07-0146 in Class Manual GMAT V9.1 [PDF]

Zitiervorschau

In Class Manual for the GMAT

®

Version 9.1 GMAT is a registered trademark of the Graduate Management Admission Council.

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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 photocopying, recording, or any information retrieval system, without the prior consent of the publisher, The Princeton Review. This Manual is for the exclusive use of Princeton Review course students and is not legal for resale. GMAT is a registered trademark of the Graduate Management Admission Council. The Princeton Review is not affiliated with Princeton University or the Graduate Management Admission Council. Permission to reprint this material does not constitute review or endorsement by ACT or the Graduate Management Admission Council of this publication as a whole or of any other sample questions or testing information it may contain. Copyright © 2012 by The Princeton Review, Inc. All Rights Reserved. 866.TPR.PREP / www.PrincetonReview.com

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Acknowledgments Special thanks to John Fulmer, Oliver Pope, and Curtis Retherford. Thanks to the following for their many contributions to this manual: Shruti Ananthpadmanabha, Monisha Banerjee, Andrew Brody, Tim Christy, Marty Cinke, Becky Robinson, Morrison Giffen, Peter Hanink, Cheryl Kreisher, Mike Matera, Nicole Pirnie, Mindy Myers, Becky Robinson, Liz Rutzel, Jake Schiff, Rebecca Scott, Allison Scovone, Ruchi Tomar, Vikram Vishwanath, Dominique Walsh, Shadna Wise, Elia Zashin, and the staff and students of The Princeton Review.

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Table of Contents Lesson 1





Verbal Introduction 1 Sentence Correction 1 2 The Two Keys to Sentence Correction Success............................ 2 The Format........................................................................................ 3 Basic Approach................................................................................. 3 Subject-Verb Agreement.................................................................. 4 Verb Tense.......................................................................................... 6 Pronouns............................................................................................ 8 Back Up Plans................................................................................. 10 Red Pencil Fever............................................................................. 11 Math 1

12 Math Introduction.......................................................................... 12 Data Sufficiency.............................................................................. 15 Algebra vs. Arithmetic................................................................... 18 Plugging In...................................................................................... 19 Hidden Plug Ins............................................................................. 22 Plugging In The Answers (PITA)................................................. 23 Math Practice 27 Math Practice Answers and Explanations 31

Lesson 2





1

33

Sentence Correction 2 33 Misplaced Modifiers...................................................................... 34 Parallel Construction..................................................................... 37 Comparisons................................................................................... 40 Idioms.............................................................................................. 42 Math 2 44 Pieces of the Puzzle........................................................................ 44 Yes-No Data Sufficiency................................................................ 46 Keep Plugging Away..................................................................... 49 Math Practice 52 Math Practice Answers and Explanations 54

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Lesson 3





57 Inequalities and Absolute Values................................................. 57 Roots and Exponents..................................................................... 58 Quadratics....................................................................................... 61 Functions and Sequences.............................................................. 62 Harder Manipulations................................................................... 65 Algebra and Data Sufficiency....................................................... 66 Integrated Reasoning 1 68 Table Analysis................................................................................. 68 Graphics Interpretation................................................................. 71 Multi-Source Reasoning................................................................ 72 Two-Part Analysis.......................................................................... 75 Math Practice 79 Math Practice Answers and Explanations 81

Lesson 4









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85

Critical Reasoning 1 85 Basic Approach............................................................................... 85 Assumption Questions.................................................................. 86 The Negation Test........................................................................... 89 Weaken Questions.......................................................................... 90 Strengthen Questions..................................................................... 92 Math 4 94 Ratios................................................................................................ 94 Averages.......................................................................................... 96 Rates................................................................................................. 98 Percent Change............................................................................. 100 Probability..................................................................................... 101 Math Practice 106 Math Practice Answers and Explanations 110

Lesson 5

57

Math 3

113

Reading Comprehension 1 113 The Basic Approach..................................................................... 113 Finding the Main Idea: Key Sentences...................................... 114 Finding the Main Idea: Follow the Author............................... 116 Finding the Main Idea: Change or Problem............................. 118 General Questions........................................................................ 119 Math 5 121 Geometry: The Basic Approach.................................................. 121 Data Sufficiency Figures.............................................................. 123 The Basic Approach and Geometry Data Sufficiency............. 124 Plugging In for Geometry........................................................... 125 Combining Concepts................................................................... 127 Shaded Regions............................................................................ 129 Coordinate Geometry.................................................................. 132 Math Practice 137 Math Practice Answers and Explanations 141

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Lesson 6



Reading Comprehension 2 145 The Basic Approach..................................................................... 145 Specific Questions and POE........................................................ 147 Critical Reasoning 2 152 Inference Questions..................................................................... 152 Integrated Reasoning 2 157 Integrated Reasoning and Inferences........................................ 157 Integrated Reasoning and Arguments...................................... 159 Plugging In for Two-Part Analysis............................................ 162 Plugging In The Answers for Two Part Analysis.................... 164

Lesson 7











183

Critical Reasoning 4 183 Identify the Reasoning Questions.............................................. 183 Resolve/Explain Questions........................................................ 186 Minor Question Types................................................................. 188 Sentence Correction 3 191 Redundancy.................................................................................. 191 Clauses and Connectors.............................................................. 192 Grammar and Meaning............................................................... 192 Math 7 196 Simultaneous Equations.............................................................. 196 Simultaneous Equations Nuances............................................. 197 Sets.................................................................................................. 199 Groups........................................................................................... 199 Venn Diagrams............................................................................. 200 Permutations and Combinations............................................... 201 Math Practice 205 Math Practice Answers and Explanations 209

Lesson 9

167

Critical Reasoning 3 167 Common Argument Patterns..................................................... 167 Math 6 172 More Problem Solving Plugging In........................................... 172 More Data Sufficiency Plugging In............................................ 174 Number Theory Topics................................................................ 175 Math Practice 179 Math Practice Answers and Explanations 180

Lesson 8

145

213

Verbal Review 213 Sentence Correction..................................................................... 213 Critical Reasoning........................................................................ 217 Reading Comprehension............................................................. 220 Math 8 223 POE Review.................................................................................. 223 Data Sufficiency Review.............................................................. 226

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Lesson 1 11

Lesson 1

Verbal Introduction Here are the basic facts for the verbal section: • 36 questions in 65 minutes • Approximately 13 Sentence Correction, 10 Critical Reasoning, and 13 Reading Comprehension questions. • Verbal scores range from roughly 6 to 51 (0–60 scale). • The verbal score is a factor in the 200 to 800 overall scale. • The verbal section is computer adaptive.

A Systematic Approach The credited responses to verbal questions may often seem subjective and arbitrary. Fortunately, that’s not the real story. Verbal questions follow definite rules. Learn the rules and you’ll be able to pick the credited response.

The Importance of POE The phrasing of the credited response is GMAC’s job. Your job is to find good reasons to eliminate bad answers. The multiple-choice format of the Verbal section actually works to your benefit because you can use Process of Elimination (POE).

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GMAT IN CLASS MANUAL

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Sentence Correction 1 While it may seem that GMAT Sentence Correction questions test hundreds of different grammatical rules, there really are only a handful of errors that get tested consistently.

The Two Keys to Sentence Correction Success There are two keys to doing well on sentence correction. Know the Commonly Tested Errors Look for these same errors as reasons to eliminate incorrect answer choices.

Here are the most commonly tested grammatical errors. We’ll show you how to spot and correct these errors. The Big Six

The most common types of errors are:



• Verb Tense





• Pronouns





• Idioms





• Misplaced Modifiers





• Parallel Construction





• Subject-Verb Agreement

Know the Characteristics of a Good Answer Good answers have four characteristics. Eliminate answer choices that lack one of these properties. Characteristics of a Good Answer

2

|





• Fixes the error





• Makes no new errors





• Doesn’t change the meaning





• Is concise versus other answers

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Lesson 1

11

The Format Each sentence correction question presents a sentence with some or all of the sentence underlined. 1. The Texas longhorn, a breed of cattle descended from herds brought by the Spanish conquistadors, are symbols of the Wild West era of American history.



Answer (A) always repeats the underlined portion of the sentence.

are symbols of the Wild West era are symbols of the Wild West are symbolizing the Wild West era is symbolic in the Wild West is a symbol of the Wild West era

Basic Approach Spotting grammatical errors is important. But, once you spot an error, you need a systematic approach to get to the credited response. Can you ID one of the common errors in the underlined portion? Yes Eliminate Choice (A)

Eliminate any answers that obviously repeat the error.

POE with the remaining answer choices. • New errors. • Changes to the meaning of the sentence.

No Can you ID an error from the answer choices? • 2/3 split • Differences in answers Yes No

See how 2 answers start with is and 3 answers start with are in the question above? That’s called a 2/3 split.

Starting at (B), use POE. • New errors. • Changes to the meaning of the sentence.

Two left? Choose the more concise answer.

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GMAT IN CLASS MANUAL

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Subject-Verb Agreement While the rule for subject-verb agreement is simple, spotting errors is not always so easy. The Rule: A singular subject requires a singular verb. Plural subjects require plural verbs.

Let’s try a few questions. Verb:________________________________

Isolate the verb and its subject and check for agreement.

Subject: ________________________________ Singular/Plural 1. Edward Abbey’s books, especially Desert Solitaire, in which Abbey recounts his adventures in the Utah desert, employs wit to convey its author’s love of the American West.

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Singular/Plural

employs wit to convey its author’s love of the American West employs wit conveying their author’s love for the American West employs wit to convey the love of the American West by the author employ wit to convey their author’s love of the American West employ wit to convey its author’s love of the American West

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Lesson 1

11 Verb:________________________________

Singular/Plural

Subject:_____________________________

Singular/Plural

2. Federally imposed restrictions on the amounts that savings banks can pay small savers has created difficulties for them as they are competing with institutions offering unregulated investment vehicles such as money market certificates.

has created difficulties for them as they are competing with has created a difficult circumstance for savings banks competing against have created a difficult circumstance when they compete against have created difficulties for savings banks competing with have created difficulties for them to compete against

To spot subject-verb agreement errors, look for:

To fix subject-verb agreement errors:

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GMAT IN CLASS MANUAL

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Verb Tense Verb tense errors are usually easy to correct once you decide which tense to use.

The Rule: Choose the correct tense to match the clues in the sentence.

Verbs:______________________________________________ Which action happens first?___________________________ 1. Until Jackie Robinson made his debut in a Brooklyn Dodgers uniform in 1947, African Americans were prohibited to play for any Major League baseball team.

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were prohibited to play have been prohibited from playing have been prohibited to play had been prohibited to play had been prohibited from playing

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Lesson 1

11 Verb:______________________________________________ Time Clue:_________________________________________ 2. So far this year, twenty elected legislators had opted not to run for reelection in the aftermath of the Bathwater scandal.



had opted not to run for reelection had opted to not run for reelection have opted for not running for reelection have opted not to run for reelection have opted for not another run at reelection

To spot verb tense errors, look for:

To fix verb tense errors:

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GMAT IN CLASS MANUAL

11

Pronouns Because pronouns are small words, you must read carefully to spot pronoun errors. The Rules: Singular pronouns replace singular nouns, and plural pronouns replace plural nouns. Also, a pronoun must unambiguously refer to one noun.

Isolate the pronouns and the nouns to which they refer.

Pronoun:______________________________ Singular/Plural Refers to:_____________________________ Singular/Plural 1. Each of the dogs now in the animal shelter had been neglected by their former owner before they were abandoned.

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had been neglected by their former owner before they were abandoned was neglected by its former owner before it was abandoned was neglected by their former owner before they were abandoned had been neglected by its former owner before it was abandoned was abandoned, but before that they had been neglected by their former owner

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Lesson 1

11 Pronoun:______________________________ Refers to:_____________________________ 2. Although aspirin irritates the stomach, it can be avoided if the aspirin tablet is given a coating that will not dissolve until the tablet reaches the intestine.

Although aspirin irritates the stomach, it



The irritation of the stomach caused by aspirin



The fact that aspirin causes irritation of the stomach



Aspirin causes stomach irritation, although it



Aspirin irritates the stomach, which

To spot pronoun errors, look for:

To fix pronoun errors:

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GMAT IN CLASS MANUAL

11

Back Up Plans If you can’t identify an error in the underlined portion, try using the answer choices. Can you ID one of the common errors in the underlined portion? Yes Eliminate Choice (A)

Eliminate any answers that obviously repeat the error.

POE with the remaining answer choices. • New errors. • Changes to the meaning of the sentence.

No Can you ID an error from the answer choices? • 2/3 split • Differences in answers Yes No

Starting at (B), use POE. • New errors. • Changes to the meaning of the sentence.

Two left? Choose the more concise answer.

How do the differences in the answer choices help you to find the error?

1. Attempts to maintain the current level of funding for museums, though impressive, has not resulted in the continuation of financial backing for the coming year.

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Attempts to maintain the current level of funding for museums, though impressive, The attempt to maintain the current level of funding for museums, though impressive, Maintaining the current level of funding, though an impressive attempt, The impressive attempts to maintain the current level of museum funding Attempts to maintain the level of funding for museums currently, though impressive,

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Lesson 1

11 2. Approximately seventy-five percent of the global freshwater supply is stored in glaciers, which cover roughly ten percent of land area.

is stored in glaciers, which cover roughly ten percent of land area is stored in glaciers, which covers roughly ten percent of land area is stored in glaciers, that covers roughly ten percent of land area are stored in glaciers, which cover roughly ten percent of land area are stored in glaciers, which covers roughly ten percent of land area

Even when you don’t find an error by checking a rule, you may be able to eliminate some answer choices.

Red Pencil Fever Don’t eliminate something just because you don’t like the way it sounds. Often, the correct answer won’t sound very good, and you don’t want to eliminate it hastily. 1. Depending on which scholar you consult, either Daniel Defoe’s Robinson Crusoe, Henry Fielding’s Joseph Andrews, or Samuel Richardson’s Pamela is believed to have been the first English novel ever written.

is believed to have been the first English novel ever written



is believed as being the first English novel ever written



are the English novels believed to be the first written



are the English novels which were believed as the first written



are the first English novels ever believed to be written

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GMAT IN CLASS MANUAL 1

MATH 1 Here are the basic facts for the math section:

• 31 questions in 62 minutes

• Approximately 16 Problem Solving and 15 Data Sufficiency • Math scores range from roughly 6 to 51 (0–60 scale). • The math score is a factor in the 200 to 800 overall scale. • The math section is computer adaptive.

Math Introduction Smart strategies can help you guess wisely on difficult questions or when time is short.

Trap Answers Determine the trap answers for these questions: 1. The original price of an article was reduced by 25 percent. During a special sale the new price was decreased by 10 percent. By approximately what percent would the price now have to be increased in order to restore the price of the article to its original amount?

32.5%



35%



48%



65%



67.5%

2. A rectangular wooden crate has inside dimensions 3 meters by 4 meters by 12 meters. What is the length, in meters, of the longest, straight, inflexible rod of negligible diameter that can be placed completely within the crate?

12

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12



12.6



13



19



24

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GMAT InClass Manual Lesson 1.indd 12

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Lesson 1

11 3. The average (arithmetic mean) of x, y, and z is 50. What is the sum of (4x + y), (3y + z), and (3z) ?

150



200



600



800



It cannot be determined from the information given.

Common Trap Answers Include



• Too Obvious





• Numbers in the Problem





• Simple Manipulations





• Partial Answers

Number Savvy Number Savvy is your ability to do calculations in smart, time efficient ways.

( −2.8 )(1.8 ) − (1.4 )( 2.4 ) 4.

105



−0.008



−0.08



−0.8



0.8



8.0

Practice looking for savvy ways to do calculations as you do problems.

=

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GMAT IN CLASS MANUAL

11 Ballparking Ballparking means knowing the approximate size of the answer.

Use Ballparking to Eliminate Answers When





• You are stuck





• Running out of time



5. Paul drives from his apartment to his parents’ house and back along the same route. On the trip to his parents’ house, he travels at an average speed of 60 miles per hour. On the return trip, Paul drives at an average speed of 80 miles per hour. Which of the following is the closest approximation of Paul’s average speed, in miles per hour, for the round trip?

60.0



68.6



70.0



71.4



80.0

X

Y

O

W

Z

6. In the diagram above, the circle with center O is inscribed within square WXYZ. If the square has area 400, what is the area of the circle?

20π



50π



75π



100π



400π



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Lesson 1

11

Data Sufficiency

Many test takers feel that data sufficiency questions are much harder than problem solving questions. Once you are familiar with the format, however, data sufficiency questions won’t seem so bad.

What the Answer Choices Mean The first step is to understand the answer choices. Answer A 1. What is the value of x ? (1) x + 7 = 12 (2) x is an integer

(A)

1

2

(B)

1

2

(C)

1

2

(D)

1

2

(E)

1

2

Answer B 2. What is the value of x ? (1) x is an integer (2) x + 7 = 12

Answer C 3. What is the value of x ? (1) x2 = 25 (2) x ≥ 0

Answer D 4. What is the value of x ? (1) x + 7 = 12 (2) x = 25

Answer E 5. What is the value of x ? (1) x ≥ 0 (2) x is an integer

Basic Approach—AD/BCE 6. What is the value of x ? (1) x + 7 = 12 (2)

A B C D E

Based on statement (1), which answers are possible?

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GMAT IN CLASS MANUAL

11 AD/BCE in Action 1. What is the value of x ? (1) If x is subtracted from 60, the result is 20. (2) If x is divided by z, the result is 20.

2. If x + y + z = 180, what is the value of x ? (1) y = 75

(A)

1

2

(B)

1

2

(C)

1

2

(D)

1

2

(E)

1

2

(2) y + z = 141

3. If x and y are positive integers and (1) 1< y < 5

x y

=2, what is the value of x ?

(2) y is odd.

4. If

3x 2y

= z, what is the value of x ?

(1) yz = 30 (2) y =10 and z = 3

5. What is the value of x ? (1) x + y = 20 (2) z – 3x = 45

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Lesson 1

1

sufficient

sufficient

insufficient

insufficient

sufficient

insufficient

sufficient

insufficient

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GMAT IN CLASS MANUAL

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Algebra vs. Arithmetic Which of the following questions would you rather answer? 1. Max has a 10 dollar bill. He goes into a candy store and buys 3 pieces of candy that cost 50 cents each. How much change, in dollars, does Max receive?

$9.50



$8.50



$7.00



$1.50



$0.50



2. Max has x dollars. He goes into a candy store and buys y pieces of candy that cost z cents each. How much change, in dollars, does Max receive?

x – yz



yz – x



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x − yz 100 100x – yz x−

yz 100

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Lesson 1

11

Plugging In There is a way to turn algebra problems into arithmetic problems. It’s called Plugging In. Just follow these steps:

Step 1: Assign a number to each variable in the problem. Step 2: Work the problem step-by-step using the numbers you chose. You should end up with a numerical answer (with no variables left over) that answers the question in the problem. Circle the answer. This is your target. Step 3: Plug the number(s) you assigned to the variable(s) into the answer choices. Choose the answer choice that matches your target. Be sure to check all five answer choices.

3. Steven is three times as old as Jean, and Jean is two years older than Ken. If Ken is k years old, then how old is Steven?

3k + 2



3k + 6



3k – 3



3k – 6 k −2



3

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GMAT IN CLASS MANUAL

11 Choose Good Numbers Make your life easier by choosing good numbers that make the calculations easier.

What’s a good way to choose a number for c?

4. The Amazing soft drink company interviewed c consumers for 2 of consumers a market-research study. The study found that 5 preferred Zing cola to Diet Zing cola. Of those who preferred Diet 1 Zing, preferred Caffeine Free Diet Zing. How many consumers, 6 in terms of c, did not prefer Caffeine Free Diet Zing?







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c 11 c 10 7c 15 9c 10 10c 11

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Lesson 1

11 5. A machine working at maximum capacity can produce x radial tires in an hour. How many tires can the machine produce if it works continuously at maximum capacity for y minutes?











x 60 y xy 60 60 x y 60 xy 60xy

Avoid numbers that can make several answer choices match your target. • Do not use 0 or 1. • Do not use numbers that appear in the question or in the answer choices. • Do not use the same number for more than one variable. Choose numbers to make the calculations easy: • If there are fractions in the question, choose a number that’s a common multiple of the denominators. (Multiplying the denominators together is an easy way to find a good number.) • If a question involves different units, use a multiple or factor of the conversion number. • If a question involves percents, use 100 or a multiple of 100.

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GMAT IN CLASS MANUAL

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Hidden Plug Ins In some Plugging In problems, the variable is hidden. Once you find the variable, you can plug into it. 1. Maggie pays



1 8

1 8

of her monthly income for food,

for student loans, and

4 5

of each month Maggie puts

1 8

for utilities,

of the remainder for rent. If at the end 1 2

of her remaining income into a CD

account, what portion of Maggie’s monthly income does she put Most hidden plug-ins involve fractions, percents, or ratios.

into the account?

1 8 1 10 7 80 1 16 1 20

2. If 20 percent of the trees in a certain park are evergreens, and 40 percent of the non-evergreens are maple trees, and there are 75 percent as many oak trees as maple trees in the park, what percent of the trees in the park are not maples, oaks, or evergreens?

22

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10%



12%



20%



24%



25%

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Lesson 1

11

Plugging In The Answers (PITA) Sometimes GMAC expects you to write and solve an equation. These problems can also be solved by plugging in the answers. 1. Rob must make 5 payments on his student loans from college. Each payment is twice the amount of the previous payment. If the total amount he has to pay back is $1,550, how much is Rob’s first payment?

$10



$20



$25



$50



$75

Work one step at a time. Write down each step as you go.

Follow these three steps: Step 1: Identify what the question is asking and label the answers. Step 2: Plug in the middle answer choice. Work one step of the problem at a time. Step 3: Eliminate answers that don’t match the condition in the problem. Keep plugging in answers until you find one that works.

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GMAT IN CLASS MANUAL

11 2. Mike has twice as many stamps as Jean has. After he gives Jean 6 stamps, he still has 8 more stamps than Jean does. How many stamps did Mike have originally?

28



32



36



38



40

Choose Good Numbers Sometimes it makes sense to test more likely answers first. 3. Julia is twice as old as her brother Paolo, who is five times as old as their dog Winnie. In 10 years, Julia will be four times as old as Winnie will be then. How old is Paolo?

24

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25



27



30



33



35

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Lesson 1

11 Identifying Plugging In Problems Plugging In is a great technique, and you should be on the lookout for opportunities to Plug In. Plug In To recognize a basic Plug In problem, look for:

Hidden Plug In To recognize a Hidden Plugging In problem, look for:

Plugging In The Answers (PITA) To recognize a Plugging In The Answers problem, look for:

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GMAT IN CLASS MANUAL

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Homework Review Use this chart to note any questions you have from the reading or examples in the homework. Page #

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Question #

What que stion do you have ?

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Lesson 1

Practice Plugging In 1. If k years from now George will be l years old, how old was George m years ago? l–k–m l + (k – m) l+k–m k – (l + m) k + (m – l) 2. If 2x = 4y = z, what is x – y, in terms of z ?



(x + 1)2 4(x + 1)2



3( x +1)2 4 4( x +1)2 3 (x –1)2

z 2

6.

z



4z

3. A group of x people are in a room. One-third of the people leave the room, and an additional 2 people enter the room. In terms of x, how many people are in the room now?

3x + 2



3x + 6



x+2

4. What must be added to

x2 +2 x − 8 x2 − 6 x + 8



1



–1



   x − 1 + 2   2  2 x +2 3









4

2z







z





5. If x = 3t – 1 and y = 12t2, what is y, in terms of x ?

1 3

=

x

x+4 x −4 x +8 x −8

7. Copper pipe costs x cents per foot in 8-foot lengths, and x + y cents per foot in shorter lengths. What is the least possible price, in cents, for 51 feet of pipe, in terms of x and y ? x+y 2

to obtain

x−y 2

51(x + y) 51x 48x + 3y 48(x + y) 51x + 3y

?

–y –x 2y 2x y–x

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GMAT MANUAL

Hidden Plug Ins 1. Twenty-five percent of the residents of City Y are 65 years old or older. Twenty percent of the residents of City Y who are under the age of 65 are age 18 or younger. What percent of the residents of City Y are between the ages of 18 and 65 ?

15% 25% 45% 60% 75%

3. A parking garage has places for a certain number of cars. If

1

of the places are left 5 2 of the places are used by empty, and 5 compact cars, non-compact cars take up what fraction of the filled spaces in the garage?

2. In an election,

3

of the voters voted for 7 3 of the remaining voters Candidate A, and 5 voted for Candidate B. Of the voters who voted 1 for neither Candidate A nor Candidate B, 2 voted for Candidate C. What fraction of all the



1 3 2 5 1 2 3 5 4 5

votes were cast for Candidate C ?

9

4. Fred and Bobbie are book collectors, and Fred has twice as many books as Bobbie does. One-fourth of Fred’s books are signed by the authors, and three-fifths of Bobbie’s books are signed by the authors. If Fred and Bobbie combine their collections, what fraction of the books are signed by the authors?

35 13



35 9



1 70 4 35

10

28

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11 30 29 60 23 30 17 20 It cannot be determined from the information given.

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Lesson 1

5. Computer retailer A is selling a computer at a 20 percent discount from its suggested retail price. Computer retailer B promises to match this price and then discount it a further 10 percent. Computer retailer B’s final price is what percent of the suggested retail price?

75% 72% 70% 68% 28%

6. At a certain university, 3 out of every 5 students live in an on-campus dormitory. If one out of every 10 students who do not live in an on-campus dormitory lives in a university-owned apartment, what fractional part of the student body does not live in either an on-campus dormitory or a university-owned apartment?

7 10 1 2 9 25 3 10 7 25

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GMAT MANUAL

Plugging In The Answers 1. If 2x2 – 2x – 12 = 0 and y2 – 5y + 6 = 0 when x = –y, then what is the value of x ?

–3 –2 0 2 3



2. Several people rented a car for $30. If there had been one more person in the group, it would have cost each person $1 less. How many people were in the group originally?

5 6 10 12 15

5. Judy is 26 years old and Diane is 5 years old. In how many years will Judy be twice as old as Diane? 16 19 21 24 26

6. Pat has a pocket full of quarters, dimes, and nickels. He takes 6 coins out of his pocket that total $0.70. If there are only two denominations of coins among the 6 coins in Pat’s hand, how many nickels is he holding?

2 3 4 5 6

3. This year, half of the clients of a certain consulting firm ended up paying the firm exactly 7. On any given Sunday, 75 percent of the people $22,000 each, while the other half ended up in a city who own TV sets turn them on. Thirty paying the firm exactly $33,000 each. If the firm percent of the people who turn their TV sets on received a total of $275,000 from its clients, how watch football. If 9,900 people watch football many clients does the consulting firm have? on Sunday, how many people in the city own TV sets? 9 10 75,000 11 44,000 12 30,000 13 24,000 20,000 4. A certain bakery produces only chocolate and vanilla cupcakes. If the bakery sells 160 8. Fredrico earns a salary of $350 in a certain week cupcakes per day, and 26 more chocolate cupcakes than vanilla cupcakes are sold per day, at an appliance store. In addition, he receives how many chocolate cupcakes does the bakery 2 sell per day? of the amount of his total a bonus equal to 5 54 sales that exceed $1,500. If he earns $770, what 67 were Fredrico’s total sales for the week? 82 93 $1,600 106 $1,750

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$1,925 $2,225 $2,550

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Lesson 1

Answers and Explanations Plugging In

Hidden Plug Ins

1. A Plug in k = 3, l = 10, and m = 5. If George will be

1. D Plug in 100 for the number of residents. There are 25 people who are 65 or older, and 15 who are 18 or younger. There are 60 people in between.

10 in 3 years, he’s 7 now. Thus he was 2 (target answer) five years ago.

2. A Plug in. Be sure to choose numbers that make the equation in the question true. Let x = 6, y = 3, and z = 12. In that case, x – y = 6 – 3 = 3 (target). Only choice (A) works. 3. B Plug in. The calculations will be easier if you make x a multiple of 3; let x = 12. If a third of the people leave, that leaves 8; if 2 come in, your new total is 10 (target answer).

x+y

= 4 and 4. A If you plug in x = 3 and y = 5, then 2 x−y = −1 . You have to add –5 (target answer) 2 to 4 in order to get –1. 5. D Plug in for t first because both x and y are based on the value of t. If t = 2, then x = 5 and y = 48. The question wants the value of y, so 48 is your target answer.

9+ 6 −8 6. D Plug in x = 3, so the fraction becomes , 9 − 18 + 8 7 which reduces to , or –7 (target answer). −1 7. E The 8-foot lengths are less expensive, so you want to get as many as possible: six. If you get six 8-foot lengths, that leaves 51 – 48 = 3 feet at the more expensive rate. Let x = 2 and y = 3; the first 48 feet cost $96, and the remaining 3 feet cost $5 each, or $15. Your target answer is $111.

2. B Use the denominators to find the ideal number to plug in for the number of voters: 70. From the data given, 30 choose Candidate A and 24 vote for Candidate B. Of the remaining 16, 8 choose Candidate C. The fraction of voters that vote for 8 4 C is , which reduces to . 70 35 3. C If there are 25 places in the garage, then there are 5 empty places and 10 of the places have compact cars in them. If you picked (B), you may have misread the question; the question involves the fraction of non-compact cars in the filled spaces. There are 10 non-compact cars and 20 filled spaces, so the fraction is 1 . 2 4. A Get rid of (E), which is a trap answer. Give Fred 20 books and Bobbie 10 books; 5 of Fred’s books are signed and 6 of Bobbie’s are signed. The total is 11 out of the 30 books. 5. B Plug in $100 for the suggested retail price. Retailer A sells the computer for $80, and retailer B sells it for $72. This second price is a 28 percent discount from the original price. Choice (C), which is too obvious, is a trap. 6. C Plug in for the number of students. Notice that 3 3 out of 5 is the same thing as . If there are 50 5 students, then 30 live in a dorm and 2 live in an apartment. There are 18 students remaining, and 9 18 reduces to . 25 50

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GMAT MANUAL

Plugging In The Answers 1. B The answers represent possible values for x. Start

with (C), which turns out to be incorrect because 0 doesn’t work in the first equation. Next, plug –2 into the first equation [ 2(–2)2 – 2(–2) – 12 = 0]. Now, plug 2 (remember x = –y) into the second equation [(2)2 – 5(2) + 6 = 0].

2. A The answers represent the number of people in the original group. For choice (C): 10 people pay $3 each, and 11 people pay $2.73. So, the difference is not $1. For (A): 5 people pay $6 each, and 6 people pay $5 each, which is $1 less.

5. A The answer choices represent the number of years in which Judy will be twice as old as Diane. For choice (C), in 21 years, Judy is 47 and Diane is 26. Judy is less than twice as old as Diane, so (C) is too big. Eliminate choices (C), (D), and (E). For choice (A): In 16 years, Judy is 42 and Diane is 21, making Judy twice as old as Diane. 6. C The answer choices represent the number of nickels. For choice (C): If Pat has 4 nickels, the other two coins must be quarters: 4 × $0.05 = $0.20, and 2 × $0.25 = $0.50.

3. B The answers represent the number of clients. Get 7. B The answers represent the number of people in the city who own TV sets. For choice (C), if 30,000 rid of all the odd answers because the first step of own sets, then 22,500 of those sets are turned on the problem divides the clients into two halves. and 6,750 are tuned to football. Since 6,750 is less Only (B) and (D) are left; try either one. For than the 9,900 who are supposed to be watching choice (B): 10 clients means that 5 pay $22,000, football, choice (C) is too small. Eliminate choices for a total of $110,000, and the other 5 pay (C), (D), and (E). For choice (B), if 44,000 people $33,000, for a total of $165,000. Since the total own sets, then 33,000 of those sets are turned on received by the firm is $275,000, choice (B) is and 9,900 have the football game on. correct. 4. D The answers represent the number of chocolate cupcakes sold by the bakery each day. For choice (C), if the bakery sells 82 chocolate cupcakes, it sells 82 – 26 = 56 vanilla cupcakes. The bakery sells a total of 82 + 56 = 138 cupcakes, which is less than the 160 cupcakes the bakery is supposed to sell. Eliminate choices (A), (B), and (C). For choice (D), if the bakery sells 93 chocolate cupcakes, it sells 67 vanilla cupcakes and a total of 93 + 67 = 160 cupcakes.

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8. E The answer choices represent Fredrico’s total sales for the week. If you noted that Fredrico’s bonus is only paid on the portion of his sales that exceed $1,500, you probably realized that choices (A), (B), and (C) are all too small. Between choices (D) and (E), choice (E) is a little easier to work with so start there. For (E), if the total sales are $2,550, then the bonus is paid on $2,550 – $1,500 = $1,050. The bonus amount is $420, which gets added to Fredrico’s base salary of $350 to make his total earnings for the week $770.

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Lesson 2

Lesson 2

22

Sentence Correction 2 The previous lesson covered three of the six most commonly tested errors. This lesson focuses on the remaining three: misplaced modifiers, parallelism, and idioms.

Review 1. Each team of business students are responsible for creating a marketable business plan.

are responsible for creating a marketable business plan are responsible to create a marketable business plan is responsible for creating a business plan that is able to be marketed is responsible for creating a marketable business plan is responsible to create a marketable business plan Can you ID one of the common errors in the underlined portion? Yes Eliminate Choice (A)

Eliminate any answers that obviously repeat the error.

POE with the remaining answer choices. • New errors. • Changes to the meaning of the sentence.

No Can you ID an error from the answer choices? • 2/3 split • Differences in answers Yes No

Starting at (B), use POE. • New errors. • Changes to the meaning of the sentence.

Two left? Choose the more concise answer.

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GMAT IN CLASS MANUAL

22

Misplaced Modifiers You learned about modifiers in the pre-class assignment. Let’s look at how they will be tested on the GMAT. The Rule: A word or phrase that describes something should go right next to the thing it modifies.

Modifying Phrase:______________________________________________ Modifies?_____________________________________________________ The modifier is usually an introductory phrase that starts with a participle.

1. Eaten in the Mediterranean countries, northern Europeans viewed the tomato with suspicion, for they assumed it had poisonous properties because of its relationship to deadly nightshade.

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northern Europeans viewed the tomato with suspicion, for they northern Europeans were suspicious of the tomato, and they the tomato was viewed with suspicion by northern Europeans, who the tomato was suspicious to northern Europeans, and it was the tomato was viewed with suspicion by northern Europeans, it being

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Lesson 2

22

Sometimes the introductory phrase is underlined. In this case, you can fix the error in two ways:

• Rewrite the phrase so it describes the subject after the comma. • Change the phrase into a clause. Since a clause has its own subject, there will be no confusion about what it describes.

Modifying Phrase:____________________________________________ Modifies?____________________________________________________ 2. Sold over the counter at the turn of the century, the government now prohibits the sale of cocaine derivatives.

Sold over the counter at the turn of the century



While sold over the counter at the turn of the century



Being sold over the counter at the turn of the century



Although they were selling them over the counter at the turn of the century



Although they were sold over the counter at the turn of the century

Always think in terms of what the phrase modifies grammatically.

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GMAT IN CLASS MANUAL

22

Modifying Phrase:____________________________________________ Modifies?____________________________________________________ 3. Controlling most inroads to business ventures in Europe, economists argue that the U.S., with its diminished economic leverage there, now has reason to fear the European Common Market.









Controlling most inroads to business ventures in Europe, economists argue that the U.S., with its diminished economic leverage there, now has reason to fear the European Common Market. Controlling most inroads to business ventures in Europe, the diminished economic leverage of the U.S. there is, according to economists, one reason to fear the European Common Market. Because it controls most inroads to business ventures in Europe, a place where the U.S. have diminished economic leverage, economists argue that they now have reason to fear the European Common Market. Because it controls most inroads to business ventures in Europe, economists argue that the U.S.’s diminished economic leverage is a reason for the U.S. to fear the actions of the European Common Market. Economists argue that the U.S., with its diminished economic leverage in Europe, now has reason to fear the actions of the European Common Market, which controls most inroads to business ventures in Europe.

To spot misplaced modifier errors, look for:

To fix misplaced modifier errors:

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Lesson 2

22

Parallel Construction Parallel construction means that words in a list share the same part of speech or that phrases in a list have the same structure. The Rule: In a list of two or more things, each item in the list must use the same grammatical structure.

List Item 1:_____________________ Part of Speech:_______________

Conjunction:

List Item 2:_____________________ Part of Speech:_______________

Lists are marked by conjunctions. The most common conjuctions used on the GMAT to test parallelism are and, but and not only,,, but also.

1. The two main goals of the Eisenhower presidency were a reduction of taxes and to increase military strength.

a reduction of taxes and to increase military strength



to reduce taxes and an increase in military strength



to reduce taxes and to increase military strength



a reduction and an increase in taxes and military strength



taxes being reduced and military strength being increased

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GMAT IN CLASS MANUAL

22

List Item 1:_____________________ Part of Speech:_______________

Conjunction:

List Item 2:_____________________ Part of Speech: _______________ 2. The Department of Education has concluded that if children learn to read and did math from an early age, they will require less remedial work in later school years.

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did math from an early age, they will require less remedial work in later school years did math from an early age, they require in later school years less remedial work do math from an early age, they require less remedial work in later school years do math from an early age, they will be required in later school years to do less remedial work did math from an early age, less remedial work will be required in later school years

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Lesson 2

List Item 1:____________________ Part of Speech:______________

22

List Item 2:____________________ Part of Speech:______________ Conjunction: List Item 3:___________________

Part of Speech:_____________

3. In response to losing a significant part of its market share to a competitor, the soft drink company has cut costs by withholding executive bonuses, changed their advertising agency, and have redesigned the company logo.



changed their advertising agency, and have changing their advertising agency, as well as has changed its advertising agency, and and changed its advertising agency, and has changed its advertising agency, and

To spot parallel construction errors, look for:

To fix parallel construction errors:

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GMAT IN CLASS MANUAL

22

Comparisons Just remember “apples to apples and oranges to oranges.”

The Rule: Only similar items can be compared.

Comparison Word

Item 1

Item 2

1. The rules of written English are more stringent than spoken English. Look for comparison words. Common comparison words used on the GMAT include: Like Unlike





than spoken English as spoken English than those of spoken English as those of spoken English so than those of spoken English

Similar to Compared to More...than Less...than Different...from As

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Lesson 2

22 Item 1

Comparison Word

Item 2

2. Scientists now suspect that imperial mammoths of the Pleistocene period were wiped out not by human predation, as were mammoths of earlier periods, but by a sudden and extreme change in climate.



as were mammoths of earlier periods like that in an earlier period as in earlier periods as were earlier periods like the mammoths in an earlier period

To spot comparison errors, look for:

To fix comparison errors:

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GMAT IN CLASS MANUAL

22

Idioms As you learned from the pre-class assignment, idioms are fixed expressions. Knowing your idioms can help you to find errors in the underlined portion and to eliminate answer choices. The Rule: Know your idioms!

The use of improper idioms is a good way to identify an incorrect answer choice.

1. The establishment of land trusts in New England has been praised not because of it restricting overdevelopment but because it allows the inheritance by future generations of the property.

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not because of it restricting overdevelopment but because it allows the inheritance by future generations of because it not only is restricting overdevelopment and also allows the inheritance by future generations of because it does not only restrict overdevelopment, it also allows future generations for inheriting because of not only the restrictions on overdevelopment but also because future generations can inherit not only because it restricts overdevelopment but also because it allows future generations to inherit

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Lesson 2

22

2. Dermatologists are trained to distinguish an irritation, which results from prolonged exposure to the offending substance, from a true allergic reaction, which manifests itself immediately upon contact with the allergen.

an irritation, which results from prolonged exposure to the offending substance, from a true allergic reaction, which manifests itself immediately upon contact with the allergen



an irritation, resulting from prolonged exposure to the offending substance, and a true allergic reaction, manifesting itself immediately upon contact with the allergen



between an irritation, which results from prolonged exposure to the offending substance, or a true allergic reaction, which manifests itself immediately upon contact with the allergen



between an irritation, resulting from prolonged exposure to the offending substance, from a true allergic reaction, manifesting itself immediately upon contact with the allergen



a true allergic reaction, which manifests itself immediately upon contact with the allergen, and an irritation, which results from prolonged exposure to the offending substance

Errors rarely occur in appositive phrases. Try reading the sentence without the appositive to spot an error.

To spot idiom errors, look for:

To fix idiom errors:

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GMAT IN CLASS MANUAL

22

Math 2 Pieces of the Puzzle When you start a data sufficiency question, always take stock of what you know from the question stem. This method is particularly helpful for value data sufficiency questions.

What Do You Know?_________________________________________ What Do You Need?__________________________________________ 1. Each week, Jesse is paid x dollars per hour for the first 40 hours and 1.5x dollars for each additional hour he works that week. How much did he earn last week? (1) Last week, Jesse worked a total of 48 hours. (2) Jesse earns $36 more when he works a total of 42 hours in a week than when he works 40 hours.

What Do You Know?_________________________________________ What Do You Need?__________________________________________ 2. At a certain bakery, cherry pies cost $15. How many cherry pies did the bakery sell on Wednesday? (1) On Tuesday, the bakery’s cherry pie sales totaled $225. (2) On Wednesday, the bakery’s cherry pie sales were $75 more than Tuesday’s cherry pie sales.

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Lesson 2

What Do You Know?_________________________________________

22

What Do You Need?__________________________________________ 3. A certain bakery sells only cherry pies and apple pies, which cost 20% more than cherry pies. If the bakery’s pie sales on Wednesday totaled $111, how many cherry pies were sold? (1) Cherry pies cost $15 each. (2) The bakery sold a total of 7 pies on Wednesday.

What Do You Know?_________________________________________ What Do You Need?__________________________________________ 4. How many square tiles, each with a side of length n, are needed to completely cover a rectangular floor with dimensions l and m ? (1) n is a factor of both l and m. (2) n is one-half of l and one-third of m.

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GMAT IN CLASS MANUAL

22

Yes-No Data Sufficiency You’ve already seen data sufficiency problems that ask about a value. Other data sufficiency problems ask questions that require a “yes” or “no” answer.

What’s different about the way this question is phrased?

1. Does x = 10 ? (1) Ten percent of x is 1. (2) One-fifth of x is an even prime number.

2. Has Brand X been purchased by more than 50 percent of the 5,000 people in Moab? (1) Brand Y has been purchased by 75 percent of the people in Moab. (2) Brand X has been purchased by exactly 3,000 people in Moab.

Has the answer changed? Why?

2. Has Brand X been purchased by more than 50 percent of the 5,000 people in Moab? (1) Brand Y has been purchased by 75 percent of the people in Moab. (2) Brand X has been purchased by exactly 2,000 people in Moab.

Now, has the answer changed? Why?

2. Has Brand X been purchased by more than 50 percent of the 5,000 people in Moab? (1) Brand Y has been purchased by 75 percent of the people in Moab. (2) Brand X has been purchased by between 2,000 and 3,000 people in Moab.

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Lesson 2

22

Plugging In for Yes-No Data Sufficiency When Yes-No data sufficiency questions involve variables, Plugging In can help you determine whether a statement is sufficient.

3. Is x + 7 an odd integer?

(1) 2x + 3 is an odd integer.

(2) x + 11 is an even integer.

Pick numbers based on the statement. No Do the numbers satisfy the statement? Yes Answer the question with the numbers.

Pick new numbers based on the statement. Try a different type of number.

No

Do the numbers satisfy the statement? Yes Answer the question with the numbers. Same Different Answers? Answers? Statement is Sufficient

Statement is Insufficient

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GMAT IN CLASS MANUAL

22

4. Is x a positive number? (1) x + 6 > 2 (2) x2 > 25

5. If x is an integer such that 9 < x < 100, is x prime? (1) Both the tens digit and the units digit of x are prime.

(2) x + 6 is prime.

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Lesson 2

22

Keep Plugging Away Some problem solving questions ask which answer choice must be true. These problems can be solved using Plugging In. 1. If a and b are distinct positive integers, and a is even, then which of the following must also be even?

2(a + b) – 3



(a – b) + 2



a+b–1



a–b



ab – 2

What’s a good type of number to try the second time you plug in?

For must-be questions: • Plug in numbers for the variables. Eliminate choices that are false. • Plug in again using the most different type of numbers allowed by the conditions in the problem. • Keep plugging away until only one choice remains.

2. If p and q are integers, such that p < 0 < q, and s is a nonnegative integer, which of the following must be true?



p2 < q2



p+q=0



sp < sq



sp ≠ sq



p q

yz, which of the following must be true? I.

‘Must Be’ questions often test one of these differences even vs odd integers vs fractions positive vs negative



III.

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II.

x y x z x yz

>z >y >1

None of the above I only III only I and II only I, II, and III

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P

Lesson 2

Homework Review

22

Use this chart to note any questions you have from the reading or examples in the homework. Page #

Question #

What que stion do you have ?

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GMAT IN CLASS MANUAL

Practice Yes-No Data Sufficiency

1. If –2 < a < 11 and 3 < b < 12, then which of the following is NOT true?

1. Does x + y = xy ? (1) x is neither a positive integer nor a negative integer. (2) y is neither a positive integer nor a negative integer. 2. Does positive integer a equal 5 ? (1) a is not a factor of 6006. (2) 5 is the largest divisor of a. 3. If x is a positive integer, is x a multiple of 5 ? (1) 5 is a factor of

Fundamentals Practice

x . 2

(2) 3x + 5 is a multiple of 5. 4. Is m3 an integer? (1) m2 is an integer. (2) m is an integer. 5. Does s = t ? (1) s = t (2) s is both a factor and multiple of t. 6. Is m a multiple of 6 ? (1) More than 2 of the first 5 positive integer multiples of m are multiples of 3. (2) Fewer than 2 of the first 5 positive integer multiples of m are multiples of 12.

1 < a + b < 23 –14 < a – b < 8 –7 < b – a < 14 1 < b + a < 23 –24 < ab < 132

2. If

1 3

y ? (1)

(2)

2. If





1 1 x− y >0 4 3

10 − x 3

< −2 x, which of the following must be true?

I. 2 < x II.

III.

x > y

x −5 ≥ 7 x −1

x

>1

I only II only III only II and III I, II, and III

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GMAT IN CLASS MANUAL

33

3. If xy ≠ 0, is What are the options for evaluating these statements?

(1)

x y

x y − xy x+y

>0 ? 0, what is the value of

m

x

m

y

?

(1) m = 3 (2) x = y

5. If x ≠ 0, is x –y > 0 ? (1) x > 0

(2) y < 0

Tips for Working with Exponents • Look for common bases. • Try factoring if you can’t see a way to apply one of the exponent rules.

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Lesson 3

Quadratics

33

Recall that a quadratic equation is any equation of the form ax2 + bx + c = 0. A root of an equation is just another word for a solution of an equation. 1. If in the equation x2 – 2x – c = 10, x is a variable and c is a constant, what is the value of c ? (1) (x + 3) is a factor of the equation x2 – 2x – c = 10.

(2) 5 is a root of the equation x2 – 2x – c = 10.

2. If xy ≠ 0, which of the following is equivalent to

x2 – y2



x



( x 2 − y 2 )2 x 2 + 2 xy + y 2

?

Look for the common quadratics.

1 x − y2 2



x2 – 2xy + y2



x2 + 2xy + y2

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33

3. If x is an integer, is x even? (1) x 2 – y2 = 0

(2) x2 + y2 = 18

Functions and Sequences To solve function questions, you typically just need to follow the directions. 1. If [a] is the least integer greater than or equal to a, then [–4.5] + [4.5] =

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[–1.5] [–0.5] [0] [0.5] [1.5]

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Lesson 3

2. If a and b are distinct positive integers and x ⊕ y =

xy

x−y −2 −3 which of the following is an expression for a ⊕ b ?



b3 − a2



a−2 + b−3



33 , then

1 b − a2 3

a2 b3 b3 − a2 a2 b3 a2 − b3

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33

3. For all integers n, the function f is defined by f(n) = kan where k and a are constants. What is the value of f(3) ? (1) f(0) = 5

(2) f(2) = 20

4. A sequence of numbers satisfies the equation An = 2(An – 1) + 1. If A4 = 10, what is the value of A1 ?

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0.375 1.375 1.75 4.5 9

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Lesson 3

Harder Manipulations For some harder algebra problems, plugging in is the tool of choice. Sometimes, it’s better to do the algebra, however.

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2

 x+y      x−y

1 and y is 1. If x ≠ y, x ≠ 0, and y ≠ 0 and if x is replaced by x 1 everywhere in the expression above, then the replaced by y resulting expression is equivalent to 2



 x+y      x−y 2  x−y      x+y x2 + y2 y2 − x2 x2 − y2 y2 + x2 2



 x+y  −    x−y

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Is plugging in a good option for this question?

2. If n > 1, which of the following is equal to



2



2n



n+1+

2 n+1−

n −1

?

n −1

2



n+1+

n −1



n+1−

n −1

Algebra and Data Sufficiency

For some data sufficiency questions, you may need to translate the statement into an equation. 1. If b and c are positive and str ≠ 0, is (1) a2 =

(2) a2 =

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(1+ a s

a

)

b+a c =

a s

+

b t

+

s b t

s c r

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c r

?

Lesson 3

2. What is the maximum weight of a package that can be measured by a certain shipping scale?

33

(1) The scale can accurately determine the weight of a 200 pound package.

(2) If 100 pounds were added to a package that weighs half

the scale’s measurement capacity, the weight of the package 1 would increase by . 4

What do you need to do to evaluate the second statement?

3. For a banquet, a caterer charges $25 per person for the first 10 diners and x dollars for each additional diner. How much does the caterer charge for each additional diner? (1) If 15 people attend the banquet, the average (arithmetic mean) cost per diner is $23.

Which statement is easier? How can that help?

(2) The average cost per diner when 30 people attend the banquet is $1 less than when 20 diners attend the banquet.

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Integrated Reasoning I

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Integrated Reasoning questions mostly test familiar GMAT math and verbal concepts. Mostly, you just need to get used to the different question formats.

Table Analysis For some questions, you may need to sort the data in the table. The table displays information about selected breakfast cereals. Cereal

Calories per Serving

Total Fat (%DV)

Sodium (%DV)

Riboflavin (mg)

Fiber Max

197

4

17

1.42

Frosted Chips

367

0

19

1.50

Golden Grains

361

6

27

5.37

Malted Crunchies

401

8

31

1.42

Multi-Grain Puffs

338

3

27

0.77

Raisin Flakes

354

2

16

0.80

For each of the following statements, select Yes if the statement can be shown to be true based on the information in the table. Otherwise, select No.

First decide if you need to sort, then what you need to sort by.

Yes

No The cereal with the greatest number of calories per serving also had the greatest percentage of the recommended daily value of Sodium. The cereal with the least amount of Riboflavin per serving also had the third lowest percentage of the recommended daily value of Total Fat. If Malted Crunchies provides 83% of the recommended daily value of Riboflavin, Golden Grains provides less than 300% of the recommended daily value for Riboflavin.

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Lesson 3

Sort By: Calories per Serving Cereal

Calories per Serving

33 Total Fat (%DV)

Sodium (%DV)

Riboflavin (mg)

Fiber Max

197

4

17

1.42

Multi-Grain Puffs

338

3

27

0.77

Raisin Flakes

354

2

16

0.80

Golden Grains

361

6

27

5.37

Frosted Chips

367

0

19

1.50

Malted Crunchies

401

8

31

1.42

For Table Analysis questions, you can sort by any column.

Sort By: Total Fat (%DV) Cereal

Calories per Serving

Total Fat (%DV)

Sodium (%DV)

Riboflavin (mg)

Frosted Chips

367

0

19

1.50

Raisin Flakes

354

2

16

0.80

Multi-Grain Puffs

338

3

27

0.77

Fiber Max

197

4

17

1.42

Golden Grains

361

6

27

5.37

Malted Crunchies

401

8

31

1.42

Sort By: Sodium (%DV) Cereal

Calories per Serving

Total Fat (%DV)

Sodium (%DV)

Riboflavin (mg)

Raisin Flakes

354

2

16

0.80

Fiber Max

197

4

17

1.42

Frosted Chips

367

0

19

1.50

Golden Grains

361

6

27

5.37

Multi-Grain Puffs

338

3

27

0.77

Malted Crunchies

401

8

31

1.42

Sort By: Riboflavin (mg) Cereal

Calories per Serving

Total Fat (%DV)

Sodium (%DV)

Riboflavin (mg)

Multi-Grain Puffs

338

3

27

0.77

Raisin Flakes

354

2

16

0.80

Malted Crunchies

401

8

31

1.42

Fiber Max

197

4

17

1.42

Frosted Chips

367

0

19

1.50

Golden Grains

361

6

27

5.37

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33

Table Analysis Basic Approach 1. Review any labels or titles that apply to the entire table. 2. Decide whether you need to read any text blurbs that go with the table. 3. For each question, decide whether you need to sort the table. 4. If you decide to sort, decide which column to sort by. 5. For calculation questions, decide whether you need to use the calculator.

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Lesson 3

Graphics Interpretation

33

For graphics interpretation questions, your first step is to take the time to understand the chart or graph.

Scores

100

50

A

B

C D E Companies

F

G

The graph represents the range of the results of an entrance exam for the potential employees of companies A, B, C, D, E, F, and G. The highest possible score on the exam is 100 and 50 represents the lowest score achieved on the exam by any of the potential employees. The circles represent the average (arithmetic mean) score accepted for employment. The squares represent the minimum accepted score. From each drop-down menu, select the option that creates the most accurate statement based on the information provided. 1. The company with the least difference between its average and minimum accepted scores is __________.

Remember to open the drop down boxes so you can use POE!

A C D G 2. The most commonly accepted minimum score is closest to _________. 60 65 80

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33

Graphics Interpretation Basic Approach 1. Review the axes for the charts. Pay attention to units. 2. Decide whether you need to read any text blurbs that go with the chart. 3. Remember to open the drop down boxes before you start working on the question. Review the answers. 4. Write down a letter for each answer choice so you can use POE. 5. For calculation questions, decide whether you need to use the calculator.

Multi–Source Reasoning Multi-Source Reasoning questions can include either two or three tabs with information presented as graphs, tables, or text.

Retail Manager

Sales Performance

In this store, the Music and DVD department occupies 2,500 square feet of floor space, which is 50% more floor space than the Televisions department. While the gross margin for the Music and DVD department may be higher than that of the Televisions department, we also need to look at sales per square foot. On slow days, the sales per square foot for the Music and DVD department are often less than $1.00 per square foot. The sales for the Televisions department, however, are almost never less than $5.00 per square foot.

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Lesson 3

Retail Manager

Sales Performance

33

The chart shows some key statistics for one day’s performance at an electronics store broken down by the store’s 6 departments. Gross margin is the difference between the store’s sales and the cost of the goods sold. Gross margin does not include costs incurred to sell the goods such as payroll, transportation, or warehousing costs. Payroll shows the amounts paid to the employees who worked that day but does not include additional costs such as taxes or benefits paid by the store. The average hourly rate is shown for each department for the employees who worked on this day. Department

Sales

Gross Margin (%)

Payroll

Average Hourly Rate

Camcorders

$4,623

11.4%

$300.72

$12.53

Computers

$8,320

8.5%

$439.36

$13.73

Televisions

$14,256

14.1%

$625.24

$14.21

Major Appliances

$9,280

12.2%

$168.48

$10.53

Audio

$7,879

18.5%

$285.60

$9.52

Music & DVD

$3,885

20.3%

$252.88

$8.72

Consider each of the following statements. Does the information supplied support the inference as stated? Yes

No Television sales for the day shown were more than three times camcorder sales.

Statement style questions are common for MultiSource Reasoning.

The store devotes less than 2,000 square feet to selling televisions. The Music and DVD’s sales per square foot for the day shown were less than $1.00 per square foot.

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33 Standard multiple choice questions can also be part of Multi-Source Reasoning.

1. If no employee can work more than 8 hours per day, what is the minimum number of employees who worked in the Televisions department on the day shown?

3



4



5



6



7

Multi-Source Reasoning Basic Approach 1. Review the information on each tab. 2. For each question, decide which tab or tabs the information you need is on. 3. For statement style questions, remember that you may not need to finish the calculation to answer the question. 4. For questions that involve calculations, decide whether you need to use the calculator.

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Lesson 3

Two-Part Analysis

33

For two-part questions, you pick two answers based on a similar situation.

1. Jason and Andrew each have $8,000 in a bank account. For each of three consecutive years, Jason withdraws

For some Two-Part Analysis questions, you determine your answer for each column separately.

1

of the 2 3 money in his account and Andrew withdraws of the money 4 in his account. In the table below, select an answer that represents the fraction of the money remaining in Jason’s account and select an answer that represents the fraction of the money that remains in Andrew’s account at the end of the three years. Make only two selections, one in each column. Jason’s Account

Andrew’s Account

Fraction of money remaining

1 256 1 64 1 8 3 16

1 2 3 4

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33

2. At a certain gas station, the price of regular grade gasoline is $3.50 per gallon and the price of premium grade gasoline is 20% greater than the price of regular grade gasoline. Krissi’s car averages 22 miles per gallon on either grade of gasoline and Krissi purchases gasoline to drive 110 miles. In the table below, select an answer that represents how much Krissi pays if she purchases regular grade gasoline. Then, select an answer that represents how much she pays if she purchases premium grade gasoline. Make only two selections, one for each column. Regular grade gasoline

Premium Cost to drive 110 grade gasoline miles $14.00 $17.50 $21.00 $28.00 $31.50 $77.00

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Lesson 3

3. Emily and Maggie collect rare books. Emily currently has 200 books in her collection and Maggie has 320. Both women make monthly additions to their collections, each at her own constant monthly rate. In three months, Emily will have the same number of books in her collection as Maggie has in hers.

For some Two-Part Analysis questions, the answers are linked in some way.

33

In the table below, select a rate of increase, in books per month, for Emily’s book collection and a rate of increase, in books per month, for Maggie’s collection that together are consistent with the informaton. Make only two selections, one for each column. Emily’s collection

Maggie’s collection

Monthly rate of increase 20 50 70 80 100 120

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Homework Review 33

Use this chart to note any questions you have from the reading or examples in the homework. Page #

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Question #

What question do you have?

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Lesson 3

Practice Roots and Exponents a4 − 3 a3 − a + 3 1. If a ≠ 3 and = −126 , then what is the value of a ? a − 3



–5



5



3

6.

1 12

2

+

2 13

2

7.

3. Is integer n greater than 3 ?

 1  (2)    100 

 1 1 1 48  + +  4 2 2 2 3 2  32

2



3



5



10



20

61 27 61



4. If the speed of sound in air is 3.316 × 102 meters per second and the speed of sound in water is 1,500 meters per second, then approximately how many times faster does sound travel in water than in air?

27



> 0.001

3



129



183

8.

50(5−2 − 2−2 ) 52

c



−



−



=

3



 a 5. If a, b, and c are positive integers, is   > 1 ?  b (1) b – a = 9 (2) c > 1

=

16



n −1

=

216

n

 1  (1)   > 0.0001  100 

215

210 23



(1) a–1 is undefined (2) b = 2

8

215 2



2. If a and b are distinct integers greater than –1, then what is the value of ab ?

2

+

212 15



25

14

210 1



126

4

1



126

+

2 3 2

21 50 21 50

−

21 25

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9. If a is not equal to zero, is a–3 a number greater than 1 ?

1. What is the sum of positive integers x and y ?

(1) 0 < a ≤ 2 (2) ab = a 10. Dr. McCoy designed a space shuttle that can theoretically travel at a maximum velocity of 8 times the speed of light. If the speed of light is 300 million meters per second, then which of the following is the theoretical maximum speed, in meters per second, of Dr. McCoy’s shuttle?

Quadratics and More Algebra

2.4 × 103 2.4 × 108 2.4 × 109 3.0 × 106 3.0 × 109

(1) x2 + 2xy + y2 = 16 (2) x2 – y2 = 8 2. Which of the following are roots of the equation

23 × 33 × 53



0.00027 × 108



0.033 × 108



1

×

12. If x is greater than 0 but less than 10 and k = x9, what is the value of integer k ? (1) x2 has a units digit of 1. (2) x

–2


0, then what is the value of a ?

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3



4



3 5



9



7 3

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Lesson 5

Slope =

y −y Rise = 2 1 x2 − x1 Run

where (x1, y1) and (x2, y2) are points on the line.

55

It doesn’t matter which coordinate you call y2 or y1 as long as you use the corresponding x2 and x1.

2. If line l passes through the origin and the point (a,b), what is b the value of ? a (1) (5,2) is on line l. 5

(2) Line m, which is defined by the equation y = − x + 4 is 2 perpendicular to line l.

3. Line m is tangent to the circle with center (0,0) at (−3,y) such that its y-intercept is positive. If the radius of the circle is 5, what is the slope of line m ?

−4



−





4 3 3 4 4 5 4

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y = mx + b x, y = variables that stand for the coordinates of any point on the line

55

m = slope of the line b = y-intercept = y-coordinate of the point (0,b) where the line crosses the y-axis

3 2 1

1 2 3 4 5 6

-1 -2 -3

4. In the rectangular coordinate system shown above, the shaded region is bounded by straight lines. Which of the following is an equation of one of the boundary lines?

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y=1





y=2



x=0



y=



y=

2 3 3 2

x–2 x–2

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Lesson 5

5. What is the x-intercept of the line defined by the equation y = 4x + 5 ?

(5,–4)



(4, 45 )



(– 45 ,0)



( 45,0)



(0,– 45 )

55



6. The points (p,q) and (p – 2,q + c) are both on the line expressed by the equation y = 2x + 5. What is the value of c ? –4

–1



1



2



4

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Homework Review Use this chart to note any questions you have from the reading or examples in the homework.

55

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Page #

Question #

What que stion do you have ?

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Lesson 5

Practice

B 105 30

A

C

Note: Figure not drawn to scale.

1. What is the perimeter of the triangle above?



3+ 3 2

3. In the triangle above, if BC = 4 2, then what is the area of ∆ABC ?

64



3



16 +16 3



2+ 2



8+8 3



3+ 3



8+4 2



3+ 5



8 2

A (-3,5)

P

2 2 R

O

2 2

2. In ∆PQR above, PQ =

1 2 2 2



1



2



2

Q

B

4. In the figure above, AOB is the diameter of a circle centered at O. If the coordinates of A are (–3,5), then the coordinates of B are

(–3,–5) (–3,5) (3,–5) (3,5)



(5,3)

5. A circle with center (0,0) and radius 8 will pass through all of the following points EXCEPT

(–8,0) (0,–8) (0,8) (8,0) (8,8)

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6. The slope of a line containing points (2,–3) and (4,p) is –1. What is the value of p ?

–6 –5 1 5 12



B x

A

60

23.1 25.65 27.125 28.35 31.25 y +2− b

2 = m + , m is x x not zero. If the line is rotated 90°, then the slope

10. For the line with equation

C

7. In the figure above, if A, B, and C are points on the circle, and if AB = AC, then what is the value of x ?

9. The length of an edge of cube A is 5% greater than the length of an edge of cube B. If the volume of cube B is 27 cubic centimeters, then which of the following is nearest to the volume of cube A ?

40 45 50 55 60

of that line would be 1



−

m 1 m



m



–m



m–2

8. A square is inscribed in a circle with area πr2. What of the following is an expression for the area of the square?

r2 2



2r 2



r2



2r2



4r2

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Lesson 5

11. A sphere with a radius of 5 is hollowed out at the center. The part removed from the sphere has the same center, and a radius of 3. What fractional part of the original sphere remained? (The formula for the volume of a sphere 4 3 is V = πr ) 3

(1) Vertex C of triangle ABC lies on the x-axis and the triangle has an area of 196. (2) The coordinates of vertex C are (x,0) and x > 0. B

2 5

C

16 25 27 125 98 125 3 5

12. A certain cube floating in a bucket of water has between 80 and 85 percent of its volume below the surface of the water. If between 12 and 16 cubic centimeters of the cube’s volume is above the surface of the water, then the length of a side of the cube is approximately

13. In the rectangular coordinate system, the coordinate of vertex A of triangle ABC is (0,56). If vertex B lies at the origin, how many points on line AC have integer values for both their x and y values?

4 A

12

D

14. In the figure above, if the area of triangle ABD is 30, what is the sum of AB and BC ?

5 8 12 16 19

B

4 5 7 8 9

C

6

A

D

15. In the figure above, what is the area of square ABCD ? 4 10 12 18 24

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y

D

C

R(3,10) A

B

18. In the rectangular solid above, if AB = 5, what is the surface area of the solid?

S(9,2) x

(1) BC = 8 (2) The volume of the solid is 80. r

16. In the rectangular coordinate system shown above, what is the distance between point R and point S ?

10

x

6 3 12 9 2 20

17. What is the greatest distance, in inches, between any two corners of a rectangular box with dimensions of 6 inches, 8 inches, and 10 inches? 10 12 10 2 10 3 24

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19. A rectangular label of width x has been wrapped around the cylinder above, encircling the cylinder without overlap. If the radius of the cylinder is 6, and the label has the same area as the base of the cylinder, then what is the value of x ?

3 5 6 6π 9π

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Lesson 5

Answers and Explanations 1. D Apply the 30:60:90 triangle relationship to this

triangle to find that the hypotenuse equals 2 and the long leg (the base) equals 3 . Now, just add up the three lengths to find the perimeter. 2. C Because the two non-hypotenuse sides of this right triangle are the same length, the triangle is a 45:45:90 triangle. Use the 45:45:90 relationship to find that the hypotenuse equals 2 × 2 , or 1. 2 3. C When you drop a perpendicular from point B to side AC (call that point D), you create a 30:60:90 triangle (∆ABD) and a 45:45:90 triangle (∆BCD). Since BC = 4 2 , BD = AC = 4. Now look at the 30:60:90 triangle: Since BD = 4, AD = 4 3 . The base AC = 4 + 4 3 and the height BD = 4. Use the area formula: 1 (4 + 4 3 (4) = 8 + 8 3 . 2 4. C B is in the quadrant where x is positive and y is negative. The only choice with a positive x-coordinate and a negative y-coordinate is (C).

)

5. E Each of the points in the wrong answer choices is 8 units from the origin. However, the point (8,8) is 8 2 units from the origin, which can be determined using either the Pythagorean Theorem or the 45:45:90 triangle relationship. 6. B Se t u p t h e s l o p e f o r m u l a , a n d s o l ve : p − ( −3 ) p+3 = −1 , which becomes = −1 4−2 2 making p = –5. 7. E Since AB = AC, ∠B = ∠C. The measure of ∠A is 60°, so ∠B + ∠C = 120°. Thus, ∆ABC is equilateral, and each angle measures 60°.

8. D Draw the diagram, and make sure the square is inside the circle. Now, plug in r = 4. The area of the circle is 16π. The diameter of the circle is 8, which is also the diagonal of the square. The diagonal of the square creates two 45:45:90 triangles, so use that relationship to find the length of the side of the square. Each side measures 4 2 , so the area of the square is 32 (target answer). 9. E This is a very work-intensive problem, but there is no way around the work. First, find the side for cube B, which is 3 since its volume is 27. The length of the edge of cube A is 5 percent greater than the length of the edge of cube B. Thus, the length of the edge of cube A is 105 percent of cube B. We can find the length of the side of cube A by multiplying 3 times 1.05. To find the volume of cube A, we must raise the side of cube A to the power of 3. (3.15)3 = 31.25. 10. B Since we are given the equation of a line in a strange form, it’s probably a good idea to rewrite it in the more familiar form of y = mx + b. Rewriting the given equation reveals that we have been given the standard line equation. Now we know the slope is m, and the only question is what happens to it when it is rotated 90°. The best way to determine that might be to draw the picture of a line and then rotate it 90 degrees, which would reveal that the slope has become negative, which means we can eliminate (A) and (C). You can also eliminate (E) because for that choice to be correct the slope would not only rotate but would also change its value, and that does not happen here. The last two choices have only one difference: whether rotating the line makes the slope merely negative or the negative reciprocal. Plugging In should resolve that.

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11. D This one sounds weird, but don’t let yourself

be thrown off by the inclusion of the sphere. Remember, any time GMAC asks you about a strange figure, they will supply you with the relevant formula, as is done for this problem. From here, it’s a lot like a shaded region question. Start by figuring the area of the whole sphere, using the formula: It’s

500 π . Now, figure out 3

the volume of the smaller sphere. It’s 36π . Now, look carefully at the question: We need to determine what fractional part of the original sphere remains. First, determine the volume of the remaining portion of the sphere:

π

π

π

To determine what fractional part remains, we need to take the remaining portion and divide 392 π 392 98 = = it by the original volume: 3 . 500 500 125 π 3

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12. A The best way to approach this problem is to Plug In The Answers since the answers give us the side of the cube. If we start with the middle choice, (C), then we have a cube with side 7. If the cube has a side of 7, then it will have a volume of 343. We are told that between 80% and 85% of the volume is below the surface of the water, which means that between 15% and 20% of the volume is above the surface. If the volume of the cube is 343, then 20% is about 68 and 15% is about 51. Neither of these numbers is between the 12 and 16 cubic centimeters that are supposed to be above water, so clearly this can’t be the answer. Since the numbers are too large, we need to try something smaller. Pick one of the smaller choices and try again. 13. A Start by translating the question to understand which pieces of the puzzle are given and which pieces are needed. The question tells us where two vertices are, point B at (0,0) and point A at (0,56). To answer the question, we need the coordinates of the last point. Statement (1) tells us that the third vertex lies on the x-axis which means that triangle ABC is a right triangle. We also know the area of the triangle so we can calculate the length of the base of the triangle. Remember that we already know that the height of the triangle is 56. Knowing the length of the base, we can find the coordinates of vertex C. We now know two points on line AC which means we can calculate the slope of line AC which allows us to answer the question. So, AD. Statement (2) only tells us that vertex C lies on the x-axis but we have no way of determining the length of the triangle’s base. So, statement 2 is insufficient.

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Lesson 5

14. D Since you know that the base of triangle ABD is 12 and that its area is 30, you can use the formula for the area of a triangle to find that the height of ABD is 5. Be sure to add this information to the figure. For triangle ABD, you now know AD is 12 and BD is 5. You can use the Pythagorean Theorem to find that the length of AB is 13. (Remember, however, that GMAC likes to test the 5:12:13 special right triangle so it’s best to have this relationship memorized.) Triangle BCD turns out to be a 3:4:5 special right triangle, another common relationship that GMAC likes to test. So, AB + BC = 13 + 3 = 16. 15. D Start by labeling everything that you know on the figure. In this case, you’ll want to add that ∠ADC = 90° and that ∠CAD = ∠ACD = 45°. You also want to write down the formula for the area of a square, A = s2. So, you need to find the side of the square. Use the 45:45:90 triangle relationship to find that the side of the square is 6 . Plugging that value into the formula gives 2 an area for the square of 18. 16. A Finding the distance between two points in a plane requires the construction of a right triangle. First, draw a line connecting points R and S. Next, draw a vertical line down from R and a horizontal line left from S. The point of intersection has coordinates (3,2). The vertical leg of the triangle has a length of 8 and the horizontal leg has a length of 6. The hypotenuse has a length of 10.

17. C There’s a formula that can be used to find the diagonal of a rectangular solid: d2 = a2 + b2 + c2, where a, b, and c are the dimensions of the rectangular solid. In this case, d2 = 62 + 82 + 102 = 200. Now, just take the square root of 200 and simplify to find the distance. 18. C Start by applying the Pieces of the Puzzle approach. In this case, you know one of the three dimensions of the box. To find the surface area, you need to find the area of each surface. So, you’ll need the statements to provide the other two dimensions of the box. Statement (1) provides only one additional dimension. So, statement (1) is insufficient and the possible answers are B, C, or E. To evaluate statement (2), the formula for the volume of a rectangular solid is V = lwh. The statement provides the value for the volume and question stem provided one of the three dimensions. Statement (2) is also insufficient. When the statements are combined, however, you can now use the volume formula to find the value of the missing dimension. 19. A Start by drawing the figure and labeling the radius as 6. Next, find the area of the base of the cylinder. Since the base of the cylinder is a circle, its area is A = πr2 = 36π. The label is a rectangle, so the formula for its area is A = lw. The length of the label is the same as the circumference of the cylinder, so substitute 2πr for the l in the formula for the area of the label. You can also substitute x for w in the formula to get: A = 2πrx = 36π. Finally, just put in the value of the radius, 6, and solve to find the x = 3.

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Lesson 6

Lesson 6 66

Reading Comprehension 2 The Basic Approach Step 1: Work the passage. Read for the passage’s main idea, and get a sense of its structure. Step 2: Understand the Question Task. Look for the question’s subject and the words that indicate its task. Step 3: Find the Information that Addresses the Task. Once you understand the question task, use the question’s subject to locate information in the passage that addresses the question task. Step 4: Use POE to find the answer. Be skeptical of each answer choice. Try to find reasons to eliminate the answer. Eliminate choices that: • Use recycled language.

• Use extreme language. Be wary of answers that make sweeping claims.



• Make bad comparisons about items in the passage. The items may be from the passage but is the comparison?

• Reverse the main idea. • Make emotional appeals or call on outside knowledge.

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Use one of the passage mapping strategies to find the main idea of this passage.

66

(5)

(10)

(15)

(20)

(25)

(30)

The wealth of morphological, phonetic, and word similarities among certain languages has led linguists to recognize the unity of the well-defined 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 original source, 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 Vedic hymns, the first recorded instance of Aryan, those tribes speaking this early language had already begun their widespread dispersal.

Issue of the Passage:

Main Idea of the Passage:

How is the passage structured?

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Lesson 6

Specific Questions and POE Specific questions ask about a fact or detail from the passage.

Detail Questions

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These questions ask you to find something the author said. Question Subject:_____________________________ Task Word:___________________________________ 1. The “misnomer” (line 5) refers to

the fact that not all Indo-Europeans are of Aryan descent the fact that the family of languages goes beyond the boundaries implied by the name the fact that the family of languages actually originated in Western China the fact that the languages are no longer spoken the fact that proto-Aryan was spoken in the area known as Latium

To learn about the POE tools, think about why somebody might pick each of the wrong answers.

POE Notes:

Detail Purpose These questions ask you why the author included a piece of information in the passage. Question Subject:_____________________________ Task Word:___________________________________ 2. The author mentions Icelandic in order to

Is this question task “What” or “Why”?

provide support for the contention that early Aryan-speaking peoples did not necessarily live in Asia provide another example of the archaic features found in the Avesta provide evidence for the inception of proto-Aryan counter the speculation that proto-Aryan was first spoken in Russia provide an alternative explanation for the similarities found in early languages

POE Notes:

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Infer/Imply/Suggest Questions These questions are really just another “what” task even though it sounds like you are supposed to do more. Question Subject:_____________________________

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Task Word:___________________________________ 3. Which of the following does the passage imply about the Tokharian languages?

They date to a far earlier period than does Celtic. They possess many of the same features as did the Old Indic and Persian of the Avesta. They were once spoken over a far greater range than they are today. They undermine the accuracy of the name “Indo-European” for their particular family of languages. They are remarkably similar to the languages spoken by current residents of the Tarim River Basin.

POE Notes:

EXCEPT Questions Here you have four questions for the price of one. Question Subject:_____________________________

How does the word ‘except’ change the process for this question?

Task Word:___________________________________ 4. According to the passage, all of the following characterize Indo-European languages EXCEPT

similarities in the structure of words and in the sounds employed common origins in some prehistoric community widespread, intercontinental dispersal recorded instance of early use in ancient literature preservation of characteristics discarded by earlier speakers

POE Notes:

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Lesson 6

Reading Comprehension POE: Learn to be suspicious of answer choice characteristics that are likely to make the answer wrong. Start with specific words in the answer choice and try to place those words into a POE category. POE can lead to an explanation why the answer is incorrect.

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Explanation: The reason an answer choice is incorrect. Coming up with explanations is often more time-consuming than POE. Explanations start with POE.

Two Pass POE Pass One • Be suspicious of every answer. • Look for characteristics that are likely to make an answer wrong, such as recycled language. See if you can use those characteristics to explain why the answer is wrong. Pass Two • Down to two? Use POE aggressively. • Eliminate the answer that sounds more like the passage. • Eliminate the answer that uses the stronger language. • Eliminate the answer that makes a comparison.

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(5)

66 (10)

(15)

(20)

(25)

(30)

(35)

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The tropical leaf-cutter, or attine, ant provides a remarkable example of complex symbiosis involving several species. The ants cultivate a fungus in underground caverns to serve as a source of food. DNA analysis reveals that the fungi in attine gardens around the world are clones of a single source. The ants do not allow their fungus crop to develop fruiting bodies, the means by which plants engage in sexual reproduction. Instead, a queen ant starting a new nest takes a sample of the fungus from the old nest to start the new garden, spreading the fungus vegetatively, or asexually. For many years, the phenomenon of sexual reproduction puzzled biologists, as it passes only half of the parents’ genes to the succeeding generation and requires a more complex mechanism than does asexual reproduction. What benefit of sexual reproduction would outweigh these limitations? One likely answer is that it provides a defense against parasitic attack. Simple parasites, such as bacteria or molds, mutate rapidly and pose a challenge to other species developing defense mechanisms. The rapid evolution of the attacking species provides an advantage in this biological arms race. Sexual reproduction allows the more complex species to shuffle its genes between generations and, as a result, evolve quickly enough to match the parasites’ mutations. A clonal monoculture, such as that of the attine, should be highly susceptible to parasites, yet preliminary research suggested no evidence of such a problem in the ants’ gardens. More comprehensive studies showed that the Escovopsis mold, a parasite related to the “green mold” known to commercial mushroom farmers, is present in the ants’ crops and poses a serious threat to the fungus. However, 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. This actinomycete bacterium produces an antibiotic used to control the mold and limit its destructive effects on the ants’ food source.

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Lesson 6

1. The phrase “clonal monoculture” (line 26) refers to which of the following?

The Escovopsis mold A species of leaf-cutter ant Sexual reproduction A fungus An antibiotic bacterium

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2. Which of the following can be most reasonably inferred about reproductive strategies from the passage?

The fruiting bodies found on numerous fungi are a means of vegetative reproduction. 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. The bacterium found on patches of green mold produces an antibiotic substance used by commercial mushroom farmers. Parasitic bacteria use sexual reproduction as a means to achieve rapid mutation.

3. The author describes the interaction between a parasite and a sexually reproducing organism as an “arms race” (line 22) 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

4. The passage suggests which of the following about the fungus grown by the attine ants?

By shuffling its genes, it is able to mutate rapidly in response to parasitic threats. Due to its asexual reproduction, it is susceptible to attack by the actinomycete bacterium. It could potentially engage in sexual reproduction. It is closely related to the crops grown by commercial mushroom farmers. Without the care of the attine ants, it would quickly become extinct.

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Critical Reasoning 2 There are a few types of critical reasoning questions that do not require you to identify the conclusion, premise, and gap.

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Inference Questions Inference questions ask you to infer or conclude something based on the passage. Step 1: Read and identify the question. Inference questions typically ask: • Which of the following can be inferred from the information above? • Which of the following conclusions is best supported by the passage? • Which of the following conclusions could most properly be drawn from the information above? • Which of the following must be true on the basis of the statements above? Step 2: Work the argument. Read the passage. There’s no need to look for the conclusion and premise. Step 3: Predict what the answer should do. Most of the time, you will not be able to come up with an answer in your own words. Simply keep in mind that you want the answer best supported by the facts. Step 4: Use POE to find the answer. Look for an answer that must be true. Avoid answers that: • Are out of scope • Use extreme language

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Lesson 6

1. According to a recent study, fifteen corporations in the United States that follow a credo of social responsibility are also very profitable. Because of their credos, these fifteen corporations give generously to charity, follow stringent environmental protection policies, and have vigorous affirmative action programs.

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Which of the following can be correctly inferred from the statements above?

Following a credo of social responsibility helps to make a corporation very profitable.



It is possible for a corporation that follows a credo of social responsibility to be very profitable.



A corporation that gives generously to charity must be doing so because of its credo of social responsibility.



Corporations that are very profitable tend to give generously to charity.



Corporations that have vigorous affirmative action programs also tend to follow stringent environmental protection policies.

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2. The two divisions of a high-tech company have performed quite consistently over the past five years. In each year, the telecommunications equipment division accounted for 35 percent of profits and 15 percent of revenues, and the high-speed internet division made up the balance. Which of the following can properly be inferred regarding the past five years from the information above?

The telecommunications equipment division has made higher profits per dollar than the high-speed internet division.



Sales for both divisions have remained flat over the five years.



The high-speed internet market involved tougher competition than the telecommunications equipment market during the past five years.



Management devoted a greater number of company resources to the telecommunications equipment division than to the high-speed internet division over the past five years.



More profitable products made up a higher percentage of the products offered by the telecommunications division.

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Lesson 6

3. A combination of anxiety and external pressure leads to nausea. All the auditioners for the new reality show Wanna Be’s suffer from external pressure. Some of the auditioners feel anxiety about performing well for the producers, but others do not feel anxious. The producers of Wanna Be’s select only those contestants who feel anxiety.

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Which of the following conclusions is most strongly supported by the passage above?

The auditions for Wanna Be’s cause more performers to feel external pressure than do auditions for other shows.



Most of the people who audition become contestants on Wanna Be’s.



There is more nausea among auditioners for Wanna Be’s than among producers of Wanna Be’s.



No auditioner who doesn’t feel anxiety has nausea.



All of the auditioners for Wanna Be’s who become contestants have nausea.

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4. In broad thermodynamic terms, the distinction between solar energy and energy derived from fossil fuel is artificial. Fossil fuel molecules represent the decayed remains of plants. All of the energy these fossil fuels contain once resided in the sun and was, so to speak, trapped by plants here on Earth through the process of photosynthesis, whereupon it was housed, principally, within the carbohydrate molecules of which the plants were composed. The process of burning unleashes that energy, and when we run our lights, factories, and automobiles by burning fossil fuels _______________. Which of the following is the most logical completion of the passage above?

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we deplete our stores of an ever more precious resource



we use energy that is, in fact, derived from the sun



we spend the legacy left to us by our prehistoric ancestors



we mimic the process of energy generation that exists in the sun



we return to the sun that which originally resided there

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Lesson 6

Integrated Reasoning 2 To answer some Integrated Reasoning questions, you use the same skills that you use when answering Critical Reasoning questions.

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Integrated Reasoning and Inferences Many types of Integrated Reasoning questions ask you to make an inference based on the data presented. The table displays performance statistics for six different luxury cars. Model

Curb Weight (lbs)

Horsepower

0–60 acceleration (sec)

Highway Fuel Economy (mpg)

Series 3

3,609

230

7.1

26

250 IS AWD

3,651

204

8.3

27

4A

3,704

211

6.3

29

Kappa Class

3,737

228

7.1

25

Gamma x37

3,822

328

5.6

25

LT

3,968

305

5.3

26

For each of the following statements, select Yes if the statement can be shown to be true based on the information in the table. Otherwise, select No.

Yes

No The car with the least horsepower also takes the most time to accelerate from 0 to 60.

Additional sorts of the table data are provided on the next page.

If the curb weight of the 4A were reduced, its highway fuel economy would increase. For each of the cars listed, as horsepower increases, 0 to 60 acceleration gets faster.

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Sort By: Horsepower Model

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Curb Weight (lbs)

Horsepower

0–60 acceleration (sec)

Highway Fuel Economy (mpg)

250 IS AWD

3,651

204

8.3

27

4A

3,704

211

6.3

29

Kappa Class

3,737

228

7.1

25

Series 3

3,609

230

7.1

26

LT

3,968

305

5.3

26

Gamma x37

3,822

328

5.6

25

Sort By: 0–60 acceleration (sec) Model

Curb Weight (lbs)

Horsepower

0–60 acceleration (sec)

Highway Fuel Economy (mpg)

LT

3,968

305

5.3

26

Gamma x37

3,822

328

5.6

25

4A

3,704

211

6.3

29

Kappa Class

3,737

228

7.1

25

Series 3

3,609

230

7.1

26

250 IS AWD

3,651

204

8.3

27

Sort By: Highway Fuel Economy (mpg) Model

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Curb Weight (lbs)

Horsepower

0–60 acceleration (sec)

Highway Fuel Economy (mpg)

Gamma x37

3,822

328

5.6

25

Kappa Class

3,737

228

7.1

25

Series 3

3,609

230

7.1

26

LT

3,968

305

5.3

26

250 IS AWD

3,651

204

8.3

27

4A

3,704

211

6.3

29

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Lesson 6

Integrated Reasoning and Arguments Some Integrated Reasoning questions are really just Critical Reasoning questions asked in a different format. 1. Allison: Childhood obesity is rampant in the public school system. In order to combat this dangerous trend, we must make a move to remove any and all non-nutritious food items from school campuses. This must start with the removal of soft drink vending machines, the most egregious offender.

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Evodio: While I agree that childhood obesity is a serious threat to the health of our nation’s children, I do not believe the removal of soft drink vending machines solves this problem. The root of the pandemic lies in a combination of uninformed parenting and limited opportunities for physical activity. Allison: You are correct that parental involvement is key to the solution. However, the school system is an influential model of nutrition and can therefore help guide parents as to what is appropriate. Evodio: That assumes the parents of the obese children pay close attention to their children’s school diet. On the contrary, those parents are the least likely to be aware of the school meal plans. In the table below, select the statement that best strengthens Allison’s argument. Then, select the statement that best strengthens Evodio’s argument. Make only two selections, one for each column. Allison

Evodio Students who attend schools without soft drink vending machines, in general, consume far fewer soft drinks outside of school than do other students. Studies have shown that students who do poorly in school by comparison are more likely to eat non-nutritious foods. Childhood obesity rates have remained constant over the past 5 years despite a concerted effort to introduce healthier meal items to school cafeterias. Students who ride the bus tend to be more obese than other students. Parents often base their meal planning around their children’s preferences, which have been shown to be influenced by food available at school. The kinds of physical activity typically found in a school environment are not particularly effective at weight reduction.

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Definitions

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Case Study

A sampling bias occurs in which a sample is collected in a particular manner as to cause a portion of the targeted population to be more or less likely to be selected than others. In such a case, the bias produces what is called a biased sample: a non-random cross section of the targeted population in which not all individuals were equally likely to have been chosen. The presence of a sample bias can adversely affect the study for which the sample was gathered. The bias often causes the results to indicate a phenomenon that may actually not be present. The following lists several common kinds of sample biases. Self-selection: This bias occurs when the group of people under study has control over whether to take part in the study. The willingness of the participants to participate may align with the characteristics of the study itself. (For example, a voluntary customer satisfaction survey may only draw responses from those participants with strong opinions.) Pre-screening: This bias occurs when participants from a specific group are asked to volunteer for the study. The participants may be incidentally drawn from groups that may have a certain interest in the study. (For example, a study designed to test the effects of health food on overall health may only advertise at a fitness center.) Exclusion: This bias occurs when a portion of the targeted population is not included in the sample. (For example, a political internet survey will exclude those who cannot gain regular access to the internet, whether because of economic or regional limitations.) Healthy User: This bias occurs when the method of sampling selects participants who are more likely to be healthy than the average population. (For example, a study using manual laborers would include participants who are more likely to be in good health.)

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Lesson 6

Definitions

Case Study

Survey Professionals conducted a survey on college students about their interests in Zapp Cola products. The intention of the survey was to gauge demand on targeted college campuses so that Zapp Cola could determine how many vending machines to field. The survey offered several samples of different Zapp Cola products and then asked the students to rate each product’s quality of taste on a scale of 1 to 5. The students were then asked what prices they felt were fair to pay for each product. In order to generate interest in the survey, Survey Professionals offered a free bottle of any Zapp Cola product upon completion of the survey. The advertisements for the survey were only posted in the various cafeterias and eateries on and surrounding the targeted college campuses.

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1. Which of the following actions, if taken by Survey Professionals, would have most effectively strengthened the results of the survey by reducing the bias present in the survey?





Instead of posting in the cafeterias on the campuses, Survey Professionals should have posted the advertisements for the survey only in the eateries surrounding the campuses. Survey Professionals should have offered an alternative incentive in place of the choice of a bottle of a Zapp Cola Product. The survey given should not have asked how much the participants were willing to pay for the Zapp Cola products. The advertisements for the survey should have encouraged anyone from the general population to participate in the survey rather than just college students. The scale used in the survey should have been changed so that the participants could write in their own impressions of each product.

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Plugging In for Two-Part Analysis For some Two-Part Analysis questions, you’ll be able to plug in! 1. A jar contains r red marbles and 2 times as many black marbles as red marbles. Two marbles are drawn from the jar at random without replacement.

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In the table below, select an expression that represents the probability of choosing two red marbles from the jar. Then, select an expression that represents the probability of choosing at least one red marble from the jar. Make only two selections, one for each column. Probability of two red marbles How can you identify this problem as a plug in?

Probability of at least one red marble r 3r − 1 r −1 3r − 1 r −1 9r − 3 3r − 1 9r − 3 5r − 1 9r − 3 7r − 1 9r − 3

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Lesson 6

2. A machine completes x percent of a certain job working at a constant rate of 2 parts per hour and the remainder of the job working at a constant rate of 8 parts per hour. In the table below, select one expression that represents, in terms of x, the average (arithmetic mean) number of parts per hour made by the machine for the entire job. Then, select an expression that represents the total amount of time required by the machine, working as described above, to complete a job consisting of 80 parts. Make only two selections, one for each column. Average parts per hour

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Total time to complete 80 parts 3 x + 100 800 800 3 x + 100 x+8 2 3 x + 100 10 3 x + 100 8 3x + 4 8

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Plugging In The Answers for Two-Part Analysis For some Two-Part Analysis questions, you’ll also be able to Plug In The Answers.

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3. The town of Clarkesville currently employs police officers and firefighters. Clarkesville wishes to increase the size of its police force by 25% while reducing the number of firefighters by 37.5% so that it employs an equal number of police officers and firefighters. In the table below, select a value for the number of police officers currently employed by Clarkesville and a value for the number of firefighters currently employed by Clarkesville that is consistent with the information provided above. Make only two selections, one for each column. police officers

firefighters 9 16 20 24 32 56

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Lesson 6

PITA for Two-Part Analysis 1. Write down the answer choices on your noteboards. Make two columns, leaving some space between. 2. Decide which column is easier to work with.

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3. Label both columns. 4. Starting with an answer in the middle of the easier column of numbers, work the steps of the problem. 5. Check for a match between the two columns that makes a condition in the problem true.

4. Kevin is ten years older than Scott. In six years, Kevin will be twice as old as Scott. In the table below, select Kevin’s age in six years. Then, select Scott’s current age. Make only two selections, one in each column. Kevin’s age in six years

Scott’s current age 4 6 10 14 16 20

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5. For the first 5 hours of a trip, a car drives at a constant rate of 70 miles per hour. For the last h hours of the trip, the car drives at a constant speed of m miles per hour. The car averages 55 miles per hour for the entire trip.

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In the table below, select a value of h, the number of hours for the second part of the trip and a value for m, the rate of speed in miles per hour for the second part of the trip, that is consistent with the information above. Make only two selections, one in each column. h (hours)

m (mph) 3 8 10 25 30 35

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Lesson 7

Lesson 7 77

Critical Reasoning 3 Common Argument Patterns Many GMAT arguments involve either causality or plans. These arguments have common assumptions. 1. A harmful algal bloom (HAB) occurred in the Gulf of Mexico three months after unusually heavy farm runoff was recorded along the Gulf Coast in July of 2005. Thus, it is evident that farm runoff causes harmful algal blooms. Which of the following statements, if true, most seriously weakens the argument above?



What’s different about scope for this argument?

The harmful algal bloom triggered by the runoff along the Gulf Coast subsided after a few months. The growth of phytoplankton in the ocean is generally limited by the amount of nutrients available in ocean waters. No harmful algal bloom occurred within one year of the unusually heavy farm runoff recorded off the coast of California in June of 2004. Farm runoff often contains key nutrients on which algae feed. Harmful algal blooms are often indicated by red discolorations on the surface of the ocean.

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2. In the past five years, there has been a marked decline in the consumption of soft drinks sweetened with sugar. During the same time, there has been increasing publicity about the adverse health effects of weight gain caused by the consumption of sugar-laden drinks. Clearly, 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.

77 How did the correct answer strengthen this argument?

Which of the following statements, if true, most strengthens the argument above?







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Many consumers have switched to drinking diet soft drinks which are not sweetened with sugar. The average person’s consumption of soft drinks sweetened with sugar has decreased by 8.2 ounces per day. Consuming large quantities of sugar-laden drinks has also been linked to mood swings throughout the day. The consumption of packaged cookies which feature sugar as a key ingredient has decreased during the time period in question. The price of sugar-laden soft drinks has remained stable for the past five years.

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Lesson 7

3. If tourists continue to visit Bridges National Park at the current rate, the fragile desert environment that the park seeks to protect will be irreparably harmed. The park’s Director has put forth a proposal to charge visitors to the park a fee based on the number of hours spent in the park. This fee will induce tourists to limit their time in the park and thus protect the fragile desert environment.

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Which of the following is an assumption made in drawing the conclusion above?







Tourists will limit the amount of time that they spend in the park by hiking only the shorter trails in the park. Most tourists will easily be able to pay the fee even if they do not reduce the number of hours that they spend in the park. The fee will not induce tourists to enter the park early in the morning before the fee collection station has opened and leave only after the fee collection station has closed for the night. Protecting the fragile desert environment is an important issue for most visitors to the park. Tourists who do not wish to pay the fee can visit nearby Chasmlands National Park.

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Which patterns do you recognize in this argument?

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4. Excessive government regulation, not the current high price of oil, is responsible for the poor industrial production in Country A since its new government came to power. Country B pays the same price for oil, but while industrial output in Country A has been falling, it has been rising in Country B. Which of the following, if true, would cast the most doubt on the argument above?

Agricultural production is also declining in Country A.



Whereas Country B must import most minerals, Country A exports minerals.



In both Country A and Country B, there has been little credit available through the credit markets.



The industrial goods produced in Country A are different from those that are produced in Country B.



Country A’s new government increased regulation of its industry to promote a cleaner environment.

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Lesson 7

5. The renewed surge in fear over the virulence of the Ebola virus is irrational and unfounded. While in 2008 only 54 deaths worldwide were directly attributed to Ebola, the US Centers for Disease Control estimates that over 30,000 deaths were caused by the influenza virus in the United States alone in that same year. Yet no such hysteria has surrounded influenza, despite the significantly higher number of fatalities.

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Which of the following, if true, would most undermine the argument above?





Pattern

Deaths due to Ebola tend to be concentrated in remote geographical locations. Ebola has a shorter incubation period than many other tropical diseases. Transmission of the influenza virus among the US population is aided by the mobility of the US population. The average fatality rate for the most common form of the Ebola virus is significantly higher than the average fatality rate for common forms of the influenza virus. Worldwide, over 30,000 people die from Yellow Fever each year.

Assumption

Weaken

Strengthen

Causality

Planning

Analogy

Sampling

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Math 6 More Problem Solving Plugging In For some plugging in questions, you may need to look a little harder to determine how to plug in!

77 Is it easier to pick a value for n or for something else in this problem?

1. A hotel has a total of n rooms and suites. If the number of 5 3 rooms is the number of suites, and of the suites have two 4 5 bedrooms, how many two bedroom suites, in terms of n, does the hotel have?

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1 4 4 15 13 20 3 4 37 20

n n n n n

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Lesson 7

2. Mike and Dave are each assigned to produce x identical widgets. Based on their respective rates, Dave calculates that it will take him 5 hours to produce the widgets while Mike calculates that it will take him 2 hours longer than Dave. Dave agrees to make y of Mike’s widgets so that they can each complete the task in the same amount of time. What is the number of widgets, in terms of y, that Mike was assigned to make?

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2y 3y 4y 5y 6y

3. At a bakery, each small loaf of sourdough bread requires

2

as 3 much flour to make as each large loaf of sourdough bread. If the store sells

What’s a good way to organize the information as you plug in on this problem?

3

as many small loaves of sourdough bread as large 5 loaves, what fraction of all the flour used by the store to make loaves of sourdough bread was used to make large loaves of sourdough bread?



1 4 2 5 3 5 2 3 5 7

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More Data Sufficiency Plugging In In some cases, you may want to either plug in or list values that satisfy statements for value data sufficiency questions.

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1. What is the sum of the units digit and tens digit of positive integer x ? (1) x = 5k where integer k ≥ 2 (2) x divided by 20 has a remainder of 5.

2. If x is a two digit prime integer, what is the value of x ? (1) x is 3 more than a multiple of 4. (2) When x is divided by 7, the remainder is 2.

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Lesson 7

Number Theory Topics Many GMAT questions involve number theory topics. 1. If a, b, c, and d are integers such that 1