1、GRE（ QUANTITATIVE）综合模拟试卷 16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 2 3 4 5 6 7 8 At Store T, the dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008 ? Give your
3、answer to the nearest 0.1 percent. _% 9 Based on the information given, which of the following statements must be true? Indicate all such statements. （ A） For 2008 the dollar amount of sales at Store R was greater than that at each of the other four stores. （ B） The dollar amount of sales at Store S
4、 for 2008 was 22 percent less than that for 2006. （ C） The dollar amount of sales at Store R for 2008 was more than 17 percent greater than that for 2006. 10 Compute 4 + . 11 Compute . 12 Find the length, to the nearest 0.01, of the hypotenuse of a right triangle with legs of length 21 and 54; that
5、is, use the Pythagorean theorem and calculate . 13 Compute(-15)3. 14 Convert 6 miles per hour to feet per second. 15 At a fund-raising event, 43 participants donated $60 each, 21 participants donated $80 each, and 16 participants donated $100 each. What was the average(arithmetic mean)donation per p
6、articipant, in dollars? 16 For each integer n 1, let A(n)denote the sum of the integers from 1 to n. For example, A(100)= l + 2 + 3+100 = 5,050. What is the value of A(200)? （ A） 10,100 （ B） 15,050 （ C） 15,150 （ D） 20,100 （ E） 21,500 17 Which of the following integers CANNOT be expressed as the sum
7、of two prime numbers? （ A） 8 （ B） 9 （ C） 10 （ D） 11 （ E） 12 18 When the positive integer n is divided by 45, the remainder is 18. Which of the following must be a divisor of n ? （ A） 11 （ B） 9 （ C） 7 （ D） 6 （ E） 4 19 Points A, B, C, and D are on the number line above, and AB = CD = (BC). What is the
8、 coordinate of C ? 20 Which of the following represents the total dollar amount that a customer would have to pay for an item that costs s dollars plus a sales tax of 8 percent, in terms of s? （ A） s/0.08 （ B） s/1.08 （ C） s/8 （ D） 0.08s （ E） 1.08s 21 Marie earned $0.75 for every mile she walked in a
9、 charity walkathon. If she earned a total of $18.00 at that rate, how many miles did she walk? （ A） 13.5 （ B） 17.5 （ C） 21 （ D） 22.5 （ E） 24 22 Which of the following operations carried out on both the numerator and the denominator of a fraction will always produce an equivalent fraction? Indicate a
10、ll such operations. （ A） Adding 2 （ B） Multiplying by 5 （ C） Dividing by 100 23 If |z| 1, which of the following statements must be true? Indicate all such statements. （ A） z2l （ B） z2z （ C） z3z 24 In a certain medical group, Dr. Schwartz schedules appointments to begin 30 minutes apart, Dr. Ramirez
11、 schedules appointments to begin 25 minutes apart, and Dr. Wu schedules appointments to begin 50 minutes apart. All three doctors schedule their first appointments to begin at 8:00 in the morning, which are followed by their successive appointments throughout the day without breaks. Other than at 8:
12、00 in the morning, at what times before 1:30 in the afternoon do all three doctors schedule their appointments to begin at the same time? Indicate all such times. A 9:30 in the morning B 10:00 in the morning C 10:30 in the morning D 11:00 in the morning E 11:30 in the morning F 12:00 noon G 12:30 in
13、 the afternoon H 1:00 in the afternoon GRE（ QUANTITATIVE）综合模拟试卷 16答案与解析 1 【正确答案】 B 【试题解析】 By dividing 4 by 11, you get the decimal form D = 0.363636., where the sequence of two digits “36“ repeats without end. Continuing the repeating pattern, you see that the 1st digit, the 3rd digit, the 5th digit
14、, and every subsequent odd-numbered digit to the right of the decimal point is 3. Therefore, Quantity A, the 25th digit to the right of the decimal point, is 3. Since Quantity A is 3 and Quantity B is 4, the correct answer is Choice B. This explanation uses the following strategy. Strategy 7: Find a
15、 Pattern 2 【正确答案】 C 【试题解析】 You can simplify both quantities. Quantity A can be simplified as follows: Quantity B can be simplified as follows: Thus the correct answer is Choice C.This explanation uses the following strategy.Strategy 5: Simplify an Arithmetic or Algebraic Representation 3 【正确答案】 D 【试
16、题解析】 In the question, you are given that x = 7n + 2 and y = 6n + 3. Substituting the given expressions for x and y in Quantity A, you get x + y = 13n + 5. Using trial and error, you can compare Quantity A, the ones digit of 13n + 5, and Quantity B, 5, by plugging in a few values for the positive int
17、eger n. If n = 1, then x + y = 18 and the ones digit is 8, which is greater than 5. So in this case Quantity A is greater than Quantity B. If n = 2, then x+y = 3l and the ones digit is 1, which is less than 5. So in this case Quantity B is greater than Quantity A. Since in one case Quantity A is gre
18、ater than Quantity B, and in the other case Quantity B is greater than Quantity A, you can conclude that the correct answer is Choice D. This explanation uses the following strategies. Strategy 10: Trial and Error Strategy 13: Determine Whether a Conclusion Follows from the Information Given 4 【正确答案
19、】 A 【试题解析】 If you substitute the given numbers into the expressions in Quantities A and B, you can compare them. Substituting in Quantity A gives(r - s)4 =(2 -(-7)4 = 94. Substituting in Quantity B gives r4 - s4 = 24 -(-7)4= 24 - 74. Without further calculation, you see that Quantity A is positive a
20、nd Quantity B is negative. Thus the correct answer is Choice A. This explanation uses the following strategy. Strategy 5: Simplify an Arithmetic or Algebraic Representation 5 【正确答案】 A 【试题解析】 Try plugging the first few even negative integers into the expressions in Quantity A and Quantity B to see if
21、 a pattern emerges. From these three examples, it looks like Quantity A and Quantity B may always be reciprocals of each other, with Quantity A greater than 1 and Quantity B less than 1. You can see this as follows.If n is an even negative integer, then n can be expressed as 2k where A: is a positiv
22、e integer. Substituting -2k for n in Quantity A and Quantity B, you get that Quantity A is . Since for all positive integers k the value of 32k is greater than 1 and the value of(1/3)2k is less than 1, it follows that the correct answer is Choice A.This explanation uses the following strategies.Stra
23、tegy 7: Find a PatternStrategy 8: Search for a Mathematical Relationship 6 【正确答案】 D 【试题解析】 Quantity A is 20 percent of yesterdays price of the table. Since yesterdays price is not given, you cannot calculate this quantity. Similarly, you cannot calculate Quantity B. In the absence of further informa
24、tion with which to compare the two quantities, the correct answer is Choice D. This explanation uses the following strategy. Strategy 13: Determine Whether a Conclusion Follows from the Information Given 7 【正确答案】 C 【试题解析】 Translating the given information, you can calculate Quantity A, the number of
25、 pages the photocopier copied in the 5 hours. Copying at the rate of 2 pages every 3 seconds is the same as copying at a rate of 40 pages every 60 seconds, or 40 pages per minute. This rate is the same as copying 2,400 pages every hour, or 12,000 pages in 5 hours. Since Quantity A is equal to 12,000
26、 and Quantity B is 12,000, the correct answer is Choice C. This explanation uses the following strategy. Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation 8 【正确答案】 108.7 【试题解析】 If A is the dollar amount of sales at Store T for 2007, then 8 percent of A, or 0.08A, is the a
27、mount of decrease from 2007 to 2008. Thus A - 0.08A = 0.92A is the dollar amount for 2008. Therefore, the desired percent can be obtained by dividing A by 0.92A, which equals = 1.0869565Expressed as a percent and rounded to the nearest 0.1 percent, this number is 108.7%. Thus the correct answer is 1
28、08.7%(or equivalent).This explanation uses the following strategies.Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation Strategy 5: Simplify an Arithmetic or Algebraic Representation 9 【正确答案】 C 【试题解析】 For Choice A, since the only data given in Figure 8 are percent change
29、s from year to year, there is no way to compare the actual dollar amount of sales at the stores for 2008 or for any other year. Even though Store R had the greatest percent increase from 2006 to 2008, its actual dollar amount of sales for 2008 may have been much smaller than that for any of the othe
30、r four stores, and therefore Choice A is not necessarily true. For Choice B, even though the sum of the two percent decreases would suggest a 22 percent decrease, the bases of the percents are different. If B is the dollar amount of sales at Store S for 2006, then the dollar amount for 2007 is 93 pe
31、rcent of B, or 0.93B, and the dollar amount for 2008 is given by(0.85)(0.93)B, which is 0.7905B. Note that this represents a percent decrease of 100 - 79.05 = 20.95 percent, which is not equal to 22 percent, and so Choice B is not true. For Choice C, if C is the dollar amount of sales at Store R for
32、 2006, then the dollar amount for 2007 is given by 1.05C and the dollar amount for 2008 is given by(1.12)(1.05)C, which is 1.176C. Note that this represents a 17.6 percent increase, which is greater than 17 percent, so Choice C must be true. Therefore the correct answer consists of only Choice C(The
33、 dollar amount of sales at Store R for 2008 was more than 17 percent greater than that for 2006). This 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 Representa
34、tion Strategy 5: Simplify an Arithmetic or Algebraic Representation Strategy 13: Determine Whether a Conclusion Follows from the Information Given Strategy 14: Determine What Additional Information Is Sufficient to Solve a Problem 10 【正确答案】 7.365 【试题解析】 11 【正确答案】 -0.2528571 【试题解析】 ExplanationSince d
35、ivision takes precedence over addition in the order of operations, you need to override that precedence in order to compute this fraction. Here are two ways to do that. You can use the parentheses for the addition in the numerator, enteringIncidentally, the exact value of the expression is the repea
36、ting decimal , where the digits 285714 repeat without end, but the calculator rounds the decimal to -0.2528571. 12 【正确答案】 57.94 【试题解析】 . This is because the square root would take precedence over the multiplication in the order of operations. Note that parentheses could be used, as in , but they are
37、 not necessary because the multiplications already take precedence over the addition.Incidentally, the exact answer is a nonterminating, nonrepeating decimal, or an irrational number, but the calculator rounds the decimal to 57.939624. Finally, note that the problem asks for the answer to the neares
38、t 0.01, so the correct answer is 57.94. 13 【正确答案】 -3,375 【试题解析】 Enter 15 to get -3,375. 14 【正确答案】 8.8 【试题解析】 The solution to this problem uses the conversion factors 1 mile = 5,280 feet and 1 hour = 3,600 seconds as follows:15 【正确答案】 73.25 【试题解析】 The solution to this problem is to compute the weight
39、ed meanWhen the button is first used, the number in the calculator display is stored in memory and an M appears to the left of the display to show that the memory function is in use. Each subsequent use of the button adds the number in the current display to the number stored in memory and replaces
40、the number stored in memory by the sum. When the button is pressed in the computation above, the current value in memory, 5,860, is displayed. To clear the memory, use the button, and the M next to the display disappears. 16 【正确答案】 D 【试题解析】 In the question, you are given that A(n)is equal to the sum
41、 of the integers from 1 to n, so A(200)= l+2+3+100+101+102+103+200. In order to be able to use the given value of A(100)= 5,050, you can rewrite the sum as A(200)= A(100)+101 + 102+103+200 = A(100)+(100+l)+(100+2)+(100+3)+(100+100) = A(100)+(l+2+3+100)+(100)(100) = A(100)+A(100)+(100)(100) = 5,050 +
42、 5,050+10,000 = 20,100 Thus the correct answer is Choice D. This explanation uses the following strategy. Strategy 12: Adapt Solutions to Related Problems 17 【正确答案】 D 【试题解析】 Trying to write each answer choice as a sum of two prime numbers by trial and error, you get: Choice A: 8 = 3 + 5 Choice B: 9
43、= 2 + 7 Choice C: 10 = 3 + 7 Choice D: 11 = 1 +10 = 2 + 9 = 3 + 8 = 4 + 7 = 5 + 6 Choice E: 12 = 5 + 7 Of the answer choices given, only 11 cannot be expressed as the sum of two prime numbers. The correct answer is Choice D. This explanation uses the following strategy. Strategy 10: Trial and Error
44、18 【正确答案】 B 【试题解析】 The given information tells you that n can be expressed in the form n = 45k +18, where k can be any nonnegative integer. Consider how the divisors of 45 and 18 may be related to the divisors of n. Every common divisor of 45 and 18 is also a divisor of any sum of multiples of 45 an
45、d 18, like 45k +18. So any common divisor of 45 and 18 is also a divisor of n. Of the answer choices given, only 9 is a common divisor of 45 and 18. Thus the correct answer is Choice B. This explanation uses the following strategies. Strategy 1: Translate from Words to an Arithmetic or Algebraic Rep
46、resentation Strategy 8: Search for a Mathematical Relationship 19 【正确答案】 D 【试题解析】 From the figure you can see that since the coordinate of A is 1/3, it follows that the coordinate of C is 1/3+AB+BC. Since you are given that AB = (BC), the coordinate of C can be rewritten in terms of AB as follows: +
47、AB+BC = +AB+3(AB)= + 4(AB)To find the coordinate of C, you need to know AB. From the figure, you know that AD = AB+BC+CD = AB+3(AB)+AB = 5(AB). On the other hand, since the coordinate of A is 1/3 and the coordinate of D is 1/2, it follows that AD = = 1/6.Therefore you can conclude that 1/6 = 5(AB)an
48、d AB = 1/30. Thus the coordinate of C is , or 7/15. The correct answer is Choice D. This explanation uses the following strategies.Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation Strategy 8: Search for a Mathematical Relationship 20 【正确答案】 E 【 试题解析】 The total dollar
49、amount that the customer would have to pay is equal to the cost plus 8 percent of the cost. Translating to an algebraic expression, you get that the total amount is s +0.08s, or 1.08s. Thus the correct answer is Choice E. This explanation uses the following strategy. Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation 21 【正确答案】 E 【试题解析】 You can translate the given information into an algebraic equation. If Marie walks m miles, she earns 0.75m dollars. Since you know that she earned a total of $18, you get 0.75m =18. Solving for m, you have m
