[外语类试卷]GRE（QUANTITATIVE）模拟试卷28及答案与解析.doc

1、GRE（ QUANTITATIVE）模拟试卷 28及答案与解析 0 For each of Questions 1 to 9, compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices and fill in the corresponding oval to the right of the quest

2、ion.(A)Quantity A is greater.(B)Quantity B is greater.(C)The two quantities are equal.(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. 9 For each of Questions 1 to 9, compare Quantity

3、A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices and fill in the corresponding oval to the right of the question.(A)Quantity A is greater.(B)Quantity B is greater.(C)The two quantities are e

4、qual.(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. 19 The ratio off 1/3 to 3/8 is equal to the ratio of （ A） 1 to 8 （ B） 8 to 1 （ C） 8 to 3 （ D） 8 to 9 （ E） 9 to 8 20 A reading list

5、 for a humanities course consists of 10 books, of which 4 are biographies and the rest are novels. Each student is required to read a selection of 4 books from the list, including 2 or more biographies. How many selections of 4 books satisfy the requirements? （ A） 90 （ B） 115 （ C） 130 （ D） 144 （ E）

6、195 21 In a graduating class of 236 students, 142 took algebra and 121 took chemistry. What is the greatest possible number of students that could have taken both algebra and chemistry? _students 22 In the figure above, if m丨丨 k and s = t + 30, then t = （ A） 30 （ B） 60 （ C） 75 （ D） 80 （ E） 105 23 If

7、 2x = 3y = 4z = 20, then 12xyz = （ A） 16000 （ B） 8000 （ C） 4000 （ D） 800 （ E） 10 24 The total amount that Mary paid for a book was equal to the price of the book plus a sales tax that was 4 percent of the price of the book. Mary paid for the book with a $10 bill and received the correct change, whic

8、h was less than $3.00. Which of the following statements must be true? Indicate all such statements. （ A） The price of the book was less than $9.50. （ B） The price of the book was greater than $6.90. （ C） The sales tax was less than $0.45. 25 If is expressed as a terminating decimal, how many nonzer

9、o digits will the decimal have? （ A） One （ B） Two （ C） Four （ D） Six （ E） Eleven 26 a1,a2,a3, .,an,. In the sequence above, each term after the first term is equal to the preceding term plus the constant c. If a1+ a3+ a5= 27, what is the value of a2+ a4? a2+ a4= 27 A desert outpost has a water suppl

10、y that is sufficient to last 21 days for 15 people. At the same average rate of water consumption per person, how many days would the water supply last for 9 people? （ A） 28 （ B） 32.5 （ C） 35 （ D） 37.5 （ E） 42 28 The fabric needed to make 3 curtains sells for $8.00 per yard and can be purchased only

11、 by the full yard. If the length of fabric required for each curtain is 1.6 yards and all of the fabric is purchased as a single length, what is the total cost of the fabric that needs to be purchased for the 3 curtains? （ A） 40 （ B） 38.4 （ C） 24 （ D） 16 （ E） 12.8 29 In the xy-plane, line A; is a li

12、ne that does not pass through the origin. Which of the following statements individually provide(s)sufficient additional information to conclude that the slope of line k is negative? Indicate all such statements. （ A） The x-intercept of line k is twice the y-intercept of line k. （ B） The product of

13、the x-intercept and the y-intercept of line k is positive. （ C） Line k passes through the points(a,b)and(r,s), where(a - r)(b - s)y, and x/y 1, which yields Choice A. You can also solve this problem without using the fact above. Instead, you can use the strategy of adapting solutions to related prob

14、lems to determine the relationship between x and y. Note that the angles in the triangle differ only a little from the angles in a 45 - 45 - 90 triangle. How do the lengths of the legs of a 45 - 45 - 90 triangle compare to the lengths of the legs of the triangle in the question? To make the comparis

15、on, add a line segment to the triangle so that the line segment cuts the 50 angle in two parts, making a 45 angle with the horizontal base, as shown in the following figure: The 45 - 45 - 90 triangle has two 45 angles, so z = y, and z/y = 1. Since z/y = 1 and x z, it follows that x/y 1. The correct

16、answer is Choice A. 5 【正确答案】 D 【试题解析】 Two approaches that you could use to solve this problem are: 1: Translate from algebra to a number line. 2: Plug in values for the variables. Approach 1: The following figure represents the information given in the problem on a number line. On the number line, 1

17、 - y is the distance between 1 and y, and y x is the distance between y and x. If y is exactly halfway between x and 1, then 1 -y is equal to y -x; and if y is not halfway between x and 1, then 1 -y is not equal to y - x. But y can be any number between x and 1, so the correct answer is Choice D. Ap

18、proach 2: Since this problem involves subtraction, it is a good idea to choose values for x and y that are close to each other as well as values that are far apart. For example, if x = 0.4 and y = 0.5, then 1 -y = 0.5 and y - x = 0.1; and if x = 0.1 and y = 0.9, then 1 - y = 0.1 and y - x = 0.8. Thi

19、s shows that the relationship cannot be determined, and the correct answer is Choice D. 6 【正确答案】 A 【试题解析】 Since event E will either occur or not occur, it follows that p + s = 1, and the value of Quantity A is always 1. Since Quantity B is the product of the two probabilities p and s, you need to lo

20、ok at its value for the cases p = 1, p = 0, and 0small fraction of 1 United States dollar. The correct answer is Choice A. 11 【正确答案】 D 【试题解析】 In this question, you are given that k is a digit in the decimal 1.3k5 and that 1.3k5 is less than 1.33. So you can see that 1.30 1.3k5 1.33. Therefore, 1.3k5

21、 must equal 1.305 or 1.315 or 1.325, and the digit k must be 0, 1, or 2. The correct answer is Choice D. 12 【正确答案】 A 【试题解析】 Recall that in a circle, any diameter is longer than any other chord that is not a diameter. You are given that AB is a diameter of the circle. It follows that AC and AD are ch

22、ords that are not diameters, since there is only one diameter with endpoint A. Hence, AB is longer than both AC and AD. Note that the average of two numbers is always less than or equal to the greater of the two numbers. Therefore, the average of the lengths of AC and AD, which is Quantity B, must b

23、e less than the length of AB, which is Quantity A. The correct answer is Choice A. 13 【正确答案】 C 【试题解析】 In this question you are asked to compare s2 with . Since it is given that st = , it follows that(st)2 =( )2 , and s2t2 = 10. Dividing both sides of the equation s2t2 = 10 by t2, you get s2= . The c

24、orrect answer is Choice C. You can look at this problem in another way. You can use the fact that st = to express Quantity A in terms of t. Since st = , it follows that s = , and Quantity A is equal to , which is the same as Quantity B. The correct answer is Choice C. 14 【正确答案】 B 【试题解析】 Two approach

25、es you could use to solve this problem are: 1: Translate from words to algebra. 2: Determine a mathematical relationship between the two quantities. Approach 1: You can represent the least of the three consecutive integers by x, and then the three integers would be represented by x, x + 1, and x + 2

26、. It is given that the sum of the three integers is -84, so x +(x + 1)+(x + 2)= -84. You can solve this equation for x as follows. x +(x+1)+(x + 2)= -84 3x + 3 = -84 3x = -87 x = -29 Since the least of the three integers, -29, is less than -28, the correct answer is Choice B. Approach 2: You could a

27、sk yourself what would happen if the least of the three consecutive integers was -28. The three consecutive integers would then be -28, -27, and -26, and their sum would be -81. But you were given that the sum of the three consecutive integers is -84, which is less than -81. Therefore, -28 is greate

28、r than the least of the three consecutive integers, and the correct answer is Choice B. 15 【正确 答案】 C 【试题解析】 Two approaches you could use to solve this problem are:1: Reason algebraically. 2: Reason geometrically. Approach 1: To solve this problem algebraically, note that given the equation of a line

29、 in the xy-plane, the x-intercept of the line is the value of x when y equals 0, and the y-intercept of the line is the value of y when x equals 0. The equation of line k is 3x - 2y = 0. If y = 0, then x = 0; and if x = 0, then y = 0. Therefore, both the x-intercept and y-intercept of the line are e

30、qual to 0, which means that the line passes through the origin. The correct answer is Choice C. Approach 2: To solve this problem geometrically, graph the line with equation 3x - 2y = 0 in the xy-plane. Since two points determine a straight line, you can do this by plotting two points on the line an

31、d drawing the line they determine. The points(0,0)and(2,3)lie on the line, and the graph of the line in the xy-plane is shown in the following figure. As you can see, the line passes through the origin, and so it crosses both the x-axis and the v-axis at(0,0). The correct answer is Choice C. 16 【正确答

32、案】 D 【试题解析】 One way to compare the two quantities is to plug in a few values of n. If you plug in n = 36, you find that both the remainder when n is divided by 12 and the remainder when n is divided by 18 are equal to 0, so Quantity A is equal to Quantity B. However, if you plug in n = 18, you find

33、that the remainder when n is divided by 12 is 6 and the remainder when n is divided by 18 is 0, so Quantity B is greater than Quantity A. Therefore, the correct answer is Choice D. Another way to compare the two quantities is to find all of the possible values of Quantity A and Quantity B. The posit

34、ive integers that are divisible by 6 are 6, 12, 18, 24, 30, 36, etc. When dividing each of these integers by 12, you get a remainder of either 0 or 6, so Quantity A is either 0 or 6. When dividing each of these integers by 18, you get a remainder of either 0 or 6 or 12, so Quantity B is either 0 or

35、6 or 12. Note that when the value of Quantity B is 12, the value of Quantity A, 0 or 6, is less than the value of Quantity B; but when the value of Quantity B is 0, the value of Quantity A is greater than or equal to the value of Quantity B. Thus, the correct answer is Choice D. 17 【正确答案】 B 【试题解析】 O

36、ne approach you could use to solve this problem is to solve the equation for x. Since fractions are defined only when the denominator is not equal to 0, the denominators of both of the fractions in the equation are nonzero. Therefore, x 0 and x 1. To solve the equation for x, begin by multiplying bo

37、th sides of the “equation by the common denominator x(x + 1)to get x(l - x)=(x - 1)(1). Then proceed as follows.x(1 -x)=(x- 1)(1)x - x2 = x - 1 x2=1Since x2= 1 and x 1, it follows that x = -1. Quantity A is equal to -1 and Quantity B is equal to . Therefore, Quantity B is greater, and the correct an

38、swer is Choice B. Another approach is to notice that for all values of x 1, the value of is equal to -1. You can try plugging in a few numbers for x to see that this is true. For example, if you plug in x = 7, you get =-1. You can also show that for all values of x 1, the value of is equal to -1 alg

39、ebraically by rewriting 1 - x as -(x - 1). Thus, = -1. Because the left side of the equationis equal to -1, it follows that -1 = 1/x, and so x = -1. Therefore, Quantity A is equal to -1, which is less than Quantity B, and the correct answer is Choice B. 18 【正确答案】 D 【试题解析】 In general, the median of a

40、 set of n positive integers, where n is even, is obtained by ordering the integers from least to greatest and then calculating the average(arithmetic mean)of the two middle integers. For this set of 24 integers, you do not know the values of the two middle integers; you know only that half of the in

41、tegers are less than 50 and the other half are greater than 50. If the two middle integers in the list are 49 and 51, the median is 50; and if the two middle integers are 49 and 53, the median is 51. Thus the relationship cannot be determined from the information given, and the correct answer is Cho

42、ice D. 19 【正确答案】 D 【试题解析】 Multiplying both parts of a ratio by the same positive number produces an equivalent ratio. While you could multiply both fractions in the ratio by any number, 24 is a good number to choose because it is the least common multiple of 3 and 8. Thus, multiplying both 1/3 and 3

43、/8 by 24, you get that the ratio of 1/3 to 3/8 is equal to the ratio of 8 to 9. The correct answer is Choice D. An alternate approach to this problem is to express the ratio of 1/3 to 3/8 as the fraction . This fraction is equivalent to(1/3)(8/3), or 8/9. The correct answer is Choice D. 20 【正确答案】 B

44、【试题解析】 The requirement to select 4 books, including 2 or more biographies, means that you have to consider three cases. A student can choose 4 biographies and no novels, or 3 biographies and 1 novel, or 2 biographies and 2 novels. Case 1: Choose 4 biographies. This case is easy, as there is only 1 w

45、ay to choose all four biographies and no novels. In the other two cases, you have to find the number of ways of choosing the biographies and the number of ways of choosing the novels and then multiply these two numbers. Case 2: Choose 3 biographies and 1 novel. First, you need to find the number of

46、ways of choosing 3 biographies out of 4. If you think of this as not choosing 1 out of the 4, you see that there are 4 choices. The number of ways of choosing 1 novel out of the 6 novels is 6. Therefore, the total number of choices is(4)(6)= 24. Case 3: Choose 2 biographies and 2 novels. First, you

47、need to find the number of ways of choosing 2 biographies out of 4. This number is sometimes called “4 choose 2“ or the number of combinations of 4 objects taken 2 at a time. If you remember the combinations formula, you know that the number of combinations is (which is denoted symbolically as ). Th

48、e value of = 6. Thus, there are 6 ways to choose 2 biographies out of 4. Similarly, the number of ways to choose 2 novels out of 6 is = 15. Thus, the total number of ways to choose 2 biographies and 2 novels is(6)(15)= 90. Adding the number of ways to choose the books for each of the three cases, yo

49、u get a total of 1 + 24 + 90 = 115. The correct answer is Choice B. 21 【正确答案】 121 【试题解析】 This is the type of problem for which drawing a Venn diagram is usually helpful. The Venn diagram below is one you could draw to represent the information given in the question. Note that the algebra and chemistry numbers given do not separate out the number of students who took both algebra and chemistry, and that this question asks for the greatest possible number of such students. It is a good idea, therefore, to redraw the Venn diagram with the number of students who took both algeb