1、GRE（ QUANTITATIVE）模拟试卷 30及答案与解析 0 Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices: (A)Quantity A is greater. (B)Quantity B is greater. (C)The two quantities are equal.
2、(D)The relationship cannot be determined from the information given. A symbol that appears more than once in a question has the same meaning throughout the question. 1 x5 x4 2 Quantity A Quantity B (x + 4)(y + 3) (x + 3)(y + 4) 3 represents the decimal in which the digit b is repeated without end.Qu
3、antity A Quantity B 1.0 4 A company plans to manufacture two types of hammers, type R and type S. The cost of manufacturing each hammer of type S is $0.05 less than twice the cost of manufacturing each hammer of type R. 5 6 List X: 2, 5,s, t List Y: 2, 5, t The average(arithmetic mean)of the numbers
4、 in list X is equal to the average of the numbers in list Y. Quantity A Quantity B s 0 7 The radius of circle A is 12 greater than the radius of circle B. 8 Quantity A Quantity Bx 120 9 S = 1,2, 3, 4, 5,6, 7, 8 10 Which of the following is closest to the percent of Internet users in Europe who were
5、in countries other than Germany, France, Britain, Italy, and Spain? （ A） 30% （ B） 34% （ C） 38% （ D） 42% （ E） 46% 11 In right triangle ABC, the ratio of the lengths of the two legs is 2 to 5. If the area of triangle ABC is 20, what is the length of the hypotenuse? （ A） 7 （ B） 10 （ C） （ D） （ E） 12 Acc
6、ording to surveys at a company, 20 percent of the employees owned cell phones in 1994, and 60 percent of the employees owned cell phones in 1998. From 1994 to 1998, what was the percent increase in the fraction of employees who owned cell phones? （ A） 3% （ B） 20% （ C） 30% （ D） 200% （ E） 300% 13 If t
7、 is an integer and 8m = 16t, which of the following expresses m in terms of t ? （ A） 2t （ B） 2t-3 （ C） 23(t-3) （ D） 24t-3 （ E） 24(t-3) 14 Three pumps, P, R, and T, working simultaneously at their respective constant rates, can fill a tank in 5 hours. Pumps P and R, working simultaneously at their re
8、spective constant rates, can fill the tank in 7 hours. How many hours will it take pump T, working alone at its constant rate, to fill the tank? （ A） 1.7 （ B） 10.0 （ C） 15.0 （ D） 17.5 （ E） 30.0 15 The perimeter of a flat rectangular lawn is 42 meters. The width of the lawn is 75 percent of its lengt
9、h. What is the area of the lawn, in square meters? （ A） 40.5 （ B） 96 （ C） 108 （ D） 192 （ E） 432 16 The greatest of the 21 positive integers in a certain list is 16. The median of the 21 integers is 10. What is the least possible average(arithmetic mean)of the 21 integers? （ A） 4 （ B） 5 （ C） 6 （ D） 7
10、 （ E） 8 17 It x and y are integers and x = , which or the following could be the value of y ? （ A） 15 （ B） 28 （ C） 38 （ D） 64 （ E） 143 18 Of the 40 specimens of bacteria in a dish, 3 specimens have a certain trait. If 5 specimens are to be selected from the dish at random and without replacement, wh
11、ich of the following represents the probability that only 1 of the 5 specimens selected will have the trait? 19 Two different positive integers x and y are selected from the odd integers that are less than 10. If z = x + y and z is less than 10, which of the following integers could be the sum of x,
12、 y, and z ? Indicate all such integers. A 8 B 9 C 10 D 12 E 14 F 15 G 16 H 18 20 For a certain probability experiment, the probability that event A will occur is 1/2 and the probability that event B will occur is 1/3. Which of the following values could be the probability that the event A B(that is,
13、 the event A or B, or both)will occur? Indicate all such values. 21 If a and b are the two solutions of the equation x2 - 5x + 4 = 0, what is the value of ? Give your answer as a fraction. 22 From 2011 to 2012, Jacks annual salary increased by 10 percent and Arnies annual salary decreased by 5 perce
14、nt. If their annual salaries were equal in 2012, then Amies annual salary in 2011 was what percent greater than Jacks annual salary in 2011 ? Give your answer to the nearest 0.1 percent. _% 23 Approximately what was the range of the numbers of Internet users in the seven areas of Europe shown in the
15、 bar graph? （ A） 6.5 million （ B） 5.5 million （ C） 3.5 million （ D） 3.0 million （ E） 2.5 million 24 The number of Internet users in the United States was approximately how many times the number of Internet users in Italy? （ A） 5 （ B） 15 （ C） 20 （ D） 25 （ E） 35 25 Based on the information given, whic
16、h of the following statements about Internet use in year X must be true? Indicate all such statements. （ A） The United States had more Internet users than all other countries in the world combined. （ B） Spain had fewer Internet users than any country in Eastern Europe. （ C） Germany and France combin
17、ed had more than 1/3 of the Internet users in Europe. GRE（ QUANTITATIVE）模拟试卷 30答案与解析 1 【正确答案】 B 【试题解析】 If x 0. Thus x5 0. In one case, the quantities are equal, and in the other case, Quantity A is greater. Therefore the correct answer is Choice D.This explanation uses the following strategies.Strat
18、egy 1: Translate from Words to an Arithmetic or Algebraic RepresentationStrategy 10: Trial and ErrorStrategy 13: Determine Whether a Conclusion Follows from the Information Given 7 【正确答案】 A 【试题解析】 Since the radius of circle A is 12 greater than the radius of circle B, if the radius of circle B is r,
19、 then the radius of circle A is r + 12. The circumference of circle A minus the circumference of circle Bis 2(r+ 12)-2r, which simplifies to 24. Since 3, it follows that 24 24(3); that is, 24 72. Since Quantity B is 72, the correct answer is Choice A. This explanation uses the following strategies.
20、Strategy 8: Search for a Mathematical Relationship Strategy 9: Estimate 8 【 正确答案】 B 【试题解析】 Note that there are four angles in the figure: the three interior angles of triangle ABC and the exterior angle at vertex A. Since the measure of the exterior angle at vertex A is x degrees, it follows that th
21、e measure of interior angle A is(180 - x). Also, since AB = BC, it follows that triangle ABC is isosceles and the measures of interior angles A and C are equal. Therefore the measure of interior angle C is also(180 - x). Since the sum of the measures of the interior angles of a triangle is 180 and y
22、ou are given that the measure of interior angle B is 40, it follows that 40 +(180 -x)+(180 -x)= 180. Solving the equation for x gives x = 110. Since Quantity B is 120, the correct answer is Choice B. This explanation uses the following strategies. Strategy 4: Translate from a Figure to an Arithmetic
23、 or Algebraic Representation Strategy 8: Search for a Mathematical Relationship 9 【正确答案】 A 【试题解析】 Recall that the number of r-member subsets of a set with n members is equal to . So Quantity A is equal to = 70. Similarly, Quantity B is equal to = 56. Thus the correct answer is Choice A.This explanat
24、ion uses the following strategy.Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation 10 【正确答案】 A 【试题解析】 The distribution of Internet users in Europe is given in the bar graph. In the graph, the countries in Europe other than Germany, France, Britain, Italy, and Spain are gro
25、uped into two areas: Eastern Europe and Rest of Europe. According to the graph, there were approximately 1.9 million users in Eastern Europe and 6.3 million users in Rest of Europe. Thus the number of users in these two areas combined was approximately 1.9 + 6.3, or 8.2 million.From the title of the
26、 bar graph, the total number of Internet users in Europe was 27.3 million. Therefore the number of users in the two areas combined, expressed as a percent of all users in Europe, is about (100%), or approximately 30%.The answer choice that is closest is 30%. The correct answer is Choice A.This expla
27、nation uses the following strategies.Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation Strategy 5: Simplify an Arithmetic or Algebraic Representation Strategy 9: Estimate 11 【正确答案】 E 【试题解析】 The ratio of the lengths of the legs of right triangle ABC is 2 to 5, so you ca
28、n represent the lengths as 2x and 5x, respectively, where x0. Since the area of the triangle is 20, it follows that = 20. Solving this equation for x gives x = 2. So the lengths of the two legs are 2(2)and 2(5), or 4 and 10, respectively. Therefore, by the Pythagorean theorem, the length of the hypo
29、tenuse is . This square root can be simplified as follows. The correct answer is Choice E.This explanation uses the following strategies.Strategy 5: Simplify an Arithmetic or Algebraic Representation Strategy 8: Search for a Mathematical Relationship 12 【正确答案】 D 【试题解析】 From 1994 to 1998, the percent
30、 of employees who owned cell phones increased from 20% to 60%. Thus the percent increase in the fraction of employees who owned cell phones was (100%), or 200%. The correct answer is Choice D.This explanation uses the following strategy.Strategy 1: Translate from Words to an Arithmetic or Algebraic
31、Representation 13 【正确答案】 D 【试题解析】 Note that all of the choices are expressions of the form 2 raised to a power. Expressing 8 and 16 as powers of 2, you can rewrite the given equation 8m = 16t as 23m =(24)t, which is the same as 23m = 24t. Solving for m and using the rules of exponents, you get m = =
32、 24t-3. The correct answer is Choice D.This explanation uses the following strategies.Strategy 5: Simplify an Arithmetic or Algebraic Representation Strategy 8: Search for a Mathematical Relationship 14 【正确答案】 D 【试题解析】 Working simultaneously, pumps P and R fill 1/7 of the tank in 1 hour. Working sim
33、ultaneously, the three pumps fill 1/5 of the tank in 1 hour. Therefore, working alone, pump T fills , or 2/35, of the tank in 1 hour. Thus, working alone, pump T takes 35/2 hours, or 17.5 hours, to fill the tank. The correct answer is Choice D. This explanation uses the following strategies.Strategy
34、 1: Translate from Words to an Arithmetic or Algebraic Representation Strategy 8: Search for a Mathematical Relationship 15 【正确答案】 C 【试题解析】 Let s and t be the width and length, in meters, of the lawn, respectively. Then the perimeter is 2s + 2t meters, so that 2s + 2t = 42. Also, the relationship be
35、tween the width and the length can be translated as s = 0.75t. Substituting 0.75t for 5 in the equation for the perimeter yields 42 = 2(0.75t)+ 2t = 3.5t. So t = = 12 and s =(0.75)(12)= 9. Since st = 108, the area of the lawn is 108 square meters. The correct answer is Choice C.This explanation uses
36、 the following strategies.Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation Strategy 8: Search for a Mathematical Relationship 16 【正确答案】 C 【试题解析】 You are given that the median of the 21 positive integers is 10 and the greatest of the 21 integers is 16. This means that whe
37、n the 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 ach
38、ieved by using the least possible value of each integer as described above in 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 i
39、s(10)(1)+ 10 +(9)(10)+ 16, or 126. Therefore the least possible average is 126/21, or 6. The correct answer is Choice C. This explanation uses the following strategies. Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation Strategy 8: Search for a Mathematical Relationship 17
40、 【正确答案】 B 【试题解析】 To simplify the equation x = , divide the numerator and denominator of the fraction by 39 to get x = . From the simplified equation, you can see that 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 answer choices
41、 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 a
42、factor of(2)(4)(5)(7)(11). The correct answer is Choice B.This explanation uses the following strategies.Strategy 5: Simplify an Arithmetic or Algebraic Representation Strategy 8: Search for a Mathematical Relationship 18 【正确答案】 E 【试题解析】 In the context of this problem, represents the number of ways
43、r specimens can be selected without replacement from n specimens.The probability that only 1 of the 5 specimens selected from the 40 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 s
44、pecimens can be selected from the 40 specimens is . To select 5 specimens, only 1 of which has the trait, you have to select 1 of the 3 specimens that have the trait and select 4 of the 37 specimens that do not have the trait. The number of such selections is the product .So the probability that onl
45、y 1 of the 5 specimens selected will have the trait is represented by . The correct answer is Choice E. This explanation uses the following strategies.Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation Strategy 8: Search for a Mathematical Relationship 19 【正确答案】 A， D， G 【试
46、题解析】 The only pairs of positive odd integers x and y that are less than 10 and satisfy the condition x + y and z is equal to 2z. The sum for each of the four possible pairs is found as follows. 1 and 3: z = 4, and the sum of x, y, and z is 2z, or 8. 1 and 5: z = 6, and the sum of x, y, and z is 12.
47、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. This explanation uses the following strategies. Strategy 1: Translate fro
48、m Words to an Arithmetic or Algebraic Representation Strategy 8: Search for a Mathematical Relationship Strategy 11: Divide into Cases 20 【正确答案】 B， C 【试题解析】 Since you know that the probability of event A is 1/2 and the probability of event B is 1/3 but you are not given any information about the rel
49、ationship between events A and B, you can compute only the minimum possible value and the maximum possible value of the probability of the event A B.The probability of A B is least if B is a subset of A; in that case, the probability of A B is just the probability of A, or 1/2.The probability of A B is greatest if A and B do not intersect at all; in that case, the probability of A B is the sum of the probabilities of A and B, or .With no further information about A and B, the probability that A or B, or both, will occur could be any number from 1/2 to 5/6. Of the
