1、GRE（ QUANTITATIVE）综合模拟试卷 2及答案与解析 0 6 If x 0, which of the following is equivalent to ? （ A） x2 （ B） x3 （ C） x4 （ D） x5 （ E） x6 7 The figure above shows the graph of the function f in the xy-plane. What is the value of f(f(-1)? （ A） -2 （ B） -1 （ C） 0 （ D） 1 （ E） 2 8 If = 1, which of the following sta
2、tements describes d in terms of n ? （ A） d is 4 less than n. （ B） d is 4 more than n. （ C） d is 3/7 of n. （ D） d is 2 times n. （ E） d is 5 times n. 9 By weight, liquid A makes up 8 percent of solution R and 18 percent of solution S. If 3 grams of solution R are mixed with 7 grams of solution S, then
3、 liquid A accounts for what percent of the weight of the resulting solution? （ A） 10% （ B） 13% （ C） 15% （ D） 19% （ E） 26% 10 Of the 700 members of a certain organization, 120 are lawyers. Two members of the organization will be selected at random. Which of the following is closest to the probability
4、 that neither of the members selected will be a lawyer? （ A） 0.5 （ B） 0.6 （ C） 0.7 （ D） 0.8 （ E） 0.9 11 The figure above represents a rectangular garden with a walkway around it. The garden is 18 feet long and 12 feet wide. The walkway is uniformly 3 feet wide, and its edges meet at right angles. Wh
5、at is the area of the walkway?_square feet 12 Line k lies in the xy-plane. The x-intercept of line k is -4, and line k passes through the midpoint of the line segment whose endpoints are(2, 9)and(2,0). What is the slope of line k ?Give your answer as a fraction. 13 If the lengths of two sides of a t
6、riangle are 5 and 9, respectively, which of the following could be the length of the third side of the triangle? Indicate all such lengths. （ A） 3 （ B） 5 （ C） 8 （ D） 15 14 On the number line shown above, the tick marks are equally spaced. Which of the following statements about the numbers x, y, and
7、 z must be true?Indicate all such statements. （ A） xyz0 GRE（ QUANTITATIVE）综合模拟试卷 2答案与解析 1 【正确答案】 A 【试题解析】 In this question you are given that machine R, working alone at its constant rate, produces x units of a product in 30 minutes. Since it is easy to see that 3 hours is 6 times 30 minutes, you ca
8、n conclude that Quantity A is 6x. You can compare 6x with Quantity B in two ways. One: In the additional information centered above the quantities, you are given that machine S, working alone at its constant rate, produces x units of the product in 48 minutes, so you can conclude that machine S can
9、produce 6x units of the product in(6)(48)minutes, or 4.8 hours. So in 4 hours, machine S produces less than 6x units, and Quantity B is less than 6x. Two: First, convert 48 minutes to 4/5 hour, then find the number of 48-minute periods there are in 4 hours by computing = 5. Thus, Quantity B is 5x. E
10、ither way, Quantity A is greater than Quantity B, and the correct answer is Choice A. 2 【正确答案】 B 【试题解析】 In this problem you are asked to compare the average with the median of the 120 numbers in list Z. Since list Z consists of the numbers in lists X and Y combined, it is reasonable to try to use th
11、e information about lists X and Y to calculate the average and the median of the numbers in list Z. To determine the average of the 120 numbers in list Z, you can use the information given about the individual averages of the numbers in lists X and Y. Because lists X and Y each contain 60 numbers, t
12、he average of the numbers in list Z is the average of the individual averages of the numbers in lists X and Y. Thus, the average of the numbers in list Z is , or 4.9. To determine the median of the 120 numbers in list Z, first note that list Z contains an even number of numbers, so the median of the
13、 numbers in list Z is the average of the middle two numbers when the numbers are listed in increasing order. If you look at the numbers in the two lists, you will see that the 60 numbers in list X are all less than or equal to 5, and the 60 numbers in list Y are all greater than or equal to 6. Thus,
14、 the two middle numbers in list Z are 5 and 6, and the average of these numbers is , or 5.5. Therefore, the median of the numbers in list Z is 5.5, and this is greater than the average of 4.9. The correct answer is Choice B. 3 【正确答案】 D 【试题解析】 You are given that the circle has a diameter of 10, and f
15、rom the figure you can assume that points A, B, C, and D lie on the circle in the order shown. However, because figures are not necessarily drawn to scale, you cannot assume anything else about the positions of points A, B, C, and D on the circle. Therefore, to get an idea of how various possible po
16、sitions of these four points could affect the area of quadrilateral ABCD, it is a good idea to see how the figure can vary but still have points A, B, C, and D in the same order as in the figure above. One way that you might vary the figure is to evenly space the four points along the circle, as sho
17、wn below. Another way is to draw points A and C opposite each other, with points B and D close to point C, as shown below. From these figures you can draw some basic conclusions about the area of ABCD. If points A and C are opposite each other, with points B and D very close to point C, the area of
18、quadrilateral ABCD is very close to 0. Clearly, the area can be less than 40(Quantity B). If points A, B, C, and D are evenly spaced, the area is not close to 0. How does the area compare with 40? To calculate the area of ABCD, draw the diameters AC and BD in the figure. The two diameters are perpen
19、dicular bisectors of each other, so they divide ABCD into four right triangles, as shown. The area of each of the right triangles is(1/2)(5)(5), or 12.5. Thus, the area ofABCD is(4)(12.5), or 50. Since the area of the quadrilateral in the first figure is less than 40 and the area of the quadrilatera
20、l in the second figure is greater than 40, the relationship cannot be determined from the information given. The correct answer is Choice D. 4 【正确答案】 B 【试题解析】 You are given that x2y 0, which means that the product of the two numbers x2 and y is positive. Recall that the product of two numbers is pos
21、itive only if both numbers are positive or both numbers are negative. The square of a number is always greater than or equal to 0. In this case, x2 cannot equal 0 because the product x2y is not 0. Thus, x2 is positive and it follows that y is also positive. You are also given that xy2 0, you can see that it is equivalent to the inequality y x, which is clearly true from the number line. Since y x is positive, the product z(y - x)must be positive. Therefore, the correct answer consists of Choices A, B, and C.
