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ExplanationRecall that the number of r-member subsets of a set withn!n members is equal to. So Quantity A, the numberr ! n r !of 4-member subsets of S, is equal to 8 7 6 5 70.8! 4! 4! 4 3 2 1 Similarly, Quantity B, the number of 5-member subsets of S,8! 8 7 6 is equal to 56. Thus the correct answer is5!3! 3 2 1 Choice A.This explanation uses the following strategy.Strategy 1: Translate from Words to an Arithmetic or AlgebraicRepresentation-23LT18 GRE Prep Materials[This footer should NOT be printed.] 02/03/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev01

This is a multiple-choice question. To answer this question, selectone answer choice.10. In right triangle ABC, the ratio of the lengths of the two legsis 2 to 5. If the area of triangle ABC is 20, what is the lengthof the hypotenuse?7104 5292 29-24LP18 GRE Prep Material[This footer should NOT be printed. 01/07/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev00

ExplanationThe ratio of the lengths of the legs of right triangle ABC is 2 to 5,so you can represent the lengths as 2x and 5 x, respectively, wherex 0. Since the area of the triangle is 20, it follows that( 2 x )( 5 x ) 20. Solving this equation for x gives x 2. So the2lengths of the two legs are 2 ( 2 ) and 2 ( 5 ) , or 4 and 10,respectively. Therefore, by the Pythagorean theorem, the lengthof the hypotenuse isas follows.42 102 . This square root can be simplified42 102 116 ( 4 )( 29 ) 2 29The correct answer is Choice E, 2 29 .This explanation uses the following strategies.Strategy 5: Simplify an Arithmetic or Algebraic RepresentationStrategy 8: Search for a Mathematical Relationship-25LP18 GRE Prep Material[This footer should NOT be printed.] 05/08/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev03

This is a multiple-choice question. To answer this question, selectone answer choice.11. According to surveys at a company, 20 percent of theemployees owned cell phones in 1994, and 60 percent of theemployees owned cell phones in 1998. From 1994 to 1998,what was the percent increase in the fraction of employeeswho owned cell phones?3 20 30 200 300 -26LP18 GRE Prep Material[This footer should NOT be printed. 01/07/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev00

ExplanationFrom 1994 to 1998, the percent of employees who owned cellphones increased from 20% to 60%. Thus the percent increasein the fraction of employees who owned cell phones was 60% 20% 100% , or 200%. The correct answer is20% Choice D, 200%.This explanation uses the following strategy.Strategy 1: Translate from Words to an Arithmetic or AlgebraicRepresentation-27LP18 GRE Prep Material[This footer should NOT be printed. 01/07/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev00

This is a multiple-choice question. To answer this question, selectone answer choice.12. If t is an integer and 8m 16t , which of the followingexpresses m in terms of t ?2t2t 33 t 32 24t 324 t 3 -28LP18 GRE Prep Material[This footer should NOT be printed. 01/07/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev00

ExplanationNote that all of the choices are expressions of the form 2 raisedto a power. Expressing 8 and 16 as powers of 2, you can rewritett34the given equation 8m 16 as 2 m 2 , which is the same as 23 m 24t. Solving for m and using the rules of exponents, you24tget m 24t 3. The correct answer is Choice D, 24t -3.23This explanation uses the following strategies.Strategy 5: Simplify an Arithmetic or Algebraic RepresentationStrategy 8: Search for a Mathematical Relationship-29LP18 GRE Prep Material[This footer should NOT be printed. 01/07/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev00

This is a multiple-choice question. To answer this question, selectone answer choice.13. Three pumps, P, R, and T, working simultaneously at theirrespective constant rates, can fill a tank in 5 hours. Pumps Pand R, working simultaneously at their respective constantrates, can fill the tank in 7 hours. How many hours will it takepump T, working alone at its constant rate, to fill the tank?1.710.015.017.530.0-30LP18 GRE Prep Material[This footer should NOT be printed. 01/07/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev00

Explanation1of the tank in711 hour. Working simultaneously, the three pumps fill of the tank51 12in 1 hour. Therefore, working alone, pump T fills , or, of5 73535hours, orthe tank in 1 hour. Thus, working alone, pump T takes217.5 hours, to fill the tank. The correct answer is Choice D, 17.5.Working simultaneously, pumps P and R fillThis explanation uses the following strategies.Strategy 1: Translate from Words to an Arithmetic or AlgebraicRepresentationStrategy 8: Search for a Mathematical Relationship-31LP18 GRE Prep Material[This footer should NOT be printed. 01/07/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev00

This is a multiple-choice question. To answer this question, selectone answer choice.14. The perimeter of a flat rectangular lawn is 42 meters. Thewidth of the lawn is 75 percent of its length. What is thearea of the lawn, in square meters?40.596108192432-32LP18 GRE Prep Material[This footer should NOT be printed. 01/07/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev00

ExplanationLet s and t be the width and length, in meters, of the lawn,respectively. Then the perimeter is 2s 2t meters, so that2 s 2t 42. Also, the relationship between the width and thelength can be translated as s 0.75t. Substituting 0.75t for sin the equation for the perimeter yields 42 2 0.75t 2t 3.5t.42 12 and s 0.75 12 9. Since st 108, the area3.5of the lawn is 108 square meters. The correct answer isChoice C, 108.So t This explanation uses the following strategies.Strategy 1: Translate from Words to an Arithmetic or AlgebraicRepresentationStrategy 8: Search for a Mathematical Relationship-33LP18 GRE Prep Material[This footer should NOT be printed. 01/07/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev00

This is a multiple-choice question. To answer this question, selectone answer choice.15. The greatest of the 21 positive integers in a certain listis 16. The median of the 21 integers is 10. What is the leastpossible average (arithmetic mean) of the 21 integers?45678-34LP18 GRE Prep Material[This footer should NOT be printed. 01/07/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev00

ExplanationYou are given that the median of the 21 positive integers is 10and the greatest of the 21 integers is 16. This means that whenthe 21 integers are listed in order from least to greatest, the 1st through 10th integers are between 1 and 10, inclusive; the 11th integer is 10; the 12th through 20th integers are between 10 and 16,inclusive; and the 21st integer is 16.The least possible average of the 21 integers would be achievedby using the least possible value of each integer as described abovein the reordered list: the 1st through 10th integers would each be 1; the 11th integer would be 10; the 12th through 20th integers would each be 10; and the 21st integer would be 16.For the least possible integers, the sum is 10 1 10 9 10 16, or 126. Therefore the least possibleaverage is126, or 6. The correct answer is Choice C, 6.21-35LP18 GRE Prep Material[This footer should NOT be printed. 01/07/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev00

This explanation uses the following strategies.Strategy 1: Translate from Words to an Arithmetic or AlgebraicRepresentationStrategy 8: Search for a Mathematical Relationship-36LP18 GRE Prep Material[This footer should NOT be printed. 01/07/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev00

This is a multiple-choice question. To answer this question, selectone answer choice.16. If x and y are integers and x ( 2 )( 3)( 4 )( 5)( 7 )(11)(13) ,39 ywhich of the following could be the value of y ?15283864143-37LP18 GRE Prep Material[This footer should NOT be printed.] 05/08/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev03

ExplanationTo simplify the equation x ( 2 )( 3)( 4 )( 5)( 7 )(11)(13) , divide the39 ynumerator and denominator of the fraction by 39 to get2 )( 4 )( 5 )( 7 )(11)(x . From the simplified equation, you can seeythat x is an integer if and only if y is a factor of ( 2 )( 4 )( 5 )( 7 )(11) .To answer the question, you need to check each of the answerchoices until you find the one that is a factor of ( 2 )( 4 )( 5 )( 7 )(11) .Choice A: 15. Since 15 ( 3)( 5 ) and 3 is not a factor of( 2 )( 4 )( 5)( 7 )(11) , neither is 15.Choice B: 28. Since 28 ( 4 )( 7 ) and both 4 and 7 are factors of( 2 )( 4 )( 5)( 7 )(11) , so is 28.You can check the other choices to confirm that none of them is afactor of ( 2 )( 4 )( 5 )( 7 )(11) . The correct answer is Choice B, 28.-38LP18 GRE Prep Material[This footer should NOT be printed.] 05/08/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev03

This explanation uses the following strategies.Strategy 5: Simplify an Arithmetic or Algebraic RepresentationStrategy 8: Search for a Mathematical Relationship-39LP18 GRE Prep Material[This footer should NOT be printed. 01/07/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev00

This is a multiple-choice question. To answer this question, selectone answer choice.17. Of the 40 specimens of bacteria in a dish, 3 specimens havea certain trait. If 5 specimens are to be selected from the dishat random and without replacement, which of the followingrepresents the probability that only 1 of the 5 specimensselected will have the trait?-40LP18 GRE Prep Material[This footer should NOT be printed. 01/07/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev00

5 1 40 3 5 1 40 5 40 3 40 5 3 37 1 4 40 3 3 37 1 4 40 5 -41LP18 GRE Prep Material[This footer should NOT be printed. 01/07/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev00

Explanation n In the context of this problem, represents the number of ways r r specimens can be selected without replacement fromn specimens.The probability that only 1 of the 5 specimens selected from the40 specimens will have the trait is equal tonumber of ways to select 5 specimens, only 1 of which has the trait.number of ways to select 5 specimensThe number of ways 5 specimens can be selected from the 40 40 specimens is . To select 5 specimens, only 1 of which 5 has the trait, you have to select 1 of the 3 specimens that havethe trait and select 4 of the 37 specimens that do not have the trait. 3 37 The number of such selections is the product . So the 1 4 probability that only 1 of the 5 specimens selected will have the 3 37 1 4 trait is represented by . 40 5 -42LP18 GRE Prep Material[This footer should NOT be printed. 06/03/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev04

3 37 1 4 The correct answer is Choice E, . 40 5 This explanation uses the following strategies.Strategy 1: Translate from Words to an Arithmetic or AlgebraicRepresentationStrategy 8: Search for a Mathematical Relationship-43LT18 GRE Prep Materials[This footer should NOT be printed.] 02/03/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev01

This is a multiple-choice question. To answer this question, selectall the answer choices that apply.18. Two different positive integers x and y are selected from theodd integers that are less than 10. If z x y and z is lessthan 10, which of the following integers could be the sumof x, y, and z ?Indicate all such integers.89101214151618-44LP18 GRE Prep Material[This footer should NOT be printed. 06/03/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev04

ExplanationThe only pairs of positive odd integers x and y that are less than10 and satisfy the condition x y 10 are the pair 1 and 3, the pair1 and 5, the pair 1 and 7, and the pair 3 and 5. Since z x y, itfollows that the sum of x, y, and z is equal to 2 z. The sum for eachof the four possible pairs is found as follows. 1 and 3: z 4, and the sum of x, y, and z is 2 z , or 8. 1 and 5: z 6, and the sum of x, y, and z is 12. 1 and 7: z 8, and the sum of x, y, and z is 16. 3 and 5: z 8, and the sum of x, y, and z is 16.Thus the only possible values of the sum of x, y, and z are 8, 12,and 16. The correct answer consists of Choices A, D, and G; thatis, 8, 12, and 16.This explanation uses the following strategies.Strategy 1: Translate from Words to an Arithmetic or AlgebraicRepresentationStrategy 8: Search for a Mathematical RelationshipStrategy 11: Divide into Cases-45LP18 GRE Prep Material[This footer should NOT be printed. 06/16/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev05

This is a multiple-choice question. To answer this question, selectall the answer choices that apply.19. For a certain probability experiment, the probability1that event A will occur is and the probability that21event B will occur is . Which of the following values3could be the probability that the event A B (that is, theevent A or B, or both) will occur?Indicate all such values.131234-46LP18 GRE Prep Material[This footer should NOT be printed.] 05/08/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev03

ExplanationSince you know that the probability of event A is1and the21but you are not given any information3about the relationship between events A and B, you can computeonly the minimum possible value and the maximum possible valueof the probability of the event A B.probability of event B isThe probability of A B is least if B is a subset of A; in that case,1the probability of A B is just the probability of A, or .2The probability of A B is greatest if A and B do not intersectat all; in that case, the probability of A B is the sum of the1 1 5probabilities of A and B, or .2 3 6With no further information about A and B, the probability that A15or B, or both, will occur could be any number from to . Of the2613answer choices given, only and are in this interval. The correct2413answer consists of Choices B and C; that is, and .24-47LP18 GRE Prep Material[This footer should NOT be printed. 01/07/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev00

This explanation uses the following strategies.Strategy 8: Search for a Mathematical RelationshipStrategy 11: Divide into Cases-48LP18 GRE Prep Material[This footer should NOT be printed. 01/07/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev00

This is a numeric entry question. To answer this question, entera fraction.20. If a and b are the two solutions of the equation 1 a 1 b x 2 5 x 4 0, what is the value of ?ab Give your answer as a 45678901234567890123456789-49LP18 GRE Prep Material[This footer should NOT be printed.] 05/08/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev03

ExplanationFactoring the quadratic equation x 2 5 x 4 0, you get( x 1)( x 4 ) 0, so the two solutions are either a 1 and b 4or a 4 and b 1. Note that a and b are interchangeable in the 1 a 1 b expression , so the value of the expression will a b be the same regardless of the choices of a and b. Thus 1 a 1 b 1 1 1 4 5 52 () ,14ab 4 2and the correct answer is5.2This explanation uses the following strategies.Strategy 5: Simplify an Arithmetic or Algebraic RepresentationStrategy 8: Search for a Mathematical Relationship-50LP18 GRE Prep Material[This footer should NOT be printed. 06/24/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev06

This is a numeric entry question. To answer this question, enteran integer or a decimal.21. From 2011 to 2012, Jack’s annual salary increased by10 percent and Arnie’s annual salary decreased by 5 percent.If their annual salaries were equal in 2012, then Arnie’sannual salary in 2011 was what percent greater than Jack’sannual salary in 2011 ?Give your answer to the nearest 0.1 456789.0123456789.0123456789.0123456789-51LP18 GRE Prep Material[This footer should NOT be printed. 06/24/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev06

ExplanationLet k be Jack’s annual salary in 2011, and let r be Arnie’s annualsalary in 2011. Then Jack’s annual salary in 2012 was 1.1k , andArnie’s was 0.95r. Since their salaries in 2012 were equal to eachother, you have 0.95r 1.1k . Solving the equation for r, you get1.11.1r k . Since 1.1578. . . , it follows that, rounded to the0.950.95nearest 0.1 , Arnie’s annual salary in 2011 was 15.8 greater thanJack’s annual salary in 2011. The correct answer is 15.8.This explanation uses the following strategies.Strategy 1: Translate from Words to an Arithmetic or AlgebraicRepresentationStrategy 5: Simplify an Arithmetic or Algebraic Representation-52LP18 GRE Prep Material[This footer should NOT be printed. 01/07/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev00

Data Interpretation SetQuestions 22 to 25 are based on the following data.-53LP18 GRE Prep Material[This footer should NOT be printed. 02/03/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev01

This is a multiple-choice question. To answer this question, selectone answer choice.22. Which of the following is closest to the percent of Internetusers in Europe who were in countries other than Germany,France, Britain, Italy, and Spain?30 34 38 42 46 -54LP18 GRE Prep Material[This footer should NOT be printed. 01/07/2015LP18 GRE Chapter 7 Set 2 Answers&Explan rev00

ExplanationThe distribution of Internet users in Europe is given in the bargraph. In the graph, the countries in Europe other than Germany,France, Britain, Italy, and Spain are grouped into two areas:Eastern Europe and Rest of Europe. According to the graph,there were approximately 1.9 million users in Eastern Europeand 6.3 million

Practice Set 2 This document begins with the answer key for questions found in the Chapter 7 Practice Set 2 Questions document. Following the answer key are the complete explanations for each question. If you wish to work through the questions before consulting the answers and explanations, please use the Chapter 7 Practice Set 2 Questions .