1、GRE（ QUANTITATIVE）模拟试卷 31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 y0 and x1. 9 10 Each of the people in three groups gave a rating of Product X on a scale from 1 through 5. For each of the groups, t
3、he table above shows the number of people in the group and the average(arithmetic mean)of their ratings. What is the average of the ratings of the product given by the 100 people in the three groups combined?Give your answer to the nearest 0.1. 11 In the winter, 2/3 of the cardinal sightings, 1/2 of
4、 the junco sightings, and 1/4 of the sparrow sightings were in January. What fraction of the total number of sightings of these three bird species in the winter were in January? 12 The relationship between temperature C, in degrees Celsius, and temperature F, in degrees Fahrenheit, is given by the f
5、ormula F = C+32. If a recipe calls for an oven temperature of 210 degrees Celsius, what is the oven temperature in degrees Fahrenheit? （ A） 320 （ B） 350 （ C） 410 （ D） 420 （ E） 500 13 Of the students in a school, 20 percent are in the science club and 30 percent are in the band. If 25 percent of the
6、students in the school are in the band but are not in the science club, what percent of the students who are in the science club are not in the band? （ A） 5% （ B） 20% （ C） 25% （ D） 60% （ E） 75% 14 Each year, the members of a book club select novels and nonfiction books to read. The club meets 3 time
7、s to discuss each novel and 5 times to discuss each nonfiction book they select. Last year, the club met 52 times and discussed 12 books. How many novels did the club discuss last year? （ A） 2 （ B） 4 （ C） 5 （ D） 7 （ E） 14 15 If -12y, and xy2 listed in order from least to greatest? （ A） xy, x2y, xy2
8、（ B） xy, xy2, x2y （ C） xy2, xy, x2y （ D） xy2, x2y, xy （ E） x2y, xy2, xy 16 The 5 letters in the list G, H, I, J, K are to be rearranged so that G is the 3rd letter in the list and H is not next to G. How many such rearrangements are there? （ A） 60 （ B） 36 （ C） 24 （ D） 12 （ E） 6 17 If j and k are eve
9、n integers and j 3, the nth term in the sequence is the average(arithmetic mean)of the first n - 1 terms in the sequence. What is the value of the 6th term in the sequence? Give your answer as a fraction. 23 For which of the following bird species is the standard deviation of the numbers of sighting
10、s shown for the four seasons least? （ A） Cardinal （ B） Junco （ C） Robin （ D） Sparrow （ E） Wren 24 Which of the following is closest to the average(arithmetic mean)number of cardinal sightings for the 4 seasons? （ A） 12 （ B） 14 （ C） 16 （ D） 18 （ E） 20 25 By what percent did the number of wren sightin
11、gs increase from spring to summer? Give your answer to the nearest whole percent. _% GRE（ QUANTITATIVE）模拟试卷 31答案与解析 1 【正确答案】 B 【试题解析】 You are given that y is a number that is less than -6. Since -6 is less than -5, it follows that y is less than -5. Thus the correct answer is Choice B. This explanat
12、ion uses the following strategy. Strategy 8: Search for a Mathematical Relationship 2 【正确答案】 D 【试题解析】 You are given that x is an integer that is greater than 23 and less than 27. So x could be 24, 25, or 26. If x = 24, the median of the five integers 23,24,26,27, and x is 24. Similarly, if x = 25, t
13、he median of the five integers is 25, and if x = 26, the median of the five integers is 26. So the median of the five integers is 24,25, or 26. Thus the median of the five integers could be less than, equal to, or greater than 25. The correct answer is Choice D. This explanation uses the following s
14、trategies. Strategy 11: Divide into Cases Strategy 13: Determine Whether a Conclusion Follows from the Information Given 3 【正确答案】 C 【试题解析】 Recall that Since p = r2+ t, the value of(-1)p depends on whether r2 + t is odd or even.If r is an odd integer, then r2 is an odd integer and, since r and t are
15、consecutive integers, t is an even integer. In this case, p is the sum of an odd integer and an even integer and is therefore an odd integer.Similarly, if r is an even integer, then r2 is an even integer and t is an odd integer. In this case, p is the sum of an even integer and an odd integer and is
16、 therefore an odd integer.In both cases, p is an odd integer. It follows that( 1)p= -1, and the correct answer is Choice C.This explanation uses the following strategies.Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation Strategy 11: Divide into Cases 4 【正确答案】 C 【试题解析】 The
17、 function/is defined by f( )= 3x2 -x+5. To find the value of f(4), you first need to find the value of x for which = 4, and then you can plug that value of x into f( )= 3x2 -x+5. Solving the equation = 4 for x yields x= 5. Plugging x = 5 into f( )= 3x2 -x+5, youget f(4)= 3(5)2-5+5, or 75. Since Quan
18、tity B is 75, the correct answer is Choice C.This explanation uses the following strategy.Strategy 8: Search for a Mathematical Relationship 5 【正确答案】 A 【试题解析】 The average of the annual salaries of the 21 teachers is , or $37,200. By definition, the median of the 21 annual salaries is the 11th salary
19、 when the 21 salaries are listed in increasing order. Note that in the question you are given that 12 of the 21 salaries are less than $37,000. Thus, when the 21 salaries are listed in increasing order, the first 12 salaries in the list are less than $37,000. Thus the median of the salaries, which i
20、s the 11th salary in the list, is less than $37,000, which is less than the average salary of $37,200. The correct answer is Choice A.This explanation uses the following strategy.Strategy 8: Search for a Mathematical Relationship 6 【正确答案】 A 【试题解析】 Note that if you draw a horizontal line segment from
21、 the point(c, d)to the y-axis, you form a 44-46-90 right triangle, with a horizontal leg of length |c| and a vertical leg of length d, as shown in the figure below. In the triangle, the horizontal leg is opposite the 44 angle and the vertical leg is opposite the 46 angle. Since the 44 angle is small
22、er than the 46 angle, the length of the horizontal leg is less than the length of the vertical leg; that is, |c| d. The correct answer is Choice A.This explanation uses the following strategies.Strategy 4: Translate from a Figure to an Arithmetic or Algebraic RepresentationStrategy 6: Add to a Geome
23、tric FigureStrategy 8: Search for a Mathematical Relationship 7 【正确答案】 B 【试题解析】 Note that the units digit of a product of positive integers is equal to the units digit of the product of the units digits of those integers. In particular, since 824x is a product of x integers, each of which is 824, it
24、 follows that the units digit of 824x is equal to the units digit of 4x. Also, the units digit of 4x is equal to the units digit of the product(4)(units digit of 4x-1).The following table shows the units digit of 4x for some values of x, beginning with x = 2. From the table, you can see that the uni
25、ts digit of 4x alternates, and will continue to alternate, between 4 and 6. Therefore, Quantity A, the number of possible values of the units digit of 824x, is 2. Since Quantity B is 4, the correct answer is Choice B.This explanation uses the following strategies.Strategy 7: Find a PatternStrategy 1
26、2: Adapt Solutions to Related Problems 8 【正确答案】 D 【试题解析】 The two quantities can be simplified as follows.Quantity A: Quantity B: So comparing Quantity A with Quantity B is the same as comparing .Since you are given that x 0 and x 1, and the quantities to be compared involve fractions and exponents,
27、it is reasonable to consider two cases: 0 1. Case 1: 02 1. If x is a number that satisfies x1, then x2x. Therefore , and Quantity B is greater than Quantity A.In one case Quantity A is greater, and in the other case Quantity B is greater. Thus the correct answer is Choice D.This explanation uses the
28、 following strategies.Strategy 5: Simplify an Arithmetic or Algebraic RepresentationStrategy 8: Search for a Mathematical RelationshipStrategy 11: Divide into CasesStrategy 13: Determine Whether a Conclusion Follows from the Information Given 9 【正确答案】 A 【试题解析】 In an isosceles right triangle, both le
29、gs have the same length. The area of an isosceles right triangle with legs of length x is equal to . The area of a square with sides of length s is s2. Since you are given that an isosceles right triangle and a square have the same area R, it follows that , and so x = s.Since is greater than 1, the
30、length of a leg of the triangle is greater than the length of a side of the square. The correct answer is Choice A.This explanation uses the following strategies.Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation Strategy 5: Simplify an Arithmetic or Algebraic Representati
31、on Strategy 8: Search for a Mathematical Relationship 10 【正确答案】 4.1 【试题解析】 For each of the three groups, the sum of the ratings given by the people in the group is equal to the number of people in the group times the average of their ratings. Therefore the sum of the ratings given by the 100 people
32、in the three groups combined is 45(3.8)+ 25(4.6)+ 30(4.2), or 412, and the average of the 100 ratings is 412/100, or 4.12. Therefore, to the nearest 0.1, the correct answer is 4.1. This explanation uses the following strategies. Strategy 1: Translate from Words to an Arithmetic or Algebraic Represen
33、tation Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation 11 【正确答案】 C 【试题解析】 The total number of sightings of cardinals, juncos, and sparrows in the winter was 30+12 + 20, or 62. In the question, you are given that 2/3 of the 30 cardinal sightings, 1/2 of the 12 junco s
34、ightings, and 1/4 of the 20 sparrow sightings were in January. Therefore the number of sightings of these three bird species in January was , or 31, which accounted for 31/62, or 1/2, of the total number of sightings of these three bird species in the winter. Thus the correct answer is Choice C. Thi
35、s explanation uses the following strategies.Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation 12 【正确答案】 C 【试题解析】 You are given the relationship F = C+32. If the temperature is 210 degrees Cel
36、sius, then C = 210 and the temperature F, in degrees Fahrenheit, is (210)+32, or 410. Thus the correct answer is Choice C.This explanation uses the following strategy.Strategy 5: Simplify an Arithmetic or Algebraic Representation 13 【正确答案】 E 【试题解析】 You are given that 20% of the students are in the s
37、cience club, 30% are in the band, and 25% are in the band but are not in the science club. You need to determine what percent of the students who are in the science club are not in the band. The information can be represented in a Venn diagram as follows. From the Venn Diagram, you can see that the
38、30% who are in the band consists of 25% who are in the band but not in the science club, and 5% who are in both the band and the science club. Then you can see that the 20% who are in the science club consists of 5% who are in both the science club and the band, and 15% who are in the science club b
39、ut not in the band, as shown in the revised Venn diagram below.Thus(100%), or 75%, of the students in the science club are not in the band. The correct answer is Choice E.This explanation uses the following strategies.Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation Stra
40、tegy 2: Translate from Words to a Figure or Diagram 14 【正确答案】 B 【试题解析】 Let n represent the number of novels the club discussed last year. Since the club discussed a total of 12 books, the number of nonfiction books is represented by 12 - n. This, together with the information that the club met 3 tim
41、es to discuss each novel and 5 times to discuss each nonfiction book, tells you that the number of times the club met last year can be expressed as 3n + 5(12 - n). Since you know that the club met 52 times last year, it follows that 3n + 5(12 - n)= 52. This equation can be solved for n as follows. 3
42、n+5(l2-n)= 52 3n+60-5n = 52 8 = 2n 4 = n Thus the club discussed 4 novels. The correct answer is Choice B. This explanation uses the following strategies. Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation Strategy 5: Simplify an Arithmetic or Algebraic Representation Stra
43、tegy 8: Search for a Mathematical Relationship 15 【正确答案】 E 【试题解析】 You are given that -1 2y and xy2are negative. So xy is greater than both x2y and xy2. Now you need to determine which is greater, x2y or xy2. You can do this by multiplying the inequality x 3, the nth term in the sequence is the avera
44、ge of the first n - 1 terms in the sequence.The 3rd term, which is the average of the first 2 terms, is , or 1.5.The 4th term, which is the average of the first 3 terms, is , or 1.5.Similarly, the 5th term is , or 1.5, and the 6th term is , or 1.5. Since you must give your answer as a fraction, the
45、correct answer is 3/2.This explanation uses the following strategies.Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation Strategy 7: Find a Pattern 23 【正确答案】 D 【试题解析】 Recall that the standard deviation of the numbers in a list is a measure of the spread of the numbers about
46、 the mean of the numbers. The standard deviation is directly related to the differences x - m between the mean m and each number x in the list. The smaller the differences, the smaller the standard deviation. Thus to answer the question, look at the values of x m for each of the five bird species in
47、 the answer choices and determine which species has the smallest values. Choice A, Cardinal. For cardinals, the numbers of sightings are 30, 18,11, and 20. The mean is approximately 20. Therefore the differences between the mean and the four numbers in the list are approximately 10, 2, 9, and 0. Cho
48、ice B, Junco. For juncos, the numbers of sightings are 12, 0, 0, and 6. The mean is approximately 5. Therefore the differences between the mean and the four numbers in the list are approximately 7, 5, 5, and 1. Choice C, Robin. For robins, the numbers of sightings are 6, 12, 28, and 18. The mean is
49、16, and the differences between the mean and the four numbers in the list are 10, 4, 12, and 2. Choice D, Sparrow. For sparrows, the numbers of sightings are 20, 19, 23, and 22. The mean is 21, and the differences between the mean and the four numbers in the list are 1, 2, 2, and 1. Choice E, Wren. For wrens, the numbers of sightings are 0, 18, 30, and 12. The mean is 15, and the differences between the mean and the four numbers in the list are 15, 3, 15, and 3. Consider how consistently small the differences are for the numbers of sightings of sparrows as compared to t
