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GRUBERâ&#x20AC;&#x2122;S COMPLETE

GRE GUIDE 2014 *

3rd Edition

*GRE is a registered trademark of the Educational Testing Service, which was not involved in the production of, and does not endorse, this book.

Gary R. Gruber, PhD

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Contents

INTRODUCTION

xiii

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I. Important Facts About the GRE / xiii

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II. The Inside Track on How GRE Questions Are Developed and How They Vary from Test to Test / xix III.

What Are Critical Thinking Skills? / xxi

IV. Multi-Level Approaches to the Solution of Problems / xxiii V. A 4-Hour Study Program for the GRE / xxvi VI. Longer-Range Study Program and Helpful Steps for Using This Book / xxvii

PART 1

STRATEGY DIAGNOSTIC TEST FOR THE GRE Directions for Taking the Diagnostic Test / 2

Section 3: Quantitative Reasoning (Quantitative Comparison) / 16

Strategy Diagnostic Test Answer Sheet / 3

Strategy Diagnostic Test Answer and Diagnostic Table / 19

Section 1:Verbal Reasoning / 4 Section 2:Quantitative Reasoning / 12

PART 2

THE WORLD’S shortest PRACTICE test—20 QUESTIONS to approximate your GRE score 25 Verbal (Critical Reading) / 26

Answers / 31

Regular Math / 28

Scoring / 32

Quantitative Comparison Math / 30

Answers and Hints / 33

PART 3

THE 101 MOST IMPORTANT MATH QUESTIONS YOU NEED TO KNOW HOW TO SOLVE 101 Math Questions Answer Sheet / 38

101 Math Questions: Answers / 52

101 Math Questions Test / 40

Basic Skills Math Diagnosis / 54

101 Math Questions: Answers, Diagnoses, Solutions, Generalizations, and Rules / 51

Solutions, Generalizations, and Rules / 55

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PART 4

STRATEGY SECTION

5 General Strategies / 66

25 Math Strategies / 72

42 Easy-to-Learn Strategies / 69

17 Verbal (Reading) Strategies / 138

PART 5

MINI-MATH REFRESHER

177

Algebra and Arithmetic / 178

Geometry / 181

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PART 6

COMPLETE GRE MATH REFRESHER Session 1—Fractions, Decimals, Percentages, Deviations, Ratios and Proportions, Variations, and Comparison of Fractions / 189

187

Session 4—Algebra Problems / 261 Algebraic Properties / 262 Fundamental Laws of Our Number System / 262

Fractions, Decimals, Percentages / 190

Algebraic Expressions / 263

Deviations / 193

Equations / 263

Ratios and Proportions / 194

Algebra of Graphs / 265

Variations / 195

Inequalities / 272

Comparison of Fractions / 196

Exponents and Roots / 277

Practice Test 1 / 198

Practice Test 4 / 278

Answer Key for Practice Test 1 / 207

Answer Key for Practice Test 4 / 286

Answers and Solutions for Practice Test 1 / 207

Answers and Solutions for Practice Test 4 / 286

Session 2—Rate Problems / 211

Session 5—Geometr y Problems / 291

Word Problem Setup / 212

Basic Definitions / 292

Distance and Time / 214

Triangles / 294

Work / 215

Properties of Triangles / 295

Mixture / 216

Four-Sided Figures / 298

Cost / 216

Many-Sided Figures / 299

Practice Test 2 / 218

Circles / 299

Answer Key for Practice Test 2 / 227

Practice Test 5 / 302

Answers and Solutions for Practice Test 2 / 227

Answer Key for Practice Test 5 / 311

Session 3—Area, Perimeter, and Volume Problems / 237 Area, Perimeter, and Volume / 238

Answers and Solutions for Practice Test 5 / 311

Session 6—Miscellaneous Problems / 321

Practice Test 3 / 246

Averages, Medians, Modes, and Standard Deviation / 322

Answer Key for Practice Test 3 / 255

Properties of Integers / 324

Answers and Solutions for Practice Test 3 / 255

Approximations / 325 Combinations / 327

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Permutations / 327

Bar Graphs / 342

Probability / 328

Circle Graphs / 343

The Absolute Value Sign / 328

Line Graphs / 344

Functions / 328

Practice Test 7 and Solutions / 345

Practice Test 6 / 329

Session 8—Modern Math / 351

Answer Key for Practice Test 6 / 335

Sets / 352

Answers and Solutions for Practice Test 6 / 335

Relations / 353

Session 7—Tables, Charts, and Graphs / 339

Solution Sets / 353 Axioms / 354

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Charts and Graphs / 340

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Closed Sets / 354

Tables and Charts / 340

Mathematical Symbols / 354

Graphs / 341

Practice Test 8 and Solutions / 355

PART 7

VOCABULARY BUILDING THAT IS GUARANTEED TO RAISE YOUR GRE SCORE

363

Knowing Word Meanings Is Essential for a Higher GRE Score / 364

The Most Important/Frequently Used GRE Words and Their Opposites / 375

8 Steps to Word Power / 365

The Gruber GRE 3,400-Word List / 379

The Gruber Prefix-Root-Suffix List That Gives You the Meanings of More Than 150,000 Words / 368

100 Tests to Strengthen Your Vocabulary / 428 Answers to Vocabulary Tests / 471

A List of Standardized Test Words Appearing More Than Once on Actual Standardized Exams Such as the GRE and SAT / 373

PART 8

Analytical Writing Section Analytical Writing 1 Test—Analyze an Issue / 476 Scoring the “Analyze an Issue” Analytical Writing 1 Section / 480

475

Scoring the “Analyze an Argument” Analytical Writing 2 Section / 491 Analytical Writing Score Level Descriptions / 494

Sample Analytical Writing Topics, Scored Sample Essay Responses, and Reader Commentary / 483

Sample Argument Essay Responses and Reader Commentary / 495

Analytical Writing 2 Test—Analyze an Argument / 487

Important Tips on How to Write the Best Essay / 499

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PART 9

A Brief Review of English Grammar Frequent Grammatical Problems / 508

Other Grammatical Terms / 511

Common Errors in Grammar / 509

Common Grammar Errors Classified by Part of Speech / 512

Some Basic Grammatical Terms / 510

507

PART 10

3 GRE PRACTICE TESTS

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5 Important Reasons for Taking These Practice Tests / 516 9 Tips for Taking the Practice Tests / 517 Guidelines to See How You Would Do on a GRE and What You Should Do to Improve / 518

515 Answer Key for Practice Test 2 / 625 Scoring the GRE Practice Test / 629 GRE Score Conversion Table / 630 Chart for Self-Appraisal Based on the Practice Test You Have Just Taken / 631

GRE Practice Test 1 / 519

Explanatory Answers for GRE Practice Test 2 / 633

How Did You Do on This Test? / 558

What You Must Do Now to Raise Your GRE Score / 650

Answer Key for Practice Test 1 / 559 Scoring the GRE Practice Test / 563 GRE Score Conversion Table / 564 Chart for 足Self-足Appraisal Based on the Practice Test You Have Just Taken / 565

Explanatory Answers for GRE Practice Test 1 / 567 What You Must Do Now to Raise Your GRE Score / 584

GRE Practice Test 2 / 586 How Did You Do on This Test? / 624

Appendixes

GRE Practice Test 3 / 652 How Did You Do on This Test? / 690 Answer Key for Practice Test 3 / 691 Scoring the GRE Practice Test / 695 GRE Score Conversion Table / 696 Chart for Self-Appraisal Based on the Practice Test You Have Just Taken / 697 Explanatory Answers for GRE Practice Test 3 / 699 What You Must Do Now to Raise Your GRE Score / 717

719

Appendix A: Hot Prefixes and Roots / 719 Appendix B: Words Commonly Mistaken for Each Other / 724

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xxi

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III. What Are Critical Thinking Skills? Critical Thinking Skills are generic skills for finding the most creative and effective way of solving a problem or evaluating a situation. The most effective way of solving a problem is to extract some piece of information or observe something curious from the problem and then use one or more of the specific strategies or Critical Thinking Skills (together with basic skills or information you already know) to get to the next step in the problem. This next step will catapult you toward a solution with further use of the specific strategies or thinking skills. 1. EXTRACT OR OBSERVE SOMETHING CURIOUS 2. USE SPECIFIC STRATEGIES TOGETHER WITH BASIC SKILLS These specific strategies will enable you to focus on the process rather than just be concerned with the end result, which usually gets you into a fast, rushed, and wrong answer. The Gruber strategies have been shown to make test takers more comfortable with problem solving and to make the process enjoyable. The skills will last a lifetime, and you will develop a passion for problem solving. These Critical Thinking Skills show that conventional “drill and practice” is a waste of time unless the practice is based on these generic thinking skills. Here’s a simple example of how these Critical Thinking Skills can be used in a math problem: Which is greater, 7 1 # 8 1 # 6 1 or 8 1 # 6 1 # 7? 7 8 6 8 6 Long and tedious way: Multiply 7 1 # 8 1 # 6 1 and compare it with 8 1 # 6 1 # 7 . 7 8 6 8 6 Error in doing the problem the “long way”: You don’t have to calculate; you just have to compare, so you need a strategy for comparing two quantities. Critical Thinking Way: 1. Observe: Each expression contains 8 1 and 6 1 . 8 6 2. Use Strategy: Since both 8 1 and 6 1 are just weighting factors, 8 6 like the same quantities on both sides of a balance scale, just cancel them from both multiplied quantities above.

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3. You are then left comparing 7 1 with 7, so the first quantity, 7 1 , 7 7 1 1 1 is greater. Thus 7 # 8 # 6 is greater than 8 1 # 6 1 # 7 . 7 8 6 8 6

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xxiii

IV. Multi-Level Approaches to the Solution of Problems

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How a student answers a question is more important than the answer given by the student. For example, the student may have randomly guessed, the student may have used a rote and unimaginative method for solution, or the student may have used a very creative method. It seems that one should judge the student by the way he or she answers the question and not just by the answer to the question. Unfortunately, standardized tests such as the GRE do not work that way. Example: Question: Without using a calculator, which is greater: 355 3 356 or 354 3 357? Case 1: Rote Memor y Approach (a completely mechanical approach not realizing the fact that there may be a faster method that takes into account patterns or connections of the numbers in the question): The student multiplies 355 3 356, gets 126,380, and then multiplies 354 3 357 and gets 126,378. Case 2: Obser ver’s Rote Approach (an approach that makes use of a mathematical strategy that can be memorized and tried for various problems): The student does the following: He or she divides both quantities by 354. He or she then gets 355 # 356 compared with 354 # 357 . 354 354 He or she then divides these quantities by 356 and then gets 355 compared with 357 . 354 356 Now he or she realizes that 355 5 1 1 ; 357 5 1 1 . 354 354 356 356 He or she then reasons that since the left side, 1 1 , is greater than the right side, 354 1 1 , the left side of the original quantities, 355 3 356, is greater than the right side 356 of the original quantities, 354 3 357. Case 3: The Pattern Seeker’s Method (the most mathematically creative method—an approach in which the student looks for a pattern or sequence in the numbers and then is astute enough to represent the pattern or sequence in more general algebraic language to see the pattern or sequence more clearly): Look for a pattern. Represent 355 3 356 and 354 3 357 by symbols. Let x 5 354. Then 355 5 x 1 1, 356 5 x 1 2, 357 5 x 1 3. So 355 3 356 5 (x 1 1)(x 1 2) and 354 3 357 5 x(x 1 3). Multiplying the factors, we get 355 3 356 5 x2 1 3x 1 2 and 354 3 357 5 x2 1 3x. The difference is 355 3 356 2 354 3 357 5 x2 1 3x 1 2 2 x2 2 3x, which is just 2. So 355 3 356 is greater than 354 3 357 by 2. Note: You could have also represented 355 by x. Then 356 5 x 1 1; 354 5 x 2 1; 357 5 x 1 2. We would then get 355 3 356 5 (x)(x 1 1) and 354 3 357 5 (x 2 1)(x 1 2). Then we would use the method above to compare the quantities. —OR— You could have written 354 as a and 357 as b. Then 355 5 a 1 1 and 356 5 b 2 1. So 355 3 356 5 (a 1 1)(b 2 1) and 354 3 357 5 ab. Let’s see what (355 3 356) 2 (354 3 357) is. This is the same as (a 1 1)(b 2 1) 2 ab, which is (ab 1 b 2 a 2 1) 2 ab, which is in turn

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xxvi

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V. A 4-Hour Study Program for the GRE For those who have only a few hours to spend in GRE preparation, I have worked out a minimum study program to get you by. It tells you what basic math skills you need to know, what vocabulary practice you need, and the most important strategies to focus on, from the 42 in this book.

General Study General Strategies, pages 66–68.

Reading Study the following Verbal Strategies beginning on page 138 (first 3 questions for each strategy): Sentence Completion Strategies 1 and 2, pages 139–141 Vocabulary Strategies 1, 2, and 3, pages 170–175 Reading Comprehension Strategies 1, 2, and 10, pages 154–158 and 168–169 Study the Most Important/Frequently Used GRE Words and Their Opposites, page 375.

Math Study the Mini-Math Refresher beginning on page 177. Study the following Math Strategies beginning on page 72* (first 3 questions for each strategy): Strategy 2, page 74 Strategy 4, page 83 Strategy 8, page 93 Strategy 12, page 102 Strategy 13, page 104 Strategy 14, page 107 Strategy 17, page 114 Strategy 18, page 117

Strategy A, page 123 Strategy B, page 125 Strategy C, page 126 Strategy D, page 129

If you have time, take Practice Test 1 starting on page 519. Do sections 124. Check your answers with the explanatory answers starting on page 567, and look again at the strategies and basic skills that apply to the questions you missed.

Writing Look through the material in Part 8—Analytical Writing Section starting on page 475.

*Make sure you read pages 69–71 before you study Math Strategies.

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Directions for Taking the Diagnostic Test For each odd-numbered question (1, 3, 5, 7, etc.), choose the best answer. In the even-numbered questions (2, 4, 6, 8, etc.), you will be asked how you solved the preceding odd-numbered question. Make sure that you answer the even-numbered questions carefully, as your answers will determine whether or not you used the right strategy. Be completely honest in your answers to the even-numbered questions, since you do want an accurate assessment in order to be helped. Note: Only the odd-numbered questions are SAT-type questions that would appear on the actual exam. The even-numbered questions are for self-diagnosis purposes only. example:

1. The value of 17 3 98 1 17 3 2 5

(A) 1,550 (B) 1,600 (C) 1,700 (D) 1,800 (E) 1,850 (The correct answer is Choice C.) 2. How did you get your answer?

(A) I multiplied 17 3 98 and added that to 17 3 2. (B) I approximated and found the closest match in the choices. (C) I factored 17 to get 17(98 1 2). (D) I guessed. (E) By none of the above methods.

• If you chose B, you probably approximated 98 by 100 and got 1,700. • If you chose C, you factored out the 17 to get 17(98 1 2) 5 17(100) 5 1,700. This was the best strategy to use. • If you chose D, you probably didn’t know how to solve the problem and just guessed. • If you chose E, you did not use any of the methods above but used your own different method. Note: In the even-numbered questions, you may have used a different approach from what will be described in the answer to that question. It is, however, a good idea to see if the alternate approach is described, as you may want to use that approach for solving other questions. Now turn to the next page to take the test.

In question 2: • If you chose A, you did the problem the long way unless you used a calculator.

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Strategy Diagnostic Test Answer Sheet

SECTION

Verbal Reasoning

SECTION

Quantitative Reasoning

SECTION

Quantitative Reasoning

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1 A B C D E 2 A B C D E 3 A B C D E F 4 A B C D E 5 A B C D E 6 A B C D E 7 A B C D E 8 A B C D E 9 A B C D E F 10 A B C D E 11 A B C D E F 12 A B C D E 13 A B C D E 14 A B C D E

15 A B C D E 16 A B C D E 17 A B C D E 18 A B C D E 19 A B C D E 20 A B C D E 21 A B C D E 22 A B C D E 23 A B C D E 24 A B C D E 25 A B C D E 26 A B C D E 27 A B C D E 28 A B C D E

1 A B C D E 2 A B C D E 3 A B C D E 4 A B C D E 5 A B C D E 6 A B C D E 7 A B C D E 8 A B C D E 9 A B C D E 10 A B C D E 11 A B C D E 12 A B C D E 13 A B C D E

14 A B C D E 15 A B C D E 16 A B C D E 17 A B C D E 18 A B C D E 19 A B C D E 20 A B C D E 21 A B C D E 22 A B C D E 23 A B C D E 24 A B C D E 25 A B C D E 26 A B C D E

37 A B C D 38 A B C D E 39 A B C D 40 A B C D E 41 A B C D 42 A B C D E 43 A B C D 44 A B C D E 45 A B C D 46 A B C D E 47 A B C D 48 A B C D E 49 A B C D

50 A B C D E 51 A B C D 52 A B C D E 53 A B C D 54 A B C D E 55 A B C D 56 A B C D E 57 A B C D 58 A B C D E 59 A B C D 60 A B C D E 61 A B C D 62 A B C D E

29 A B C D E 30 A B C D E 31 A B C D E 32 A B C D E 33 A B C D E 34 A B C D E 35 A B C D E 36 A B C D E 37 A B C D E 38 A B C D E 39 A B C D E 40 A B C D E 41 A B C D E 42 A B C D E

43 A B C D E 44 A B C D E 45 A B C D E 46 A B C D E 47 A B C D E 48 A B C D E 49 A B C D E 50 A B C D E 51 A B C D E 52 A B C D E 53 A B C D E 54 A B C D E 55 A B C D E 56 A B C D E

27 A B C D E 28 A B C D E 29 A B C D E 30 A B C D E 31 A B C D E 32 A B C D E 33 A B C D E 34 A B C D E 35 A B C D E 36 A B C D E

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Section 1: Verbal Reasoning

Text Completions and Sentence Equivalence Questions Fill in the blank with the best choice.

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1. He believed that because there is serious unem-

ployment in our auto industry, we should not ———— foreign cars. (A) build (B) repair (C) review (D) import (E) consolidate

2. How did you get your answer?

(A) I tried the word from each choice in the blank and came up with the best answer. (B) I chose a word from the choices that “sounded good” but that I am really not sure is correct. (C) I tried to figure out, before looking at the choices, what word would fit into the blank. Then I matched that word with the choices. (D) I guessed. (E) None of these.

3. Until we are able to improve substantially the

———— status of the underprivileged in our country, a substantial ————— in our crime rate is remote. Blank 1

Blank 2

(A) financial (B) enormous (C) questionable

(D) ascension (E) development (F) attenuation

4. How did you get your answer?

(A) I first tried combinations of words from the blanks to see which made for the best sentence. (B) I tried to see what words I could come up with for the blanks before looking at the choices. (C) I tried the first word from each of the choices in the first blank in the sentence to see which made the most sense. Then I eliminated the choices whose first words didn’t make sense in the sentence. Finally, I tried both words in the remaining choices to further eliminate incorrect choices. (D) I noticed “until” indicated result. I also noticed that the word “improve” indicates that we could “reduce” the crime rate. (E) None of these. 5. Many buildings with historical significance are

now being ——— instead of being torn down. (A) built (B) forgotten (C) destroyed (D) praised (E) repaired 6. How did you get your answer?

(A) I tried each of the choices in the blank. (B) I tried to find my own word that would fit the blank before looking at the choices. Then I matched one of the choices with my word. (C) I looked for a word that meant the opposite of “being torn down.” (D) I guessed. (E) None of these. 7. Being ——— person, he insisted at the conference

that when he spoke he was not to be interrupted.

(A) a successful (B) a delightful (C) a headstrong (D) an understanding (E) a solitary

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PART 2

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The WORLD’S Shortest PRACTICE test— 20 Questions to approximate your GRE score And the Exact Strategies You Need to Improve Your Score Although it shouldn’t take you more than 40 seconds to answer each Verbal (Reading) question and 1 minute to answer each Math question, you may take this test untimed and still get a fairly accurate prediction.

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Verbal (Critical Reading)

Allow 7 minutes for this part. Circle the correct answer(s).

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Sentence Completions

4. Select the correct answer choice for each blank.

1. The instructor displayed extreme stubbornness; although he the logic of the student’s argument, he to acknowledge her conclusion as correct.

Crusty and egotistical, Alfred A. Knopf, the shirts from the most publisher, wore exclusive tailors; was a connoisseur of music, food, and wine; nurtured a garden of exotic plants; and enjoyed rare cigars. His self-assured, manner, together with his insistence on the best of everything, shaped his ostentatious house’s image as a of work of enduring value.

Fill in the blank(s) with the appropriate choice: Select one choice for each blank.

Blank 1 (A) accepted (B) denounced (C) rejected

Blank 2 (D) refused (E) consented (F) decided

2. Select one choice for each blank. In spite of the people were and ideas.

Blank 1 (A) long- windedness (B) formulation (C) forcefulness

of his presentation, many with the speaker’s concepts

Blank 2 (D) enthralled (E) bored (F) gratified

3. Select two answer choices that fit the sentence and give the sentence the same meaning. Richard Wagner was frequently intolerant; moreover, his strange behavior caused most of his acquaintances to the composer whenever possible. (A) contradict (B) interrogate (C) shun (D) revere (E) tolerate (F) reject

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Blank 1

Blank 2

Blank 3

(A) expensive (D) decorous (G) connoisseur (B) immaculate (E) irascible (H) purveyor (C) flamboyant (F) congenial ( I ) solicitor

Reading Comprehension Read the following passage. Then answer the questions: Sometimes the meaning of glowing water is ominous. Off the Pacific coast of North America, it may mean that the sea is filled with a minute plant that contains a poison of strange and terrible virulence. About four days after this 5 minute plant comes to alter the coastal plankton, some of the fishes and shellfish in the vicinity become toxic. This is because in their normal feeding, they have strained the poisonous plankton out of the water. 1

5. Fish and shellfish become toxic when they (A) swim in poisonous water (B) feed on poisonous plants or animals (C) change their feeding habits (D) give off a strange glow (E) take strychnine into their systems 6. In the context of the passage, the word virulence in line 4 means (A) strangeness (B) color (C) calamity (D) potency (E) powerful odor

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42 Easy-to-Learn Strategies

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25 Math Strategies 1 17 Verbal (Critical Reading) Strategies Critical thinking is the ability to think clearly in order to solve problems and answer questions of all types—GRE questions, for example, both math and verbal! Educators who are deeply involved in research on critical thinking skills tell us that such skills are straightforward, practical, teachable, and learnable. The 25 Math Strategies and 17 Verbal Strategies in this section are critical thinking skills. These strategies have the potential to raise your GRE scores dramatically from approximately 50 points to 300 points (5 to 30 points on the new GRE scale) in verbal and quantitative reasoning. Since each correct GRE question gives you an additional 10 points or an additional 1 point on the new GRE scale, it is reasonable to assume that if you can learn and then use these valuable GRE strategies, you can boost your GRE scores phenomenally! BE SURE TO LEARN AND USE THE STRATEGIES THAT FOLLOW!

How to Learn the Strategies 1. For each strategy, look at the heading describing the strategy.

tedious, when in fact you can use another problemsolving method or shortcut. So you must be selective on when and when not to use a calculator on the test. Here’s an example of when a calculator should not be used: 2 # 5 # 6 # 7 # 8 # 9 # 10 = 5 6 7 8 9 10 11

2. Try to answer the first example without looking at the EXPLANATORY ANSWER. 3. Then look at the EXPLANATORY ANSWER, and if you got the right answer, see if the method described will enable you to solve the question in a better way with a faster approach. 4. Then try each of the next EXAMPLES without looking at the EXPLANATORY ANSWERS. 5. Use the same procedure as in (3) for each of the EXAMPLES. The MATH STRATEGIES start on page 72, and the VERBAL STRATEGIES start on page 138. However, before you start the Math Strategies, it would be wise for you to look at the Important Note on the Allowed Use of Calculators on the GRE; the Important Note on Math Questions on the GRE, page 70; and The Grid-Type Math Question, page 70.

Important Note on the Allowed Use of Calculators on the GRE

(A) 9 11 (B) 2 11 (C) 11 36 (D) 10 21 (E) 244 360 Here the use of a calculator may take some time. However, if you use the strategy of canceling numerators and denominators (Math Strategy 1, Example 3 on page 73) as shown, Cancel numerators/denominators: 2 5 6 7 8 9 10 2 # # # # # # = 5 6 7 8 9 10 11 11 you can see that the answer comes easily as 2 . 11

Although the use of calculators on the GRE will be allowed, using a calculator may be sometimes more

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80 • GRUBER’S COMPLETE GRE GUIDE 2014

Math gy strate

Know How to Find Unknown Quantities (Areas, Lengths, Arc and Angle Measurements) from Known Quantities (the Whole Equals the Sum of Its Parts)

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When asked to find a particular area or length, instead of trying to calculate it directly, find it by subtracting two other areas or lengths—a method based on the fact that the whole minus a part equals the remaining part.

example ——

In the diagram below, AE is a straight line, and F is a —— point on AE. Find an expression for m+DFE.

This strategy is very helpful in many types of geometry problems. A very important equation to remember is

The whole 5 the sum of its parts

example

X Z Y

In the diagram above, ΔXYZ has been inscribed in a circle. If the circle encloses an area of 64, and the area of ΔXYZ is 15, then what is the area of the shaded region? (A) 25 (B) 36 (C) 49 (D) 79 (E) It cannot be determined from the information given. Choice C is correct. Use equation 1 . Here, the whole refers to the area within the circle, and the parts refer to the areas of the shaded region and the triangle. Thus, Area within circle 5 Area of shaded region 1 Area of ΔXYZ 64 5 Area of shaded region 1 15 or Area of shaded region 5 64 2 15 5 49 (Answer)

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60° y°

x°

Equation 1 is often disguised in many forms, as seen in the following examples:

(A) x 1 y 2 60 (B) x 1 y 1 60 (C) 90 2 x 2 y (D) 120 2 x 2 y (E) 180 2 x 2 y Choice D is correct. Use equation 1 . Here, the whole refers to the straight angle, +AFE, and its parts refer to +AFB, +BFC, +CFD, and +DFE. Thus, m+AFE 5 m +AFB 1 m+BFC 1 m+CFD 1 m+DFE 180 5 x 1 60 1 y 1 m+DFE or m+DFE 5 180 2 x 2 60 2 y m+DFE 5 120 2 x 2 y (Answer) example

In the diagram below, AB 5 m, BC 5 n, and AD 5 10. Find an expression for CD. (Note: Diagram represents a straight line.)

(A) 10 2 mn (B) 10 2 m 2 n (C) m 2 n 1 10 (D) m 1 n 2 10 (E) m 1 n 1 10

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216 • GRUBER’S COMPLETE GRE GUIDE 2014

Mixture 204. In mixture problems you are given a percent or a fractional composition of a substance, and you are asked questions about the weights and compositions of the substance. The basic relationship here is that the percentage of a certain substance in a mixture 3 the amount of the mixture 5 the amount of substance. Note that it is often better to change percents to decimals because it makes it easier to avoid errors. Example: A chemist has two quarts of 25% acid solution and one quart of 40% acid solution. If he mixes these, what will be the concentration of the mixture?

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Solution: Let x 5 concentration of the mixture. At the end of Step 6, our table will look like this: concentration 3 amount of sol 5 amount of acid qt (acid) qt (sol)

qts (sol)

qts (acid)

25% solution

0.25

0.50

40% solution

0.40

mixture

We now have one additional bit of information: The amount of acid in the mixture must be equal to the total amount of acid in each of the two parts, so 3x 5 0.50 1 0.40. Therefore x is equal to 0.30, which is the same as a 30% concentration of the acid in the mixture.

Cost 205. In cost problems the rate is the price per item, the input is the number of items, and the output is the value of the items considered. When you are dealing with dollars and cents, you must be very careful to use the decimal point correctly. Example: Jim has $3.00 in nickels and dimes in his pocket. If he has twice as many nickels as he has dimes, how many coins does he have altogether? Solution: After Step 6, our chart should look like this (where c is the number of dimes Jim has): rate 3 number 5 value cents/coin

coins

cents

nickels

10c

dimes

10c

Now we recall the additional bit of information that the total value of the nickels and dimes is $3.00, or 300 cents. Thus, 5(2c) 1 10c 5 300; 20c 5 300; so c 5 15, the number of dimes. Jim has twice as many nickels, so 2c 5 30. The total number of coins is c 1 2c 5 3c 5 45.

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Bar Graphs 704. The bar graph shows how information is compared by using broad lines, called bars, of varying lengths. Sometimes single lines are used as well. Bar graphs are good for showing a quick comparison of the information involved; however, the bars are difficult to read accurately unless the end of the bar falls exactly on one of the divisions of the scale. If the end of the bar falls between divisions of the scale, it is not easy to arrive at the precise figure represented by the bar. In bar graphs, the bars can run either vertically or horizontally. The sample bar graph following is a horizontal graph.

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EXPENDITURES PER PUPIL—1990

New England

Great Lakes

Great Plains

Rocky Mountains

$430

$440

$450

$460

$470

$480

The individual bars in this kind of graph may carry a label within the bar, as in this example. The label may also appear alongside each bar. The scale used on the bars may appear along one axis, as in the example, or it may be noted somewhere on the face of the graph. Each numbered space on the x-axis (or horizontal axis) represents an expenditure of $10 per pupil. A wide variety of questions may be answered by a bar graph, such as: (1) Which area of the country spends least per pupil? Rocky Mountains. (2) How much does the New England area spend per pupil? $480. (3) How much less does the Great Plains spend per pupil than the Great Lakes? $464 2 447 5 $17/pupil. (4) How much more does New England spend on a pupil than the Rocky Mountain area? $480 2 433 5 $47/pupil.

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COMPLETE GRE MATH REFRESHER – Session 7 • 343

Circle Graphs 705. A circle graph (or pie chart) shows how an entire quantity has been divided or apportioned. The circle represents 100 percent of the quantity; the different parts into which the whole has been divided are shown by sections, or wedges, of the circle. Circle graphs are good for showing how money is distributed or collected, and for this reason they are widely used in financial graphing. The information is usually presented on the face of each section, telling you exactly what the section stands for and the value of that section in comparison to the other parts of the graph.

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SOURCES OF INCOME—PUBLIC COLLEGES OF THE U.S.

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Government* 62¢ Other 8¢ Tuition Dormitory 3¢ Endowment Fees 10¢ 17¢ *Government refers to all levels of government—not exclusively the federal government.

The circle graph above indicates where the money originates that is used to maintain public colleges in the United States. The size of the sections tells you at a glance which source is most important (government) and which is least important (endowments). The sections total 100¢, or $1.00. This graph may be used to answer the following questions: (1) What is the most important source of income to the public colleges? Government. (2) What part of the revenue dollar comes from tuition? 10¢.

(3) Dormitory fees bring in how many times the money that endowments bring in? 5 2 times 3 17 2 = 5 m. c 3 3

(4) What is the least important source of revenue to public colleges? Endowments.

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487

Here are directions for the Analyze an Argument part with an example.

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Analytical Writing 2 Test— Analyze an Argument

ANALYZE AN ARGUMENT Time—30 minutes You have 30 minutes to plan and compose a response in which you evaluate the argument passage that appears below. A response to any other argument will receive a score of zero. Make sure that you respond according to the specific instructions and support your evaluation with relevant reasons and/or examples. Note that you are NOT being asked to present your own views on the subject.

The following appeared in an article in the Grandview Beacon. “For many years the city of Grandview has provided annual funding for the Grandview Symphony. Last year, however, private contributions to the symphony increased by 200 percent and attendance at the symphony’s concerts-in-the-park series doubled. The symphony has announced an increase in ticket prices for next year. Given such developments, some city commissioners argue that the symphony can now be fully self-supporting, and they recommend that funding for the symphony be eliminated from next year’s budget.” Write a response in which you discuss what questions would need to be answered in order to decide whether the recommendation and the argument on which it is based are reasonable. Be sure to explain how the answers to these questions would help to evaluate the recommendation. Trained GRE readers will evaluate your response for its overall quality based on how well you: • • • • •

Respond to the specific task instructions Consider the complexities of the issue Organize, develop, and express your ideas Support your ideas with relevant reasons and/or examples Control the elements of standard written English

Before you begin writing, you may want to think for a few minutes about the issue and the specific task instructions and then plan your response. Use the next page to plan your response, then write your response starting on the first lined page that follows. A total of four lined pages are provided for your response. Be sure to develop your position fully and organize it coherently, but leave time to reread what you have written and make any revisions you think are necessary. Write your response within the boxed area on the pages provided. Any text outside the boxed area will not be scored.

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Here are three more examples:

The following appeared in a health magazine published in Corpora.

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“Medical experts say that only one-quarter of Corpora’s citizens meet the current standards for adequate physical fitness, even though twenty years ago, one-half of all of Corpora’s citizens met the standards as then defined. But these experts are mistaken when they suggest that spending too much time using computers has caused a decline in fitness. Since overall fitness levels are highest in the regions of Corpora where levels of computer ownership are also highest, it is clear that using computers has not made citizens less physically fit. Instead, as shown by this year’s unusually low expenditures on fitness-related products and services, the recent decline in the economy is most likely the cause, and fitness levels will improve when the economy does.”

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Write a response in which you examine the stated and/or unstated assumptions of the argument. Be sure to explain how the argument depends on these assumptions and what the implications are for the argument if the assumptions prove unwarranted.

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Questions 10–25 have several different formats. Unless otherwise directed, select a single answer choice. For Numeric Entr y questions, follow the instructions below.

Numeric Entry Questions To answer these questions, enter a number by filling in circles in a grid. • Your answer may be an integer, a decimal, or a fraction, and it may be negative. • Equivalent forms of the correct answer, such as 2.5 and 2.50, are all correct. Although fractions do not need to be reduced to lowest terms, they may need to be reduced to fit in the grid.

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• Enter the exact answer unless the question asks you to round your answer. • If a question asks for a fraction, the grid will have a built-in division slash (/). Otherwise, the grid will have a decimal point. • Start your answer in any column, space permitting. Fill in no more than one circle in any column of the grid. Columns not needed should be left blank. • Write your answer in the boxes at the top of the grid and fill in the corresponding circles. You will receive credit only if the circles are filled in correctly, regardless of the number written in the boxes at the top. Examples of acceptable ways to use the grid:

Integer answer: 502 (either position is correct) 5 0 2

–.

–

Fraction answer: 2 2 10

Decimal answer: 24.13

5 0 2 .

– –

4 .

– –

2 ⁄

1 1 1 1 1 1 1

1 1 1

2 2 2 2 2 2 2

2 2 2

1 1 1 2 2 2

3 3 3 3 3 3 3

3 3 3

4 4 4 4 4 4 4

4 4 4

5 5 5 5 5 5 5

5 5 5

6 6 6 6 6 6 6

6 6 6

7 7 7 7 7 7 7

7 7 7

8 8 8 8 8 8 8

8 8 8

9 9 9 9 9 9 9

9 9 9

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GRE PRACTICE TEST 2 – Section 4: Quantitative Reasoning • 621 10. If 9 and 12 each divide Q without remainder, which

of the following must Q divide without remainder? (A) 1 (B) 3 (C) 36 (D) 72 (E) The answer cannot be determined from the given information. A

P (1,2) A (0,0)

6 4

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(x, y)

7 5

13. If points (1, 2) and (x, y) are on the line represented

11. Box A contains 3 cards, numbered 3, 4, and 5.

Box B contains 3 cards, numbered 6, 7, and 8. If one card is drawn from each box and their sum is calculated, how many different numerical results are possible? (A) eight (B) seven (C) six (D) five (E) four

in the above diagram, which of the following could represent the value of x and y? (A) (B) (C) (D) (E)

x 5 3, y 5 5 x 5 4, y 5 8 x 5 5, y 5 11 x 5 6, y 5 15 x 5 7, y 5 17

14. Over the first few weeks of the baseball season, the league’s five leading pitchers had the following won–lost records. (All games ended in a win or loss for that pitcher.)

For the following question, use the grid to enter your answer. 12. During a party attended by 3 females and 3 males,

3 people at random enter a previously empty room. What is the probability for any different combination that there are now exactly 2 males and 1 female in the room?

–

⁄ .

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

Won

Lost

Pitcher A Pitcher B Pitcher C Pitcher D Pitcher E

4 3 4 2 3

2 2 1 2 1

At the time these statistics were compiled, which pitcher was leading the league in winning percentage? (That is, which pitcher had won the greatest percentage of his games?) (A) Pitcher A (B) Pitcher B (C) Pitcher C (D) Pitcher D (E) Pitcher E

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What You Must Do Now to Raise Your GRE Score 1. Follow the directions on page 695 to determine your scaled score for the GRE Test you’ve just taken. These results will give you a good idea about how hard you’ll need to study in order to achieve a certain score on the actual GRE. 2. Eliminate your weaknesses in each of the GRE

test areas by taking the following Giant Steps toward GRE success:

Sentence Completion and Reading Part Giant Step 1 Take advantage of the Sentence Completion and Reading Strategies that begin on page 138. Read again the Explanatory Answer for each of the Sentence Completion and Reading questions that you got wrong. Refer to the Reading Strategy that applies to each of your incorrect answers. Learn each of these strategies thoroughly. These strategies are crucial if you want to raise your GRE Verbal score substantially.

Giant Step 2 You can improve your vocabulary by doing the following: 1) Study the GRE 3,400-Word List beginning on page 379. 2) Take the 100 Tests to Strengthen Your Vocabulary beginning on page 428. 3) Study the Gruber Prefix-Root-Suffix List beginning on page 368. 4) Learn the Hot Prefixes and Roots beginning on page 719. 5) Read through the List of Standardized Test Words Appearing More Than Once beginning on page 373.

7) Learn the 3 Vocabulary Strategies beginning on page 170. 8) Read as widely as possible—not only novels. Nonfiction is important too…and don’t forget to read newspapers and magazines. 9) Listen to people who speak well. Tune in to worthwhile TV programs. 10) Use the dictionary frequently and extensively—at home, on the bus, at work, etc. 11) Play word games—for example, crossword puzzles, anagrams, and Scrabble. Another game is to compose your own Sentence Completion questions. Try them on your friends.

Math Part Giant Step 3 Make good use of the 25 Math Strategies that begin on page 72. Read again the solutions for each Math question that you answered incorrectly. Refer to the Math Strategy that applies to each of your incorrect answers. Learn each of these Math Strategies thoroughly. We repeat that these strategies are crucial if you want to raise your GRE Math score substantially.

Giant Step 4 You may want to take the 101 Most Important Math Questions You Need to Know How to Solve test beginning on page 40 and follow the directions after the test for a basic math skills diagnosis. For each Math question that you got wrong in the test, note the reference to the Math Refresher section beginning on page 187. This reference will explain clearly the mathematical principle involved in the solution of the question you answered incorrectly. Learn that particular mathematical principle thoroughly.

6) Look through the Most Important/Frequently Used GRE Words and Their Opposites beginning on page 375.

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mis wrong, badly

mistreat—to treat badly mistake—to get wrong

PREFIXES THAT MEAN “AWAY FROM,” “NOT,” OR “AGAINST” PREFIX

MEANING EXAMPLES

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ab away from

absent—not present, away abscond—to run away

anti against antifreeze—a substance used to prevent freezing antisocial—someone who is not social

away from, down, depart—to go away from de, dis the opposite of, apart, not decline—to turn down dislike—not to like dishonest—not honest distant—apart ex, e, ef out, from

exit—to go out eject—to throw out efface—to rub out, erase

in, il, ir, im not

inactive—not active impossible—not possible illiterate—not literate irreversible—not reversible

not non

nonsense—no sense nonstop—having no stops

ob against, in front of obstacle—something that stands in the way of obstinate—inflexible un not

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unhelpful—not helpful uninterested—not interested

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