the smaller circular region. how many of the male employees are white-collar? 18 23 32 43 50 4+4 3 Question 14 of 15 12 8+4 3 Fred and Bobbie are book collectors. . what is the measure of ∠DEA ? 40° 50° 60° 65° 80° 20 cm In the figure above. One-fourth of Fred’s books are signed by the authors. what fraction of the books are signed by the authors? 8+8 3 24 Question 12 of 15 B C 50° F E Question 15 of 15 D A G In the figure above. BD = 2 and AC = 4 3 ? Of the 125 employees at a manufacturing company. and Fred has twice as many books as Bobbie does. how many centimeters long is the radius of the smaller circular region? 5 2 5 5 2 10 10 2 156 | © The Princeton Review. | 157 . Inc.LESSON 5 MATH SCRATCH PAPER 5 © The Princeton Review. . Lesson 5 Verbal .  . . . POE: Yes! = ✓ No! = Don’t Know Vocab = ? Maybe = Question 1 Despite _________ cynicism about the commercialization of holidays such as Christmas and Easter. few can resist getting caught up in the spirit of the season. . . 3. 4. . . . . guileless widespread lewd pervasive disingenuous naïve Question 2 Many suburbanites are _________ by public transportation as it lacks the privacy and security afforded by a private automobile. . SCRATCH PAPER . Come up with your own word or phrase for the blank.MANUAL FOR THE GRE SENTENCE EQUIVALENCE REVIEW Steps for Sentence Equivalence Questions 5 1 2. . . Check each answer choice and use your scratch paper. Find the story. Inc. 160 | assuaged unnerved enervated discomfited mollified bemused © The Princeton Review.  . . . unlike their parents who remained at one employer for life. . rarity cliché nuisance atavism curiosity simulacrum Question 5 Not even the most _________ traveler can resist the rustic charms of the small fishing villages of western Ireland. the a cappella group is now a relative _________. . . dogged crafty unstinting querulous jaded benevolent © The Princeton Review. . . . . | 161 . . Inc. . stingy cunning itinerant famous peripatetic famous 5 Question 4 Once a fixture on countless street corners throughout the country.LESSON 5 VERBAL Question 3 SCRATCH PAPER Young adults are becoming _________ workers. . . . . . .  . .MANUAL FOR THE GRE Question 6 5 Most often. . SCRATCH PAPER . a science fiction _________. parody picaresque roman à clef fable adventure satire Question 8 Unlike linguistics. . . has thrilled generations since 1963 with its cliff-hanging plots and roguish main protagonist. philology also includes literature and history within its _________. . . . 162 | ambit purview mythos phoneme lore ontogeny © The Princeton Review. . but that she is so myopic that she cannot _________ which traits are so indelibly human they must remain unaltered. . . . . . Inc. discern articulate approximate communicate appreciate propitiate Question 7 One of the longest running series in history. . the futurist’s greatest flaw is not that she has the hubris to suppose she can imagine the technologies and social structures of tomorrow. . which focuses on morphology and syntax. Doctor Who. . . LESSON 5 VERBAL Clues & Triggers—Not Just for Sentence Equivalence! Steps for Text Completions Questions 1 2. | 163 . Question 4 Having bestowed her patronage on many writers and performers. Question 3 Because of their _________ personalities. © The Princeton Review. Inc. 4. the chestnut tree flourished along the Eastern Seaboard. 3. no one expected their marriage to last. but it had been almost completely _________ by the 1950s. not least among them Shakespeare’s theater company. and the increasing winds indicated that the storm was _________. Come up with your own word or phrase for the blank. the darkening clouds. Question 2 In the eighteenth and nineteenth centuries. Find the story. Queen Elizabeth I was quite aptly labeled a grand _________ of the arts. POE: Yes! = ✓ No! = Don’t Know Vocab = ? Maybe = Question 1 5 SCRATCH PAPER The sudden drop in temperature. Check each answer choice and use your scratch paper. the darkening clouds. Queen Elizabeth I was quite aptly labeled a grand _________ of the arts. judge . cultivated decimated assuaged appended challenged Question 3 Because of their _________ personalities. pervasive controversial irrelevant deliberate imminent Question 2 In the eighteenth and nineteenth centuries. but it had been almost completely _________ by the 1950s. no one expected their marriage to last. not least among them Shakespeare’s theater company. connoisseur critic ally regent 164 | © The Princeton Review. Inc. apposite variegated disparate evanescent affable Question 4 Having bestowed her patronage on many writers and performers.MANUAL FOR THE GRE Now with Answer Choices! SCRATCH PAPER Question 1 5 The sudden drop in temperature. and the increasing winds indicated that the storm was _________. the chestnut tree flourished along the Eastern Seaboard. offering designs indifferent to location. and it was not until many years later that Melville’s achievements were (ii)________.. Question 8 Proponents of the International Style in architecture called for reducing buildings to purely functional form and found beauty in highlighting (i)_________ features. the service and decor were (ii)________. his (ii)__________ contributing to his ultimate success. | 165 . SCRATCH PAPER 5 Question 6 Moby Dick. a quality subsequently (iii)_________ by those who viewed the style as bland or unappealing. Edison eventually triumphed.. Rinse. Repeat. was virtually (i)________ when it was first published. Question 7 Pushing forward. claiming that while the food was innovative and well-executed.LESSON 5 VERBAL Multiple Blanks: Wash. Question 5 The reviewer gave the new bistro a (i)________ review. Inc. © The Princeton Review. They rejected references to (ii)________ styles. despite hundreds of (i)__________ attempts to produce a working light bulb. now regarded as a great work of American literature. despite hundreds of (i)__________ attempts to produce a working light bulb. Blank (i) Blank (ii) glowing inappropriate scathing stunning guarded lackluster Question 6 Moby Dick. his (ii)__________ contributing to his ultimate success. now regarded as a great work of American literature. claiming that while the food was innovative and well executed. the service and decor were (ii)________. Blank (i) Blank (ii) parodied relegated hailed celebrated ignored merited Question 7 Pushing forward.MANUAL FOR THE GRE Now with Answer Choices! Question 5 5 The reviewer gave the new bistro a (i)________ review. Blank (i) Blank (ii) felicitous grandiloquence unavailing indifference auspicious tenacity SCRATCH PAPER . Inc. 166 | © The Princeton Review. and it was not until many years later that Melville’s achievements were (ii)________. Edison eventually triumphed. was virtually (i)________ when it was first published. offering designs indifferent to location. | 167 . They rejected references to (ii)________ styles. Blank (i) Blank (ii) Blank (iii) structural oracular disparaged aesthetic provincial embraced hackneyed secular reclaimed 5 © The Princeton Review. Inc. a quality subsequently (iii)_________ by those who viewed the style as bland or unappealing.LESSON 5 VERBAL SCRATCH PAPER Question 8 Proponents of the International Style in architecture called for reducing buildings to purely functional form and found beauty in highlighting (i)_________ features. increasingly.MANUAL FOR THE GRE Text Completions SCRATCH PAPER Question 1 5 Though it is not as high profile as a light rail or subway. . _________ cities are turning to a concept called bus rapid transit as an affordable transportation option. bounty succor overabundance paucity rubric 168 | © The Princeton Review. sprawling impecunious resilient provincial ambitious Question 2 The television critic attributed the enduring popularity of police and medical “procedurals” such as CSI and House to the _________ desire to see mysteries solved and diseases cured. Inc. ephemeral perennial nascent hackneyed intermittent Question 3 The _________ of information about the recently discovered species meant that ornithologists had limited familiarity with the bird’s mating and nesting practices. his demeanor could change from affable to irascible in the space of a few minutes. Blank (i) Blank (ii) Blank (iii) diabolical vie for obstinacy isolated propitiate synergy inexorable rely on rivalry © The Princeton Review. such (iii)________ is ultimately counter-productive and in the end makes it more likely that there would be gaps in relief services. even though natural disasters are (i)________ and therefore unavoidable.LESSON 5 VERBAL SCRATCH PAPER Question 4 The staff found themselves (i)_________ by their supervisor’s (ii)________ personality. Blank (i) Blank (ii) lambasted exemplary sanctioned sophomoric circumscribed scrupulous Question 6 The speaker claimed that. Inc. | 169 . much of the associated suffering could be avoided if charitable relief organizations were to collaborate rather than (ii)________ donations and media attention. 5 Blank (i) Blank (ii) perplexed voracious assuaged priggish sated mercurial Question 5 The critic (i)_________ the playwright. Though understandable. describing his latest work as (ii)_________ and not illustrative of the work of a supposedly mature talent. MANUAL FOR THE GRE SCRATCH PAPER Question 7 5 The image of the architect as the lonely artist drawing three-dimensional forms is (i)________ the public’s understanding of the architect’s role. and skilled builders. Blank (i) Blank (ii) Blank (iii) at odds with tangentially related to virtuoso performance central to but an afterthought to collaborative effort irrelevant to justifiably embodied by physical triumph Question 8 To mistake (i)__________ for (ii)__________is to confuse braggadocio for skill. The architect relies heavily upon façade consultants. Certainly architects should take much of the credit for the form of a unique building. Inc. in addition. upon zoning regulations. but the final product is hardly a (iii)________. 170 | © The Princeton Review. Blank (i) Blank (ii) hubris denouement mendacity satire hedonism competence . As a result. buildings are viewed as the singular creations of an artistic vision (ii)________ the architect. while the form of the building may depend. engineers. cost. and market demands. Blank (i) Blank (ii) unaware of scant cognizant of unintelligible apathetic to apposite © The Princeton Review.LESSON 5 VERBAL Relationships Between the Blanks It would be (i)________ for any ambitious politician to (ii)________ such a powerful group of voters. | 171 . Inc. Blank (i) Blank (ii) a diligent ignorance a listless dismissal an insolent approbation Question 2 Since the producer was (i)________ the staggering costs typically associated with post-production editing. she was surprised when she saw the (ii)________ amount allocated to that line item in her editor’s budget. SCRATCH PAPER 5 Question 1 Elizabeth was (i)________ worker and therefore expected (ii)________ of her work. It took millions of years of evolution to engender such diverse biota. Every species is unique and irreplaceable. the Earth’s biota also presents a potential source for massive untapped material wealth in the form of food. summarily explained. Furthermore.MANUAL FOR THE GRE READING COMPREHENSION Line 5 5 10 15 20 25 30 35 40 45 172 | © The Princeton Review. The list of comparable disasters is substantial.000 years. 65 million years ago. some have termed this The Biodiversity Crisis. the rate of humaninduced extinctions is accelerating. Decimated forests and excessive hunting have eliminated half of the bird species of Polynesia. making the loss of biodiversity the most profound process of environmental change. Humans have adversely affected species diversity. Final consequences of this devastation are beyond calculation. assessments of biological wealth are almost non-existent and and thus usually taken for granted. The careless introduction of the Nile perch has threatened hundreds of fish species native to Lake Victoria. Yet today. and ultimately a slow but steady climb through the Mesozoic and Cenozoic eras until biological diversity reached its apex. Inc. In the past 10. initiated after the incipient proliferation of multi-cellular animals. Such a long and storied history intimates that this heterogeneity was a hard-fought battle. Moreover. and other commercially important substances— resources that are essential for the ever-expanding human species. biological diversity has entered a new era. an egregious and catastrophic error. The human species emerged at this seemingly optimal time of extreme biological diversity. they transform their environments. medicine. as human populations swell. drastic change to this equilibrium cannot be anything but disastrous. The history of global diversity. This gave rise to a precipitous increase in the number of species in early Paleozoic times (between 600 and 430 million years ago) followed by stagnation for the remaining 200 million years of the Paleozoic era. . a level not seen since the end of the Mesozoic era. reducing biological diversity to its lowest level. its consequences are also the least predictable since the Earth’s biota—the fauna and flora collectively—remains largely unstudied and unappreciated. Unlike the quotidian calculations of material and cultural wealth. Biodiversity reached its peak during the Paleozoic era. © The Princeton Review.LESSON 5 VERBAL Question 1 The passage is primarily concerned with cautioning against the massive extinction of numerous species that would make past extinctions look minor by comparison tracing the evolution of biodiversity to contrast with that of humans explaining the origins of diversity of life on Earth to warn against conferring preeminence on one species over others warning against irreversibly reducing the biodiversity of the planet. Hunting . Polluting . Inc. | 173 . Which of the following are explicitly mentioned in the passage as contributing to the extinction of species? . The loss of biodiversity is the most perilous predicament to befall the inhabitants of Earth. thereby representing a momentary setback both for science and for humanity as a whole describing the current decline in species diversity precipitated by humans as a tragedy of incalculable proportions that could have dire consequences SCRATCH PAPER 5 Question 2 Consider each of the choices separately and select all that apply. The value of biodiversity is often overlooked. The current level of biodiversity is unique. Human-induced changes in the environment Question 3 The author would most likely agree with which of the following statements about biodiversity? There is a precise and optimal level of biodiversity that should be maintained. Inc. as it passes only half of the parents’ genes to the succeeding generation and requires a more complex mechanism than does asexual reproduction. This actinomycete bacterium produces an antibiotic used to control the mold and limit its destructive effects on the ants’ food source. or attine. The tropical leaf-cutter. Instead. The ants do not allow their fungus crop to develop fruiting bodies. as a result. such as bacteria or molds. DNA analysis reveals that the fungi in attine gardens around the world are clones of a single source. spreading the fungus vegetatively. a parasite related to the “green mold” known to commercial mushroom farmers. such as that maintained by the attine. mutate rapidly and pose a challenge to other species. ant provides a remarkable example of complex symbiosis involving several species.MANUAL FOR THE GRE Line 5 5 10 15 20 25 30 35 40 174 | © The Princeton Review. The ants cultivate a fungus in underground caverns to serve as a source of food. A clonal monoculture. What benefit of sexual reproduction would outweigh these limitations? One likely answer is that it provides a defense against parasitic attack. a queen ant starting a new nest takes a sample of the fungus from the old nest to start the new garden. the attine ants provide the defense mechanism lacking in the fungus’s asexual reproduction by means of a bacterium that grows in patches on their skin. The rapid evolution of the attacking species provides an advantage in this biological arms race. evolve quickly enough to match the parasites’ mutations. is present in the ants’ crops and poses a serious threat to the fungus. . Sexual reproduction allows the more complex species to shuffle its genes between generations and. the means by which plants engage in sexual reproduction. the phenomenon of sexual reproduction puzzled biologists. should be highly susceptible to parasites. For many years. More comprehensive studies showed that the Escovopsis mold. However. or asexually. Simple parasites. yet preliminary research suggested no evidence of such a problem in the ants’ gardens. 5 Question 2 The author describes the interaction between a parasite and a sexually reproducing organism as an “arms race” (line 25) in order to  emphasize the aggressive nature of the parasitic organism  warn of the dangers of biological weapons  underscore the need for the attine ants to defend their gardens  point out the devastating effects of the Escovopsis mold  depict the result of rapid evolution by both organisms Question 3 The passage suggests which of the following about the fungus grown by the attine ants?  By shuffling its genes.  The bacterium found on patches of green mold produces an antibiotic substance used by commercial mushroom farmers. © The Princeton Review.  Plants that rely on sexual reproduction are highly susceptible to parasitic attack by bacteria and molds.  Sexual reproduction is an inefficient method for transmitting a parent’s genes to its offspring.LESSON 5 VERBAL Question 1 Which of the following can be most reasonably inferred from the passage? SCRATCH PAPER  The fruiting bodies found on numerous fungi are a means of vegetative reproduction. it would quickly become extinct. Inc. it is able to mutate rapidly in response to parasitic threats. it is susceptible to attack by the actinomycete bacterium. | 175 .  Without the care of the attine ants.  Parasitic bacteria use sexual reproduction as a means to achieve rapid mutation.  It is closely related to the crops grown by commercial mushroom farmers.  It could potentially engage in sexual reproduction.  Due to its asexual reproduction. MANUAL FOR THE GRE TEXT COMPLETIONS SUMMARY Steps for Text Completions Questions 176 | © The Princeton Review. Find the story. POE: Yes! = ✓ Maybe = No! = Don’t Know Vocab = ? . 1. Come up with your own word or phrase for the blank. If you’re still stumped. try finding a Relationship Between the Blanks. • Look for Clues and Triggers. Check each answer choice and use your scratch paper. 3. 2. 4. Inc. Lesson 6 Math . Four coins are selected at random from the bank. one at a time. Inc. and 20% of the remaining tiles are green.MANUAL FOR THE GRE Question 1 A piggy bank holds exactly 6 dimes and 10 nickels. 1 of the tiles are 3 blue. what is the probability that the next coin selected will also be a nickel? TRIGGER 6 1 1 3 1 7 16 13 13 4 13 Trigger: _______________________________________________________________ Question 2 75 colored tiles are placed in a bag. without replacing the coins. what is the probability that a tile selected at random will be a white tile? Give your answer as a fraction. . If all the other tiles are white. 178 | © The Princeton Review. If the first 3 coins selected are all nickels. Inc. © The Princeton Review. | 179 .LESSON 6 MATH SCRATCH PAPER 6 0≤ want total ≤1 RESPONSE Draw a line for each event and find the total. If an employee is selected at random. What is the probability that he will get heads on the first 2 throws and tails on the last 2 throws? 1 1 1 1 3 16 8 4 2 4 Question 6 The probability that event A will occur is 0. Question 4 Griffin has a bag of marbles that contains only six black marbles and four red marbles. Quantity B The probability that both event A and event B will occur .MANUAL FOR THE GRE Question 3 6 A questionnaire was sent to all 40 employees of a certain company to determine if they were available for a meeting on either Monday or Wednesday. If he removes three marbles at random without replacing any of the marbles. Eight employees were unavailable on either day. and 17 were available on Wednesday.57. what is the probability that he or she is available both Monday and Wednesday? Give your answer as a fraction. 20 were available on Monday. what is the probability that all three marbles selected will be red? 2 1 3 8 1 5 6 25 125 30 Question 5 Alejandro flips a coin four times. Quantity A 0.61 180 | © The Princeton Review. Inc. Probability of A and B = Probability of A × Probability of B 6 © The Princeton Review. multiply the probability of each event. | 181 .LESSON 6 MATH SCRATCH PAPER To find the probability of multiple events happening in a row. Inc. If she selects a card at random. 6 2 except on the first day. each with cards numbered 1 through 13. and on the last 5 4 day when it is .MANUAL FOR THE GRE Question 7 Ann has a deck of 52 cards. made up of four suits. when it is . Quantity B The probability that at least two of the people roll the same number . What is the probability that rain 5 will occur on at least one of the five days? 1 5 5 22 67 675 72 27 27 72 Question 9 Four people are playing a game in which each person rolls a six-sided die at the same time. what is the probability that she selects a 2 or a 7 or a 9 ? 6 1 1 3 3 3 3. Quantity A 2 3 182 | © The Princeton Review. Inc.825 64 52 13 4 Question 8 1 The probability of rain on each of five days is . Inc. find the probability that the event does not happen. and subtract it from 1. Probability of A = 1 – Probability of not A © The Princeton Review. to find the probability that any one of several different events happens. Probability of A or B = Probability of A + Probability of B 6 To find the probability for NOT or “at least” questions. | 183 . add the probability of each event.LESSON 6 MATH SCRATCH PAPER On the GRE. What is the probability that a randomly selected point on the circle lies on minor arc AC ? 1 1 1 1 1 360 60 6 8 2 6 Question 11 B C 5 4 A D E Note: Figure not drawn to scale. ABCD is a rectangle. 1 1 2 3 2 3 1 It cannot be determined from the information given. . Inc. In the figure above. what is the probability that a randomly chosen point that lies in ABCD will lie in the shaded region? 184 | © The Princeton Review.MANUAL FOR THE GRE Question 10 Points A and C lie on the circle (not shown) with center O such that AOC is equilateral. If BC = 15. what is the probability that a randomly chosen point that lies in ABCD lies inside the shaded region? 1 1 1 1 9 15 10 5 3 10 Question 12 B C A D If rectangle ABCD shown above has an area of 24. Inc. use the following formula: area you want .LESSON 6 MATH SCRATCH PAPER For probability with questions involving area. total area 6 © The Princeton Review. | 185 .  . . . .MANUAL FOR THE GRE Question 1 x2 + 9x + 20 = 0 Quantity A x Quantity B 3 TRIGGER 6 Trigger: _______________________________________________________________ Question 2 If x2 + 19x + 48 = 0. . what is the greatest possible value of x ? 186 | © The Princeton Review. . –2 –3 –6 –8 –12 –16 –24 –48 Question 3 x2 + 15x + 56 = 0 If x satisfies the equation above. . Inc. then which of the following is a possible value of x ? Indicate all such values. . . | 187 .M. write out every factor of c. If necessary. RESPONSE • Underneath equation. Add x2 + bx Multiply +c = 0 • Find two numbers that multiply to c and add to b. write down (x © The Princeton Review.LESSON 6 MATH SCRATCH PAPER 6 • Put the equation in the form x2 + bx + c = 0 )(x )=0 • Remember A. Inc. Quantity B is greater. . Inc. The relationship cannot be determined from the information given. what is the value of ab ? 188 | © The Princeton Review.MANUAL FOR THE GRE Question 4 x2 – 12x – 13 = 0 Quantity A x 6     Quantity B –2 Quantity A is greater. Question 5 What is the least possible value of x which satisfies the equation x2 + 5x – 6 ? Question 6 a2 + b2 = 16 (a + b)2 = 30 Given the equations above. The two quantities are equal. Inc. | 189 .LESSON 6 MATH SCRATCH PAPER 6 © The Princeton Review. and a = 15. 13 190 | © The Princeton Review. . which of the following is a possible value for x ? Indicate all such values. 5 . –3 . 6 Question 8 ( 7 + 2 ( ( 5 − 1( ( 5 + 1( ( 7 − 2( = Question 9 If a = x2 + 2x. then x could be which of the following?  –10  –5  2  5  There is no such value of x. 3 . –13 . Inc.MANUAL FOR THE GRE Question 7 If x is an integer such that x2 = –3x + 10. –5 . . LESSON 6 MATH SCRATCH PAPER 6 © The Princeton Review. Inc. | 191 . where c is a constant. and p is a constant. . one of the roots is 6. What is the value of k ? 192 | © The Princeton Review. k is a constant.MANUAL FOR THE GRE Question 10 In the equation x2 + px – 18 = 0. Which of the following is one possible value of x ?  –5  –2  2  5  11 Question 12 x2 + kx + 12 = 0 y2 + ky – 30 = 0 In the above equations. What is the value of p ?  –3  –1  3  6  18 6 Question 11 One of the factors of the equation x2 + 9x + c is (x + 11). Inc. LESSON 6 MATH SCRATCH PAPER 6 © The Princeton Review. Inc. | 193 . and oatmeal. Five years ago. Marshall was three times older than Jordan will be in two years. . . In terms of j. . . peanut butter. Inc. how old is Marshall now?   j 3 j – 11 –5 3  3j + 5  3j + 11 j+7 194 | © The Princeton Review.MANUAL FOR THE GRE DRILL Question 1 of 10 0≤ g≤5 0≤ h≤1 Which of the following could be the value of g − h ? 6 Select all such values. . what is the probability that one of the two cookies will be chocolate chip? 1 1 1 2 3 12 6 2 3 4 Question 3 of 10 Jordan is j years old. . . . sugar. –1 0 1 2 3 4 5 Question 2 of 10 There are four cookies in a jar: chocolate chip. If two are chosen at random. Inc. | 195 .LESSON 6 MATH SCRATCH PAPER 6 © The Princeton Review. A player scores a single point if and only if he rolls a 1 or a 5 on at least one of the dice. Inc. what is the probability that at least one of Debbi’s chosen candidates will win the election? 1 27 123 133 15 16 160 160 160 16 Question 7 of 10 x2 ≥ 36 and y2 ≤ 9 Quantity A x y 196 | © The Princeton Review. her chosen candidate for senator has a 75% chance of winning. two six-sided dice are rolled. what are the chances that a player will score a point? 6 Question 5 of 10 ab ≠ 0 Quantity A (3a − 3b) Quantity B 9a2 + 9b2 2 Question 6 of 10 Debbi is voting for three different offices in a statewide election.5% chance of winning. and her chosen candidate for county supervisor has a 37. If her chosen candidate for governor has an 60% chance of winning. Quantity B –2 . On any given roll.MANUAL FOR THE GRE Question 4 of 10 In a certain dice game. | 197 . Inc.LESSON 6 MATH SCRATCH PAPER 6 © The Princeton Review. in degrees. The two quantities are equal. B. Quantity B is greater. The two quantities are equal. Quantity B is greater. and C. If the circle has a diameter of 2 and arc BCA has a length of π .MANUAL FOR THE GRE Question 8 of 10 Points A. of angle BOA? 6 Question 9 of 10 (q + 5)(q – 7) = 0 Quantity A 2 q − 2q − 35     Quantity B q Quantity A is greater. . The relationship cannot be determined from the information given. The relationship cannot be determined from the information given. lie on the circumference of a circle with center O. what is the least 30 possible measure. Inc. Question 10 of 10 Quantity A Quantity B (y + 4) – 8y y2 + 15 2     198 | © The Princeton Review. Quantity A is greater. | 199 .LESSON 6 MATH SCRATCH PAPER 6 © The Princeton Review. Inc. write down (x ) (x ) = 0.MANUAL FOR THE GRE SUMMARY TRIGGER 6 x and x 2 in the same equation or anything that looks like a quadratic Underneath the equation. total RESPONSE TRIGGER If necessary. .M. find every factor of c. Inc. 200 | © The Princeton Review. “…probability…” want Find the total(s). Remember A. RESPONSE Put the equation in the form x + bx + c = 0. Draw a space for each event. Lesson 6 Verbal . MANUAL FOR THE GRE COMMON FLAWS Ninety percent of the population of Prelandia lived in rural areas in 1800. subways. a town with a population of 30. Therefore. only 20 percent of the population lives in rural areas. Clearly. subways. and light rail. 202 | © The Princeton Review. Motorboating accidents and ice cream sales increase at the same time of year. Ogdenville. New York City has a mass transit system which relies upon buses. and light rail. more people lived in the countryside two centuries ago. increased consumption of ice cream causes motorboating accidents. Ogdenville should build a mass transit system which relies upon buses.000. wishes to overhaul its mass transit system. 6 Contrary to popular belief. high school students overwhelmingly approve of the high school administrative staff. . We know this to be true because the student council expressed admiration for the high school principal and her staff in the council’s editorial for the school paper. Inc. Today. Thus. LESSON 6 VERBAL SCRATCH PAPER Type of Flaw: ______________________________________________________________________ __________________________________________________________________________________ How to strengthen: __________________________________________________________________ __________________________________________________________________________________ How to weaken: ____________________________________________________________________ __________________________________________________________________________________ 6 Type of Flaw: ______________________________________________________________________ __________________________________________________________________________________ How to strengthen: __________________________________________________________________ __________________________________________________________________________________ How to weaken: ____________________________________________________________________ __________________________________________________________________________________ Type of Flaw: ______________________________________________________________________ __________________________________________________________________________________ How to strengthen: __________________________________________________________________ __________________________________________________________________________________ How to weaken: ____________________________________________________________________ __________________________________________________________________________________ Type of Flaw: ______________________________________________________________________ __________________________________________________________________________________ How to strengthen: __________________________________________________________________ __________________________________________________________________________________ How to weaken: ____________________________________________________________________ __________________________________________________________________________________ © The Princeton Review. | 203 . Inc. Inc. Cars from Lyme are better as well: Seven years ago. Thus. . Of the two leading used car lots in our town— Lyme Cars and Limmon Automobiles—Lyme Cars is clearly better. and in every case. which are generally more expensive. we gave out free samples of our new savory-flavored candy chews at a number of national gourmet food fairs. with fewer cars to choose from. Although many of these restaurants have since tried to compete with CheapSteak by lowering their prices and adding drive-thru windows.000. the growth of boutique ice cream brands specializing in unusual. and it broke down within a year.MANUAL FOR THE GRE Question 1 The following appeared in an email from the president of CheapSteak Foods. gross sales in the candy market have remained static. I purchased a car from Limmon for $7. basil. whereas Limmon Automobiles has a much smaller indoor showroom. Lyme also has twelve sales associates. A car I purchased from Lyme Cars last year cost only $4. if you want to buy an inexpensive. Limmon only has four.. Specifically. we should jump to the forefront of this trend and launch our savory candy chews nationally at all of our retail outlets. Question 3 The following appeared in a letter from a car owner to a business associate. in contrast. Given our success with our first restaurant. 6 Six months ago. we believe it is time to open another CheapSteak restaurant and launch a frozen food line. has exploded. In response. has experienced huge increases. we opened our first restaurant. In the last four years. Therefore. another confectionary product. you should use Lyme Cars. CheapSteak has made a profit every month since it opened. 204 | © The Princeton Review. an established candy company. CheapSteak. Lyme Cars has more than a square mile of cars to choose from. two of whom work only part-time. Question 2 The following appeared in a memo to the head of marketing for Dulcified Treacle Co. savory ice cream flavors such as pink peppercorn. Waitstaff have reported that the price and convenience drew many customers away from nearby restaurants. our supplies ran out within minutes.000 and is still running smoothly. which sells quickly-prepared and low-priced steak sandwiches. and ginger. quality used car. but ice cream. | 205 . Inc.LESSON 6 VERBAL Conclusion: _______________________________________________________________________ Premise: __________________________________________________________________________ __________________________________________________________________________________ Assumptions: ______________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 6 __________________________________________________________________________________ __________________________________________________________________________________ Conclusion: _______________________________________________________________________ Premise: __________________________________________________________________________ __________________________________________________________________________________ Assumptions: ______________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Conclusion: _______________________________________________________________________ Premise: __________________________________________________________________________ __________________________________________________________________________________ Assumptions: ______________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ © The Princeton Review. In a study completed last year. traditional treatment to help reduce obesity—coconut oil—has recently been proven effective. 50 volunteers who had issues maintaining a healthy weight were fed a special diet rich in coconut oil for two weeks. the study proves that coconut oil reduces obesity within a short period of time. No volunteer was allowed to eat outside foods during the trial. Conclusion: _______________________________________________________________________ Premise: __________________________________________________________________________ __________________________________________________________________________________ Assumptions: ______________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Essay Question Types • • • • 206 | What are the stated or unstated assumptions of this argument? What questions would need to be answered to determine whether the recommendation is valid? What evidence is needed to evaluate the argument? What other explanations could rival the proposed explanation? © The Princeton Review. 6 Write a response in which you discuss one or more alternative explanations that could rival the proposed explanation and explain how your explanation(s) could plausibly account for the facts presented in the argument.MANUAL FOR THE GRE An ancient. . Therefore. Inc. the volunteers had lost an average of 8 pounds each. and each volunteer had his or her weight measured several times each day. After 2 weeks. | 207 .LESSON 6 VERBAL SCRATCH PAPER Introduction: _______________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Flaw #1 6 What is the assumption: ______________________________________________________________ __________________________________________________________________________________ Why that is a problem: _______________________________________________________________ __________________________________________________________________________________ How to fix it: _______________________________________________________________________ __________________________________________________________________________________ Flaw #2 What is the assumption: ______________________________________________________________ __________________________________________________________________________________ Why that is a problem: _______________________________________________________________ __________________________________________________________________________________ How to fix it: _______________________________________________________________________ __________________________________________________________________________________ Flaw #3 (optional) What is the assumption: ______________________________________________________________ __________________________________________________________________________________ Why that is a problem: _______________________________________________________________ __________________________________________________________________________________ How to fix it: _______________________________________________________________________ __________________________________________________________________________________ Conclusion: ________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ © The Princeton Review. Inc. Inc. would suffer once its only competitor. on average. No other hormone affects overeating. No other hormone is as responsible for overeating as is ghrelin. People with low or normal concentrations of ghrelin will never overeat. Question 2 A recent study revealed that participants who overate also produced high concentrations of the hormone ghrelin while patients who did not overeat had normal or low concentrations of this hormone. 2. opened across the street last year. The profit per meal is higher. Dissect the argument. . Cindy’s Cafe. ghrelin is at least partly responsible for overeating. for meals served at Jack’s Bistro than for those served at Cindy’s Cafe. Use POE to find the answer. Yet. the average number of lunches served at Jack’s Bistro has actually increased significantly in the past 12 months. 6 Identify the question and set up your scratch paper. Cindy’s Café serves considerably more meals on weekends than it does on weekdays. The number of restaurant patrons in Santa Monica has doubled in the past 18 months. Most of Jack’s Bistro’s patrons had never dined in Santa Monica before this restaurant opened. previously the only restaurant in Santa Monica. Question 1 Many people predicted that business at Jack’s Bistro. Predict what the answer should do. Jack’s Bistro has hired away a significant proportion of the staff who formerly worked at Cindy’s Cafe. if true.MANUAL FOR THE GRE ARGUMENT QUESTIONS 1. Which of the following. The argument assumes which of the following? Overeating does not affect the production of ghrelin. 4. Ghrelin is a more important causative factor for overeating than willpower. 3. most helps to explain the increase? Unlike Jack’s Bistro. Clearly. 208 | © The Princeton Review. LESSON 6 VERBAL SCRATCH PAPER 6 © The Princeton Review. | 209 . Inc. 210 | © The Princeton Review. if true. Given that other recorded formats did not cause people to stop paying for musical entertainment. stockholders should not sell their shares of the company. People value the social interaction provided by concerts and live music venues. but this concern is unwarranted. As recorded music became widely available in the form of LPs. the stock price of steel manufacturer Y rebounded after the company reduced its accounts receivable backlog. The bolded phrases play which of the following roles in the argument above? The first phrase contains the author’s conclusion and the second phrase contains unrelated information. Inc.MANUAL FOR THE GRE Question 3 6 Music industry executives have recently expressed concern that the easy access to free digital recordings will dampen the willingness of customers to purchase music. . The first phrase states a position and the second phrase provides evidence to undermine that position. The first phrase states the conclusion and the second phrase supports the conclusion with an analogy. A substantial number of music aficionados are intrigued by the art on CD covers. and later cassette tapes and CDs. and such art is not provided with digital recordings. people continued to attend concerts and live music venues. The first phrase offers advice and the second phrase draws a contrast between two companies. The first phrase states a premise on which the conclusion is based and the second phrase provides the conclusion. Which of the following. most seriously undermines the argument? The quality of free digital recordings varies widely depending on their source. Question 4 Although computer manufacturer X has experienced decreasing sales in the last quarter. The stock price of a financially troubled company can rise dramatically once those problems are solved. People who attend concerts frequently are more likely than others both to purchase music and to download free recordings. it is unlikely that the availability of digital recordings will encourage customers to cease making music purchases. Some of the most popular forms of music cannot be released in a digital format. Last year. Inc.LESSON 6 VERBAL SCRATCH PAPER 6 © The Princeton Review. | 211 . there has been a marked decline in the consumption of soft drinks sweetened with sugar. if true. but while industrial output in Country A has been falling. Clearly. not the current high price of oil. there has been increasing publicity about the adverse health effects of weight gain caused by the consumption of sugar-laden drinks. most stengthens the argument above? Many consumers have switched to drinking diet soft drinks which are not sweetened with sugar. if true. Country A exports minerals. The credit markets in both Country A and Country B have been tight. is responsible for the poor industrial production in Country A since its new government came to power. Inc. The consumption of packaged cookies which feature sugar as a key ingredient has decreased during the time period in question.MANUAL FOR THE GRE 6 Question 5 Question 6 Excessive government regulation. During the same time. the public’s awareness of the harmful health effects of weight gained by consuming sugar-laden drinks caused the decline in the consumption of such drinks. Whereas Country B must import most minerals.2 ounces per day. In the past five years. it has been rising in Country B. 212 | © The Princeton Review. Consuming large quantities of sugarladen drinks has also been linked to mood swings throughout the day. Country B pays the same price for oil. The industrial goods produced in Country A are different from those that are produced in Country B. . The average person’s consumption of soft drinks sweetened with sugar has decreased by 8. Which of the following. Country A’s new government increased regulation of its industry to promote a cleaner environment. The price of sugar-laden soft drinks has remained stable for the past five years. would cast the most doubt on the argument above? Agricultural production is also declining in Country A. Which of the following. | 213 .LESSON 6 VERBAL SCRATCH PAPER 6 © The Princeton Review. Inc. causing unemployment to increase. .MANUAL FOR THE GRE Question 7 Poppy: High taxes have a chilling effect on the economy. thus reducing the amount of credit available. When individuals and corporations are taxed. Inc. 6 Lilly: But you must also consider that taxes generate funds for the government. Unable to borrow money easily. they have less money to spend. Demand for products and services is reduced. Taxes must be lowered. the government will be forced to borrow more money. If taxes are lowered. businesses and individuals will be forced to limit their purchases. Lilly objects to Poppy’s argument by claiming that Poppy has exaggerated the adverse effects of high taxes indicating that Poppy has based his argument on insufficient evidence about the effects of taxes on the economy noting that Poppy has failed to adequately define the term “taxes” demonstrating that danger of reducing taxes is far more severe than the threat of maintaining them at current levels suggesting that the economic benefits of easy credit outweigh the danger of unemployement 214 | © The Princeton Review. | 215 .LESSON 6 VERBAL SCRATCH PAPER 6 © The Princeton Review. Inc. . Lesson 7 Math . she turns and drives 5 miles due west. Inc.MANUAL FOR THE GRE COORDINATE GEOMETRY Question 1 y Q (4. what is the length of PQ ? 5 6 4 3 7 TRIGGER 5 2 Trigger: _______________________________________________________________ Question 2 A courier is making a series of deliveries. . she drives 3 miles due west. she turns and drives 6 miles due south. 5) P (1. 1) 7 x In the figure above. What is the distance between her starting and ending locations? 218 | © The Princeton Review. Then. First. Finally. LESSON 7 MATH SCRATCH PAPER 7 RESPONSE Draw triangles and look for Pythagorean triples. Inc. | 219 . © The Princeton Review. Inc. respectively. Selina drives east at 30 miles per hour for 4 minutes and then south at 40 miles per hour for 3 minutes. and C are points on the x-axis. D.MANUAL FOR THE GRE Question 3 Coworkers Max and Selina are both driving to their respective homes from work. What is the straightline distance in miles between Max’s home and Selina’s home? 7 Question 4 y A G F D B C x E In the figure above. . A. G. and E are points on the y-axis. What is the length of line BF (not shown) ? 9 9 2 10 3 20 2 41 220 | © The Princeton Review. D. Max drives west at 30 miles per hour for 20 minutes and then north at 60 miles per hour for 3 minutes. and squares ABCD and DEFG have areas of 16 and 25. LESSON 7 MATH SCRATCH PAPER 7 © The Princeton Review. Inc. | 221 . 4) and (5. What is the slope of a line that is perpendicular to line m ?  –4  –2  −   222 | © The Princeton Review.MANUAL FOR THE GRE SLOPE Question 1 Line k passes through points A and B. the coordinates of which are (2. 10). Line m passes through points C and D. 3) and (5. What is the slope of line k ? TRIGGER 7 Trigger: _______________________________________________________________ Question 2 Points C and D are located at (–3. respectively. Inc. –12) respectively. 1 2 1 2 2 . Inc.LESSON 7 MATH SCRATCH PAPER 7 2 1 RESPONSE vertical change Δy Rise y 2 − y 1 = = = horizontal change Δx Run x − x © The Princeton Review. | 223 . ⎟ ⎝ 3 3⎠ 7 ⎛ 3⎞ ⎜ 0. − ⎟ 2⎠ ⎝ ⎛ 3 ⎞ ⎜ − .MANUAL FOR THE GRE EQUATION OF A LINE Question 1 What is the x-intercept of the line defined by the equation y = 2x + 3 ? ⎛ 2 2⎞ ⎜ . 0⎟ ⎝ 2 ⎠ (–2. Trigger: _______________________________________________________________ . –3) 224 | © The Princeton Review. Inc. 0) TRIGGER (0. you can find any other point on the line. © The Princeton Review. Inc. Park the information you have directly underneath. If you know a point and the slope.LESSON 7 MATH SCRATCH PAPER 7 RESPONSE Write y = mx + b on your scratch paper. | 225 . you can find the slope. If you know two points. The relationship cannot be determined from the information given. q) (8.MANUAL FOR THE GRE Question 2 y (p. what is the value of p ? 6 8 9 12 Question 3 y •H • G x O The equation of the line graphed on the rectangular coordinate system above is: y= 10 x +2 11 Quantity A GO     226 | © The Princeton Review. Quantity B HO Quantity A is greater. If the line passes through the origin. Inc. Quantity B is greater. O. 13 . q = 9. 6) O 7 x In the rectangular coordinate system above. The two quantities are equal. LESSON 7 MATH SCRATCH PAPER 7 © The Princeton Review. Inc. | 227 . Quantity A 10     228 | © The Princeton Review. Inc. The two quantities are equal. The relationship cannot be determined from the information given. Quantity B The total number of possible arrangements for the runners from first place to third place Quantity A is greater. and a Chief Scientist. and 3 for Chief Scientist. If no candidate applies for more than one position. then how many different shuttle crews are possible? 7 Question 2 There are five runners in a race. Quantity B is greater. . a Medical Officer. There are 5 candidates for Commander. 4 for Medical Officer.MANUAL FOR THE GRE ARRANGEMENTS & COMBINATIONS Question 1 A space shuttle crew has a Commander. | 229 . How many options can go in each spot? 4. 2. Inc.LESSON 7 MATH SCRATCH PAPER Arrangements & Combinations 1. Label any restrictions. 3. Write dashes for each spot. Does order matter? 7 © The Princeton Review. how many different ways could the children be arranged? 720 480 360 240 120 7 Question 4 A congressional committee on legislative procedures is to be made up of four members.MANUAL FOR THE GRE Question 3 Six children. must stand in a line. If 10 representatives are available. Inc. If the boy cannot stand first or last in line. . one boy and five girls. how many different ways are there to make up the fourmember committee? 60 120 210 400 720 230 | © The Princeton Review. Inc. | 231 .LESSON 7 MATH SCRATCH PAPER 7 © The Princeton Review. How many different omelets can the chef possibly make? 9 18 20 120 720 Question 3 of 5 Griffith Bank & Trust assigns each of its depositors a 4-digit personal identification number (PIN).MANUAL FOR THE GRE ARRANGEMENTS & COMBINATIONS DRILL Question 1 of 5 Beth has five trophies. How many different arrangements of trophies can she create on the mantle? 20 60 120 176 216 7 Question 2 of 5 On Random Omelet Monday. Inc. She wants to put them on her mantle from left to right. What is the probability that a randomly generated PIN will have no repeated digits? 232 | © The Princeton Review. a chef creates omelets by randomly choosing three out of a possible six fillings. . Inc.LESSON 7 MATH SCRATCH PAPER 7 © The Princeton Review. | 233 . . The relationship cannot be determined from the information given.800 234 | © The Princeton Review. Quantity A The number of different ways to order a sundae with two toppings 7     Quantity B The number of different ways to order a sundae with five toppings Quantity A is greater. Question 5 of 5 The co-op board of a certain residential building must consist of two men and three women. Inc. how many different make-ups of the committee exist?  65  525  1. The two quantities are equal. Quantity B is greater. If there are six men and seven women who want to be on the committee.287  100.MANUAL FOR THE GRE Question 4 of 5 A sundae may be ordered with any of seven possible toppings.050  1. Inc.LESSON 7 MATH SCRATCH PAPER 7 © The Princeton Review. | 235 . . Lesson 7 Verbal . both thought to be vital to controlling egregious speculative investing and preventing oligopolistic control of the financial sector. The primary intent of the legislation was to ensure a safer financial sector. Thus legislation that receives a majority of votes will be enacted. that ensuring the security of individual banks will ensure the security of the banking system as a whole. a benefit not just for the sector itself but also for every consumer of financial services. one cannot avoid the conclusion that the harms engendered by the removal of safeguards. Humans are made up of atoms. no one has ever seen a purple swan. but in times of privation people save. However laudable the aims of the act and whatever impact it might have on consumers. insurance companies. Therefore. and insurance company. Therefore humans may not always be visible to the naked eye. Question 3 The author would consider which of the following fallacies most similar to the fallacy perpetrated by GBL?  747s can fly. its critics overlook the act’s greatest weakness: its overreliance upon a fallacious assumption. namely. of the Gramm-Leach-Bliley Act. This had the potential to minimize the distress felt by financial institutions when banking customers react to changes in the economy. commercial bank. 747s also have engines.  Savings accounts are a secure form of investment. according to the passage. GBL allowed a financial institution to provide both services to its customers thereby allowing it to prosper in both economically good times and bad. was passed to streamline the financial services industry by allowing any financial institution to act as any combination of an investment bank. . Inc. Question 1 The primary purpose of the passage is to discuss the implications of a legislative act  summarize a historical change in regulatory principles  propose guidelines for future. those engines can also fly. Some consumer advocates argued however. no one will ever see a purple swan. therefore everyone should have a savings account. Thus.  Currently.MANUAL FOR THE GRE Line 5 10 7 15 20 25 30 35 40 45 50 238 | Initially the Gramm-Leach-Bliley Act—also known as the Financial Services Modernization Act of 1999—which repealed parts of the GlassSteagall Act of 1933 and of the Bank Holding Company Act of 1956. © The Princeton Review. This response may be motivated in part by the natural reluctance to repeal government regulation that had been enacted as a safeguard. In prosperous times.  Atoms are not visible to the naked eye. The Gramm-Leach-Bliley Act (GLB) efficiently allowed the consumer to save and invest with the same institution. Critics go on to point out that. corrective legislation  stipulate conditions for acceptance of corrective legislation  defend a corrective legislative act against its detractors Question 2 Select the sentence within the first paragraph that best exemplifies the ultimate aim. people invest. and investment banks. that such protection for investment banks came at the expense of consumer protection from socalled “mega-banks”—banks that were the result of mergers among commercial banks.  Any legislation that does not receive a majority of votes will not be enacted. after lengthy consideration of the act’s admirable and legitimate aims. even now. preventing both oligopoly and the malfeasance that would surely result from allowing those banks that control credit (lending) to also control the use of credit (investing) outweigh the benefits of added security for individual financial institutions. Inc. | 239 .LESSON 7 VERBAL SCRATCH PAPER 7 © The Princeton Review. That the appendix may help facilitate proper development of the immune system in young mammals has been intimated by some studies on animals. Utilizing cladistics. In fact throughout medical history. evolutionary biology allows for a vestige to be a complex or specialized structure—as they are in the wings of an ostrich and the eyes of the blind cavefish—yet still be a rudimentary and degenerate relative to the same homologous structures in other organisms. Admittedly the appendix contains a concentration of lymphoid tissue but such studies as those conducted by Andersson and Buergal provide evidence that the appendix is actually maladaptive. Inc. classify the appendix as a vestigial organ. Parker and his colleagues found supporting evidence that further suggests that the appendix may confer some evolutionary benefit. endocrine. Those physicians © The Princeton Review. it would be as large and developed as the cecum is in other primates and would contribute significantly to cellulose fermentation. several possible purposes for the appendix have been offered. and refuted. which uses genetic information in combination with a variety of other data to evaluate biological relationships that emerge over the ages.  It contributes significantly to cellulose fermentation. Question 2 The author suggests that the reason medical researchers believe that the vermiform appendix is not vestigial is ultimately explained by  recent studies that depict the immunizing function of the appendix in humans  incontrovertible evidence that demonstrates immune function  their correct application of cladistics  the fact that doctors receive no training in evolutionary biology and are limited solely to expertise regarding human anatomy and physiology  partial ignorance on the part of medical researchers regarding the field of evolutionary biology and its precise taxonomy Question 3 In the context. a new approach to evolutionary biology. which was once used for digesting food by ancestral organisms long-since extinct. 55 who attempt to breach the domain of the evolutionary biologist and engage in phylogenetic analysis of the appendix do so with a misguided and long since abandoned assumption that evolutionary “progress” accompanies evolutionary change. giving it the appearance of a vestigial organ. A consensus among medical specialists has begun to emerge. However. this lymphoid tissue seems prone to pathological inflammatory states. the cecum. Some scientists. if the human appendix were not vestigial. citing the organ’s concentrations of lymphoids and its highly vascular structure as apparently homologous features between it and primate ceca. not compelling evidence that the appendix must serve a function.  It is a vestigial organ. Some have concluded that the appendix is the evolutionary remains of a larger structure. though not conclusively proven. such a classification does not enjoy universal support. which of the following is true regarding the vermiform appendix?  It aids the body in immunization.  It is as large as primate ceca. certain other rodents. such as Charles Darwin in On the Origin of Species (1859). and exocrine functions. including neuromuscular.  Its immunizing functions are rendered useless by modern sanitation. by itself.MANUAL FOR THE GRE Line 5 10 7 15 20 25 30 35 40 45 50 240 | The vermiform appendix is an unctuous deadend sac that hangs between the small and large intestines. the “breach” mentioned on line 54 most clearly refers to  the penetration of foreign bodies in an organism  the perforation of a ruptured appendix  the misguided research conducted by Parker and his colleagues  the lack of communication between evolutionary biologists and physicians  the interdisciplinary research conducted by doctors . speculating that the appendix serves some sort of gastrointestinal immune function. That the appendix has existed for at least 80 million years and has evolved at least twice. evaluated. However. Question 1 According to the author. Moreover. and particular primates is. once among Australian marsupials and later among rats. Inc. | 241 .LESSON 7 VERBAL SCRATCH PAPER 7 © The Princeton Review. . Lesson 8 Math . where a ≠ 0 and b ≠ 0. 1 a∇ b = 1 1 + a b Quantity A Quantity B 3∇4 3 4 Question 3 If 15! is an integer. 5 6 7 8 .MANUAL FOR THE GRE Distribution of Employees by Education and Gender in 2010 Highest Level Completed Males Females High School 15 26 Undergraduate Degree 29 34 Graduate Degree 16 12 Doctorate 5 8 Total 65 80 Question 1 8 If the total number of employees in 2010 was 16 percent greater than it was in 2009. Inc. how many total employees were there in 2009 ? Question 2 For all positive integers a and b. what is the greatest possible 3m value of m ? 4 244 | © The Princeton Review. LESSON 8 MATH SCRATCH PAPER 8 © The Princeton Review. Inc. | 245 . The fifth student runs for 0. Which of the following is the average speed.3 miles at 8 miles per hour.2 miles each at 5 miles per hour. The third student runs for 0. for all of the students? 5.4 246 | © The Princeton Review.4 miles at 10 miles per hour. The area of square ACDF is 16. Inc. Quantity A Quantity B The perimeter of the shaded region 10 Question 5 2 x + 5y = 5 x – 2y = 7 Quantity A Quantity B The value of x The value of y Question 6 Five students are participating in a relay race. The first and second students run for 1. 5. rounded to the nearest tenth. The fourth student runs for 0.7 6.9 miles at 6 miles per hour.5 8.MANUAL FOR THE GRE Question 4 A B C E D G F 8 In the figure above.0 .8 7. equilateral triangle BEG is inscribed in square ACDF. Inc. | 247 .LESSON 8 MATH SCRATCH PAPER 8 © The Princeton Review. which of the following points would lie outside the circle? Indicate all such points. 3) (4. 3n = (−3)n . Inc. Quantity A Quantity B z 6 . 2n is an integer. . then which of the following must be true ? Indicate all such statements. –1) (–3. 5) (5. Question 9 z O z The area of the circular region with center O is 25π. . 4) (4.MANUAL FOR THE GRE Question 7 If a circle with a radius of 6 is graphed on a coordinate plane such that the center of the circle is at the origin. n2 + 1 is a multiple of 3. . 8 (–5. . 2) Question 8 For a positive integer n. if the remainder is 1 when 2n is divided by 3. . . –5) (–3. 248 | © The Princeton Review. . . Inc.LESSON 8 MATH SCRATCH PAPER 8 © The Princeton Review. | 249 . and 5 different dressings.MANUAL FOR THE GRE Question 10 A sequence of numbers satisfies the equation An = 2(An − 1) + 1. 8 different vegetables. If the area of ΔABE is 3 8 the area of parallelogram ABCD. 3 different cheeses. She must also decide whether or not to have croutons. She must choose one item from each category. Nicole can choose from 4 different lettuce mixes. If A4 = 10. AD = 12. what is the value of A1 ? 8 Question 11 B E A C D In the parallelogram ABCD above. 4 . then EC = 3 2 2 8 3 3 Question 12 At the salad bar. Inc. How many different combinations are possible? 250 | © The Princeton Review. LESSON 8 MATH SCRATCH PAPER 8 © The Princeton Review. | 251 . Inc. if d ≠ 0. 3 scuba divers are practicing in the pool.MANUAL FOR THE GRE DRILL Question 1 of 8 2d + e + 2f = 0 3d – e – 5f = 0 For the above system of equations. x+ x+ 2 9 2 15 y ? y . Inc. and a depth of 6 meters. the ratio of f to d is − 8  −  −     3 2 5 3 2 3 3 5 5 3 Question 2 of 8 A scuba instructor sits on the edge of a square pool with a side length of 8 meters. Quantity A Quantity B The product of the distances from the scuba instructor to each of the divers 1000 meters Question 3 of 8 2 What is the value of 3 2 5 252 | © The Princeton Review. | 253 . Inc.LESSON 8 MATH SCRATCH PAPER 8 © The Princeton Review. If d = a 18 what is the value of a ? 2 8 3 3 2 2 3 2 Question 5 of 8 B C 2xº A xº D In the rectangle ABCD above. 254 | © The Princeton Review. Inc. what is the area of the shaded region?  50 2  50 3  100  100 3  200 Question 6 of 8 4≤j≤7 6≤k≤9 Which of the following could be the value of jk ? Indicate all such values. c. . . .MANUAL FOR THE GRE Question 4 of 8 In the sequence a. b. each number after the first is three times the number before it. . d. . 10 13 16 24 48 90 9 2 . . if AC = 20. LESSON 8 MATH SCRATCH PAPER 8 © The Princeton Review. Inc. | 255 . 4  13.000 Question 7 of 8 8 Of the money Company X spent on print advertising 1 was spent on newspaper advertisements 2 3 and of the remainder was spent on flyers.2  33. 4 Approximately how many thousands of dollars more in 2006. Inc.6  25.MANUAL FOR THE GRE Advertising Budget for Company X by Expenditure Expenditure Percentage of Budget Television 52% Internet 11% Print 32% Other 5% Total in 2006: $210.6  39. .9 Question 8 of 8 Which of the following is NOT a factor of 1515 ?  3  9  135  180  225 256 | © The Princeton Review. was spent on newspaper advertisements than on flyers?  8. LESSON 8 MATH SCRATCH PAPER 8 © The Princeton Review, Inc. | 257 Lesson 8 Essays MANUAL FOR THE GRE Analytical Writing Instructions Analyze an Issue You will be given a brief quotation that states or implies an issue of general interest, and you will also be given specific instructions on how to respond to that issue. Trained GRE readers will evaluate your response according to how well you 8 260 | • • • • • respond to the specific task instructions consider the complexities of the issue organize, develop, and express your ideas support your position with relevant reasons and/or examples control the elements of standard written English © The Princeton Review, Inc. LESSON 8 ESSAYS SAMPLE ISSUE ESSAY PROMPTS 1. Issue: One should not expect respect for disregarding the opinions of others. Only when every point of view is taken into consideration should people take action. • Task: Write a response in which you discuss the extent to which you agree or disagree with the statement and explain your reasoning for the position you take. In developing and supporting your position, you should consider ways in which the statement might or might not hold true and explain how these considerations shape your position. 2. Issue: An idea alone, no matter how great, is meaningless unless it is put into practice. • Task: Write a response in which you discuss the extent to which you agree or disagree with the claim. In developing and supporting your position, be sure to address the most compelling reasons or examples that could be used to challenge your position. 3. Issue: A student who wishes to succeed in business should study anything but business while in school. Once in the workplace, he or she will learn the skills of business, but the opportunity to gain additional perspectives by studying other fields of knowledge while in school is too valuable to pass up. • Task: Write a response in which you discuss the extent to which you agree or disagree with the recommendation and explain your reasoning for the position you take. In developing and supporting your position, describe specific circumstances in which adopting the recommendation would or would not be advantageous and explain how these examples shape your position. 4. Issue: Unexamined conservatism is far more dangerous than reckless change. • Task: Discuss the extent to which you agree or disagree with the opinion stated above. Support your views with reasons and/or examples from your own experience, observations, or reading. 8 © The Princeton Review, Inc. | 261 MANUAL FOR THE GRE Step 1: Brainstorm Examples Here’s a sample prompt. Issue: To achieve great success, one must reject conventional thinking. On your scratch paper draw a T that looks like this. Success must be unconventional Success can be conventional 8 On one side write “I agree” and on the other write “I disagree.” Now take a moment to ask yourself, “What does it mean to agree or disagree with this prompt?” Your essay prompt could come in one of three forms. Here are some examples. Extreme “No one can possibly achieve success in the world by conforming to conventional practices and conventional ways of thinking.” Wishy-washy “People should treat experts with suspicion and mistrust because experts who have specialized in a particular field often have an overly narrow frame of reference.” Open-ended “The purpose of education is...” When your thinking runs dry, use this checklist: Me, Friends, Family, School, City, Country, Company, Species, The Very Old/Young, Science, History, Literature 262 | © The Princeton Review, Inc. Example 1: _________________________________ Notes: _________________________________ 8 Example 2: _________________________________ Notes: _________________________________ Example 3: _________________________________ Notes: _________________________________ © The Princeton Review. | 263 .LESSON 8 ESSAYS Step 2: Organize Thesis: I believe ______________________________________________________________________ ______________________________________because________________________________________ ____________________________________ as seen through the examples of _____________________. Inc. ______________________. and _____________________. Must have: Topic Sentences Transitions 8 Could have: Specifics Quotations Commands Analogies Rhetorical Questions Length Big Words 264 | © The Princeton Review. Inc. there are two things that all essays must have. and then a laundry list of things they could have to augment your score. .MANUAL FOR THE GRE Step 3: Write When it comes to writing. LESSON 8 ESSAYS Practice Issue: Unexamined conservatism is far more dangerous than reckless change. or reading. Example 1: _________________________________ Notes: _________________________________ Example 2: _________________________________ Notes: _________________________________ Example 3: _________________________________ Notes: _________________________________ Step 3: Write First Paragraph: _____________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ © The Princeton Review. Support your views with reasons and/or examples from your own experience. observations. | 265 . Task: Discuss the extent to which you agree or disagree with the opinion stated above. and ______________. Step 1: Brainstorm 8 Step 2: Organize Thesis: I believe ______________________________________________________________________ ___________________________________________ because __________________________________ __________________________________________ as seen through the examples of ______________. ______________. Inc. . Verbal Practice . florid painstaking laconic effusive erratic 9 Question 2 The teen’s explanations. So (ii)________ was this new form of writing—the most ancient surviving text of nearly every classical literary work is in Carolingian miniscule—that Italian Renaissance scholars assumed it was the original and called it “Roman. Stanton was unfazed when she quickly changed her opinion and just as quickly changed it back.MANUAL FOR THE GRE DRILL Question 1 Accustomed to his wife’s _________ nature. only exacerbated his parents’ ire: they considered every increasingly elaborate and tortuous excuse a new offense. Inc. the first recognizably modern handwriting. opaque conventional lucid byzantine boorish Question 3 One example that (i)________ the common impression of the “Dark Ages” as a period of intellectual stagnation is the development of Carolingian miniature. each more _________ than the last. Blank (i) Blank (ii) caricatures intermittent belies equivocal substantiates ubiquitous .” 268 | © The Princeton Review. | 269 . Inc.VERBAL PRACTICE SCRATCH PAPER 9 © The Princeton Review. MANUAL FOR THE GRE Question 4 Despite the recent (i)________ of ads that attack political adversaries by name. Consequently. they warn that using scarce campaign resources to publicize your opponent— even in condemnation—could easily backfire. 9 Blank (i) Blank (ii) paucity dubious novelty convivial proliferation mercurial Question 5 Economic policy is primarily reactionary. Inc. many analysts have begun to regard the strategy with a (ii)________ eye. Especially in crowded primaries. unrestrained financial growth leads to rampant speculation. it is unlikely that the savings would be passed down to the taxpayers to help (iii)________ increased food expenditures. As a result. 270 | © The Princeton Review. designed solely to avoid downturns rather than foster upturns. in which name recognition is vital. Blank (i) Blank (ii) Blank (iii) unexpected squander augment adverse abate offset advantageous drive flag . Blank (i) Blank (ii) Blank (iii) ignorant of prudent solid responses to sparing tenuous peripheral to irrational unstable Question 6 An increase in the cost of food staples would have (i)________ consequences for the general population. rather than focusing on (ii)________ management of the current boom. Although such an increase would (ii)________ the need for the steep agricultural subsidies that the government currently pays farmers. economic policies tend to be (i)________ the previous crisis. and soon even seemingly (iii)________ investments collapse as another recession begins. | 271 . Inc.VERBAL PRACTICE SCRATCH PAPER 9 © The Princeton Review.  Before classifications were understood. when used together. even after eliminating disbursement of mismatched blood due to clerical error. the majority of blood transfusion recipients died.  Donor-to-recipient blood compatibility depends more on some blood groups than others. the necessity of transfusing blood as soon as it was drawn. Later advances in blood analysis revealed not only that there are numerous additional blood groups with which donors may be incompatible. or symptoms similar to one.  White blood cells are classified according to different classifications than are the other components of blood. often accompanied by fever or nausea. and Landsteiner’s classification of ABO blood groups in 1900 was presumed capable of concluding the second. due to coagulation. However. the occasionally fatal hemolytic reactions. Question 9 The primary purpose of the passage is to highlight two major problems with human blood transfusions describe the origins of human blood transfusions examine the difficulties associated with transfusing blood recommend improvements to human blood transfusion methods illustrate the problems presented by blood type in human blood transfusions . notably the Rh system. a small percentage of recipients still experienced symptoms that paralleled those of a hemolytic reaction.MANUAL FOR THE GRE Line 5 10 15 9 20 Human-to-human blood transfusions in the nineteenth century were plagued by two major problems: first. and second. but also that white blood cells may attack new blood from even seemingly suitable donors. Inc. Question 8 The passage suggests that the author believes which of the following about transfusions?  ABO and Rh matching. are sufficient to ensure a successful transfusion. solving the first obstacle. Rudimentary anticoagulants were developed as early as 1860.  Accurate blood group matching during transfusions will eliminate the chance of having a hemolytic reaction. that afflicted many patients. Question 7 The author mentions the difficulties associated with blood transfusions in order to criticize the simplicity of early attempts at transfusions  present supplemental information that could be used to help reduce these difficulties  suggest that it will never be possible to understand all the causes of a hemolytic reaction  argue for increased measures of compatibility across various blood groups  describe best practices for blood transfusions in order to prevent the difficulties 272 | © The Princeton Review. Inc. | 273 .VERBAL PRACTICE SCRATCH PAPER 9 © The Princeton Review. or emperor. was the division of the Empire into two types of provinces: imperial and Senatorial.  An autonomous Senate was considered a significant element.” or joint rule between princeps and Senate. In particular. The exact nature of Augustus’s authority has long been a subject of debate among historians. Augustus had created a “dyarchy.  The army should be evenly distributed throughout the Empire. and Syria. The most visible element of the provincial reform. carried out between 27 and 23 BCE. No historian has suggested an equal division of power between Augustus and the Senate—the frontier nature of the imperial provinces meant that the provinces held most of the army—but this division was widely held to be real by modern observers. conversely. Question 11 Which of the following questions can be answered by information provided in the passage?  Why did Augustus resign the Roman consulship in 23 BCE?  What accounts for the preservation of the Cyrene Edicts?  What were some of the offices that affected how Roman society judged its elites?  Was Augustus the first to present himself as princeps?  Were there more imperial or Senatorial provinces? Question 12 According to the passage. In addition to restoring prestige to the Senate as a body. Augustus took pains to present himself not as king. © The Princeton Review. which came to be known as the Cyrene Edicts.  Traditional republican values allowed the Emperor to have proconsular imperium over the entire Empire. Senatorial provinces. the greatest classicist of the nineteenth century. In the words of Mommsen. Augustus retained the highest official form of power. The Roman Revolution. thus reflecting the time-honored republican belief in the balance of power. more than a decade after Creta et Cyrenaica was created as a Senatorial province. Nonetheless. Inc.MANUAL FOR THE GRE Line 5 10 15 9 20 25 30 35 40 45 50 274 | Despite his unquestioned preeminence in Rome from 31 BCE to 14 CE. this development also opened up one of the primary offices by which Roman aristocrats had traditionally achieved status. The degree to which the discovery of the Cyrene Edicts shattered the historical orthodoxy is best seen in Syme’s epoch-making 1974 work. granted proconsular imperium over the entire Empire. Gaul. In imperial provinces. proconsular imperium. This vision dominated accounts of Augustus’s rule until the discovery of a series of inscriptions in North Africa in the early 1920s. dictator. Syme contends that Augustus was. the Cyrene Edicts are important because they  prevented Senators from being empanelled as jurors in imperial provinces  suggested that Syme’s views on imperial authority were too extreme  conclusively refuted Mommsen’s assessment of provincial reorganization  authorized Augustus to reorganize the Roman provinces  cast doubt on the clear distinction between Senatorial and imperial provinces . much attention has been paid to the role played by Augustus’s provincial reform in both consolidating his power and furthering his public image as a champion of traditional republican values. as did Augustus’s resignation of the Roman consulship in 23 BCE. date to around 6 BCE. which included such troublesome frontier areas as Spain. and that Senatorial proconsuls were effectively his legates. but as princeps—first among equals.  Traditional republican values were rooted in the dual mythos of the farmer-soldier. they show Augustus intervening in such local issues as the empanelling of jurors. These inscriptions. Question 10 The passage suggests which of the following about traditional republican values in the era of Augustus?  Roman nobles could only achieve status through office-holding. in fact. were governed by proconsuls chosen by the Senate. ending his decade-long monopolization of one of the Republic’s highest offices. Inc.VERBAL PRACTICE SCRATCH PAPER 9 © The Princeton Review. | 275 . Inc. Audiences were rapt during the first half of the movie. . .  Over the last year. . Which of the following. an expert pointed to a 27% drop in sales of American-made cars in the state of California over the last year.  Total car sales in the state of California did not significantly decrease over the last year. dichotomous suspect heretical middling critical inconsequential . the tradition of _________ lives on. oft rarely frequently seldom redundantly significantly Question 15 Although our current permissive society allows more explicit expressions. . . As evidence of the severe damage inflicted on the American automobile industry by competition from foreign automakers. . it was only after the jejune plot twist that their interest began to _________.  Major improvements in public transportation were made in California eighteen months ago.MANUAL FOR THE GRE Question 13 Question 16 Every new scientific theory that challenges the reigning orthodoxy is viewed as _________ until it is supported by mounting evidence and eventually adopted as truth. flag wax swell prevaricate converge ebb Question 17 Question 14 9 The concepts of “please” and “thank you” are usually taught together in the same lesson when we are young. . . . . . if true. foreign auto companies have significantly increased their advertising budgets for American television commercials. .  Fewer than one-third of California drivers report having negative feelings about American-made cars. . . most seriously weakens the argument that the American automobile industry has been weakened by foreign competition?  Only 68% of Californians over the age of 16 own cars. . . . . . . 276 | rhetoric euphemism excoriation garrulousness genteelism pragmatism © The Princeton Review. which makes it ironic that the former is _________ used while the latter is quite commonly heard and read in daily communication. . . . . Inc.VERBAL PRACTICE SCRATCH PAPER 9 © The Princeton Review. | 277 . The study found that the assistants who spent the most time engaged in sedentary activities were most likely to report frequent back pain. For Ferdinand de Saussure. is both rare and to some extent socially constructed. an office commissioned a study to determine whether sitting for long periods of time induces back pain. commonly defined as language that sounds like its meaning (“bam. philology. Saussure dismissed this objection by suggesting that true onomatopoeia. and they all said that they did not.  The researchers did not ask the administrative assistants whether the back pain they experienced was severe or mild. such linguistic paradigms were unsatisfactory. Researchers asked the assistants how often they completed assignments requiring long periods of sitting. The word derives its meaning purely from the fact that speakers use it as a sign for a mutually agreed upon concept.” etc.MANUAL FOR THE GRE Line 5 10 15 9 20 25 30 Until about 1870. One objection Saussure anticipated to his theory was the existence of onomatopoeia. Language was studied first through grammar. the field of linguistics was marked by three successive approaches. The study thus concluded that sitting for long periods of time does indeed cause back pain.). and finally through comparative linguistics. would most undermine the argument?  A third question in the survey asked whether respondents engaged in a regular exercise regimen. if true. Saussure theorized that the constructs of language are inherently arbitrary. Which of the following. as opposed to that produced by conscious attempts at onomatopoeic pronunciation. then through philology. he suggested that there is no real relationship between the word “tree” and the concept that people associate with that word.” “squish.  Administrative assistants who reported frequent sedentary activity were no more dissatisfied with their jobs than were those who did not report frequent sedentary activity. Inc. which posited a series of affinities between seemingly diverse languages. which sought to discover truths about the customs and traditions of ancient cultures through language. As an example.  Administrative assistants who said that they experienced frequent back pain were especially likely to over-report the amount of time they spent sitting down. and comparative linguistics as linguistic disciplines  Demonstrated that not all linguists agree on the frequency with which onomatopoeic words occur in language  Provided an example of a particular word generally regarded as onomatopoeic and gave a detailed explanation of why it is not true onomatopoeia 278 | © The Princeton Review. and that to truly understand linguistics one needed to retreat from the notion that the evolution of words themselves was significant. . which provided a set of rules for a particular language. Question 18 Saussure’s dismissal of onomatopoeia as a challenge to his theory would be most strengthened if he did which of the following?  Showed that conscious attempts at onomatopoeic pronunciation were socially constructed  Offered an example of an onomatopoetic word that emerged independently in several languages  Challenged the validity of grammar. Question 19 In which sentence does the author present a set of methodologies that Saussure finds inadequate? Question 20 Responding to complaints from administrative assistants about back pain after long periods of sedentary assignments.  Another recent study has shown that sitting for long periods of time can cause leg pain. and how often they had experienced back pain during the past six months. | 279 .VERBAL PRACTICE SCRATCH PAPER 9 © The Princeton Review. Inc. . Math Practice . Shaded = Total – Unshaded Draw lines (split. TRIGGER Geometry on Quant Comp or Must Be questions Draw the shape twice. RESPONSE Right triangle with 45° or 2 . drop heights. Stretch and squash. draw radii. a big side that is twice the small side. 60°.” “sector.” or a fraction of a circle Write your formula: angle 360F = arc area sector = circumference area circle TRIGGER TRIGGER Overlapping shapes Find the elements the two shapes have in common. Inc. RESPONSE TRIGGER Right triangle with 30°. or height of equilateral triangle Find the 30°-60°-90° triangle (you know it’s in there somewhere). or 3 . RESPONSE “Arc.TRIGGER Find the 45°-45°-90° triangle (you know it’s in there somewhere). RESPONSE | Shaded regions or strangelooking shapes RESPONSE 282 RESPONSE Find familiar shapes. . or diagonal of a square TRIGGER MANUAL FOR THE GRE © The Princeton Review. or otherwise play with the shape). connect. Inc.“…percent change…” “…percent decrease/less…” difference ×100 original Draw a pie every time the word average appears in the question. RESPONSE “…ratio…” RESPONSE TRIGGER Percent change = TRIGGER “…percent increase/more…” Write formula: RESPONSE TRIGGER MATH PRACTICE © The Princeton Review. RESPONSE TRIGGER “…speed…” RESPONSE TRIGGER TRIGGER “…average…” RESPONSE Draw ratio box on scratch paper. | 283 . “…median…” Find a bunch of numbers and list them in order on your scratch paper. try to cancel out common factors. regroup. “…rate…” Exponents Write formula: D = R × T Factor. Work the problem. Label the first column. Eliminate two answer choices. Variables in the answer choices 3. Inc. 4. 3. List answers on your scratch paper.TRIGGER Convert large bases to their prime numbers.E on scratch paper. 4. . RESPONSE 284 1. 1. TRIGGER | © The Princeton Review. 5.” “how much. 4. If percentages.B. plug in common denominator. Plug in an easy number.C. RESPONSE TRIGGER 1. Repeat using FROZEN. Repeat using FROZEN. Identify and circle target number. Answer choices expressed as fractions or percentages RESPONSE TRIGGER Numbers too big to calculate RESPONSE TRIGGER MANUAL FOR THE GRE 2. “Must be” 2.D.” “what is the value of” 1. An urge to write your own algebraic formula 4. or 3. Assume (C) to be correct. Plug in an easy number. 3. Draw set-up. RESPONSE TRIGGER 5. Quant Comp with variables 2. Check all answer choices. 2. RESPONSE Plug In for the unknown value or amount. Draw set-up. If fractions. Replace variable with number. POE. The phrases “how many. Eliminate answer choices. Use (C) to work the problem. List A. plug in 100 for total. ..” RESPONSE TRIGGER MATH PRACTICE © The Princeton Review.normal distribution..” Plug in information directly underneath...TRIGGER TRIGGER Fill in the percentages.. circumference. and add the sides together.. l1 || l2 Find and label your big and small angles.. RESPONSE “. RESPONSE Circles Write the area formula on scratch. Find radius.” “..” RESPONSE TRIGGER Draw the curve. RESPONSE TRIGGER “ “...perimeter. diameter......” Plug information directly underneath. label the sides.area of rectangle. Draw the shape. Write “r d C A” vertically on scratch paper. | 285 ..... Parallel lines Write area formula on scratch.area of parallelogram. and area. Inc. RESPONSE TRIGGER ...standard deviation. “.” “...area of triangle. RESPONSE x and x 2 in the same equation. “both. RESPONSE Probability question asks “not” or “at least” Look to factor or expand. 5:12:13) .MANUAL FOR THE GRE 45°-45°-90° Right triangles 30°-60°-90° Pythagorean triples RESPONSE TRIGGER Look for: TRIGGER TRIGGER TRIGGER TRIGGER Draw Group Table. or anything that looks like a quadratic Total = [Group 1] + [Group 2] – [Both] + [Neither] RESPONSE Group question in which elements are in either one group or other (no overlap) Write down group formula: RESPONSE Group problem with overlap. find every factor of c. 6:8:10. Inc. RESPONSE Factorials TRIGGER (3:4:5.M. write down (x )(x ) = 0 Remember A. 286 | © The Princeton Review.” or “neither” Find the probability an event won’t happen and subtract from 1. Put the equation in the form x + bx + c = 0 Underneath the equation. If necessary. slope.” Park the information you have directly underneath....Question asks for the distance between two points Draw triangles and look for Pythagorean triples.. “. Inc..” vertical change Δy Rise y 2 − y 1 = = = horizontal change Δx Run x − x 2 1 TRIGGER TRIGGER TRIGGER Interior diagonal of a box Draw a space for each event.probability.” RESPONSE Write y = mx + b on scratch paper.. want Find the total(s)... RESPONSE TRIGGER RESPONSE TRIGGER MATH PRACTICE © The Princeton Review. | 287 .. total a2 + b2 + c2 = d 2 RESPONSE “. RESPONSE “...on a coordinate plane.. after taxes.  The two quantities are equal. What is 95 percent of that number? Question 2 n is an even integer. what is the total amount of the prize?  $15. Quantity A Quantity B (–3)n –(3n)  Quantity A is greater.000  $20.800. of a winning lottery ticket. At this rate.  Quantity B is greater.000  $17.500.000. how much will Miki pay for seven books?  7b d  7db  288 | b 7d  7d  d b 7b © The Princeton Review.  The two quantities are equal.MANUAL FOR THE GRE DRILL Question 1 Question 4 40 percent of a certain number is 1. k is an integer.  The relationship cannot be determined from the information given.000.500. Question 5 A group of 5 coworkers is going to equally divide the proceeds. Inc.  Quantity B is greater.992. Question 3 Miki learns that b books cost d dollars. such that 5 < n < 15.  The relationship cannot be determined from the information given. and each coworker will receive $1. If taxes consume 40% of the total prize.000  $25.000.000 .000. Quantity A 5 Quantity B 5 5 + 3k 5 + 7k  Quantity A is greater.000  $22. | 289 .MATH PRACTICE SCRATCH PAPER © The Princeton Review. Inc. Of the Paleolithic artifacts. 45° 55° 80° 100° 115° 135° 225° Question 10 B 105 A 30 C If the length of BC is 6 2. . . . . . then how many of the water heaters are eligible for the federal tax rebate?  4  12  14  15  18 3 of the artifacts are 5 Paleolithic. . and the number of water heaters eligible for the federal tax rebate is 3 times the number that are neither Energy Star certified nor eligible for the federal tax rebate. . . . Indicate all such values. and the remaining 16 are Neolithic. 2 x 2x 1 – x2 1 – 2x x2 – 2 2 – x2 Question 7 Of the 20 water heaters for sale at AAA Appliances. then the area of triangle ABC =  18  18 3  36  18 + 18 3  36 + 36 3 290 | © The Princeton Review.MANUAL FOR THE GRE Question 6 Question 8 If 0 < x < 1. half are both Energy Star certified and eligible for a federal tax rebate. If 14 water heaters are Energy Star certified. Inc. . which of the following must be greater than x ? In a certain museum exhibit. how many Neolithic artifacts are NOT Mediterranean? Question 9 B C 135º A D Which of the following could be an angle measurement within parallelogram ABCD above? Indicate all such values. . 3 are Mediterranean. . If 4 26 of the artifacts are Mediterranean. . . MATH PRACTICE SCRATCH PAPER © The Princeton Review. Inc. | 291 . What is the distance 4 from point S to point R ? Question 12 36 . Inc. what is the area of the square with sides of length s ? 4  π2  2π2 8  16 292 | © The Princeton Review. ? . What is the π circumference of Circle O ? Circle O has an area of 5  5 5  12  13 5 17 Question 15 Question 13 What is the value of the expression 12! + 11! 10!  2. what is the area of the parallelogram ABCD ?  16  32  32 2  32 3  64 The equation of the line in the rectangular coordinate 5 system above is y = − x + 10.MANUAL FOR THE GRE Question 14 Question 11 y C B R (20.3  23!  13!  143  264 s s If the area of the circular region above is 4π. if BC = 8 and CD = 4 2 .5) A Note: Figure not drawn to scale Q D x S In the figure above. | 293 .MATH PRACTICE SCRATCH PAPER © The Princeton Review. Inc. each team plays two games against schools from a neighboring county. which of the following must be true? Three students. Inc.200 teenagers watched between 95 and . then what is the probability that 8 at lease one of the students will get the problem Indicate all such statements. the number of hours of television watched per teenager in the month of October had a normal distribution.663. 2600 teenagers watched fewer than 80 hours of television in October. but she can fit only four photos on the mantel. She has one photo of each of her 11 grandchildren. . 1 1 If of the male partygoers and of the female 5 2 partygoers arrive late. . In addition.000 teenagers. respectively. At the end of the party. 18. and 4 5 3 . 100 hours of television in October. Each team plays each of the other teams in the county exactly once.920  1. . If the average number of hours watched was 90 and the standard deviation was 5 hours. How many total games are played?  36  54  90  108  126 294 | © The Princeton Review. 75 of whom are male. and Wanda. Question 17   partygoers will be chosen by lottery to win a prize.MANUAL FOR THE GRE Question 16 Question 18 In a study of 130. one of the 3  32 80 39 40 Question 19 A grandmother wants to display photos of her grandchildren on her mantel.200  9. How many different arrangements of photos are possible?  330  484  7.200 Question 20 There are nine high school basketball teams in Johnston County. If their 1 2 individual probabilities of success are . Peter.979. what is the probability that the prize will be won by a partygoer who arrives late? 80 9 32  23  77 Colleen is hosting a party for 125 people. Mark. are all working on the same math problem. More than 25% of the teenagers watched between 80 and 85 hours of television in October. correct? . MATH PRACTICE SCRATCH PAPER © The Princeton Review. | 295 . Inc. . Between Now and Test Day . Inc.MANUAL FOR THE GRE PICK A SUBJECT AND MASTER IT There are only about 20 concepts tested on the whole GRE. Between now and test day. Some of these you are comfortable with and some you are not. 298 | © The Princeton Review. pick one or two distinct topics you haven’t yet mastered and master them. . Sequences. and Statistics Parallel Lines Triangles Quadrilaterals Circles 3D Figures Coordinate Geometry Charts. Median. Inc. | 299 .BETWEEN NOW AND TEST DAY HI M AS TE GH R E D L O PRI W OR PR I T IO Y RI TY Verbal … … … … … … … … … … … … … … … … … … Vocab Text Completion Strategy Sentence Equivalence Strategy Reading Comprehension Passage Profiling Reading Comprehension Question Strategy Argument Question Strategy M HI AS TE GH R E D L O PRI W OR PR I T IO Y RI TY Math … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … Fundamentals Plugging In Plugging In the Answers (PITA) Quantitative Comparison/Must Be Fractions/Decimals/Percentages Ratios and Proportions Exponents and Square Roots Mean. Graphs Linear Equations and Inequalities Quadratic Equations Probability Rates Groups. and Functions Factorials Arrangements and Combinations HI M AS TE GH R E D L O PRI W OR PR I T IO Y RI TY Essays … … … Issue Essay … … … Argument Essay © The Princeton Review. Mode. There should be no surprises. Stick to the Plan It’s easy to get stressed out on test day. Focus on accuracy. The second time around. Practice your technique and use your scratch paper. mark it and come back. delete them all and do them again. The First Run Is a Practice Run If possible. This allows you to relax the first time. 300 | © The Princeton Review. Do the easy questions first. you’ve got a second option. If you get stuck on a problem. Inc. Most of what you see will look very familiar. If you need more points. Don’t Start Cold Bring your warm-up page and do it before the test. so focus on the positive: You have a plan. plan to take the GRE more than once. . Go slowly. Standardized = Predictable You have now seen every subject and question type you could see on test day. That’s okay. you are done. the score is moot because you will have seen many of the questions. If you get a great score. Stick to it.MANUAL FOR THE GRE A FEW LAST THINGS TO NOTE Practice Tests and Drills Once you have taken them all. You’ve applied it on the practice tests. Not prime. z (variable) (x – y)2 = x 2 – 2xy + y2 Percent Change = difference original (x + y)(x – y) = x 2 – y2 d+e=b de = c (x + y)2 = x 2 + 2xy + y2 Rate Groups Total = Group 1 + Group 2 + Neither – Both Probability Distance = Rate × Time Work = Rate × Time Avg Speed = Total Distance ÷ Total Time Average 0≤ want ≤1 total Probability of events A and B = A × B Total # of Average things Probability of events A or B = A + B Probability of “at least once” = 1 – probability of never © The Princeton Review. Not positive. 13. 3. 19 Multiply Add Divide Subtract Power Multiply Order of Operations (PEMDAS): x1 = x x0 = 1 Parentheses E xponents 1x = 1 0x = 0 (–x)even = positive (–x)odd = negative Multiplication & Division Addition & Subtraction Percents Quadratics %: ÷ 100 x 2 + bx + c = 0 ĺ (x + d)(x + e) = 0 of: × (times) is. First prime Primes less than 20: 2. y.BETWEEN NOW AND TEST DAY Arithmetic 0: 1: 2: Exponents Even integer. 17. 5. Not prime Even prime integer. | 301 . Not negative Odd positive integer. are. 11. was: = what: x. 7. Inc. 60° Diagonal of Box: a2 + b2 + c 2 = d2 . and smaller than the sum. b is y-intercept) 45° a √2 a Slope: 45° a rise y 2 − y1 = run x 2 − x1 Solids Volume of Cube: V = s3 a : a 3 : 2a (30°:60°:90°) Volume of Box: V = l × w × h Volume of Cylinder: V = πr 2h 30° 2a a √3 a 302 | © The Princeton Review. Circles d = 2r C = πd = 2πr A = πr 2 Third Side Rule Any side of a triangle is greater than the difference of the other two sides. Length of Arc = angle × Circumference 360° Right Triangles Area of Section = angle × Area of Circle 360°  a +b =c 2 2 2 3 : 4 : 5.MANUAL FOR THE GRE Triangles Quadrilaterals Angles add up to 180° Angles add up to 360° Perimeter: add up the sides 1 A = b×h 2 Area of parallelogram (rectangle or square) = b × h Isosceles triangle: Two equal sides are opposite two equal angles. Inc. 5 : 12 : 13 a : a : a 2 (45°:45°:90°) Coordinate Geometry Line Formula: y = mx + b (m is slope. then corresponding sides are proportional. Similar triangles: If all angles of two triangles are the same. 6 : 8 : 10. NOTES . NOTES . NOTES . NOTES . 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