1、GRE（ QUANTITATIVE）综合模拟试卷 3及答案与解析 0 7 A manager is forming a 6-person team to work on a certain project. From the 11 candidates available for the team, the manager has already chosen 3 to be on the team. In selecting the other 3 team members, how many different combinations of 3 of the remaining cand
2、idates does the manager have to choose from? （ A） 6 （ B） 24 （ C） 56 （ D） 120 （ E） 462 8 Which of the following could be the graph of all values of x that satisfy the inequality ? 9 If 1+x + x2 + x3 = 60, then the average(arithmetic mean)of x, x2, x3 , and x4 is equal to which of the following? （ A）
3、12x （ B） 15x （ C） 20x （ D） 30x （ E） 60x 10 Parallelogram OPQR lies in the xy-plane, as shown in the figure above. The coordinates of point P are(2,4)and the coordinates of point Q are(8, 6). What are the coordinates of point R ? （ A） (3,2) （ B） (3,3) （ C） (4,4) （ D） (5,2) （ E） (6,2) 11 The relations
4、hip between the area A of a circle and its circumference C is given by the formula A = kC2, where k is a constant. What is the value of k ? （ A） （ B） （ C） 1/4 （ D） 2 （ E） 42 12 The sequence of numbers a1,a2,a3,.,an,. is defined by for each integer n 1. What is the sum of the first 20 terms of this s
5、equence? 13 The table above shows the frequency distribution of the values of a variable Y. What is the mean of the distribution?Give your answer to the nearest 0.01._ 14 Let S be the set of all positive integers n such that n2 is a multiple of both 24 and 108. Which of the following integers are di
6、visors of every integer n in S ? Indicate all such integers. （ A） 12 （ B） 24 （ C） 36 （ D） 72 15 The range of the heights of the female students in a certain class is 13.2 inches, and the range of the heights of the male students in the class is 15.4 inches. Which of the following statements individu
7、ally provide(s)sufficient additional information to determine the range of the heights of all the students in the class? Indicate all such statements. （ A） The tallest male student in the class is 5.8 inches taller than the tallest female student in the class. （ B） The median height of the male stud
8、ents in the class is 1.1 inches greater than the median height of the female students in the class. （ C） The average(arithmetic mean)height of the male students in the class is 4.6 inches greater than the average height of the female students in the class. GRE（ QUANTITATIVE）综合模拟试卷 3答案与解析 1 【正确答案】 B
9、【试题解析】 In this question you are asked to compare the area of a parallelogram with an area of 24, given two side lengths and the measure of one interior angle of the parallelogram. Since the measure of the interior angle given is 125, you can conclude that the parallelogram is not a rectangle. Recall
10、 that the area of a parallelogram is found by multiplying the length of a base by the height corresponding to the base. It is helpful to draw the vertical height from vertex C to base AD of the parallelogram, as shown in the figure below. Note that the newly drawn height is a leg in a newly formed r
11、ight triangle. The hypotenuse of the triangle is a side of the parallelogram and has length 6. Thus, the leg of the triangle, which is the height of the parallelogram, must be less than the hypotenuse 6. The area of the parallelogram is equal to the length of base AD, which is 4, times the height, w
12、hich is less than 6. Since the product of 4 and a number less than 6 must be less than 24, the area of the parallelogram must be less than 24. Quantity B is greater than Quantity A, and the correct answer is Choice B. 2 【正确答案】 A 【试题解析】 From the histogram, you can observe that all of the measurement
13、intervals are the same size, the distribution has a peak at the measurement interval 6-10, and more of the measurement intervals are to the right of the peak than are to the left of the peak. Since in the histogram the 95 measurements have been grouped into intervals, you cannot calculate the exact
14、value of either the average or the median; you must compare them without being able to determine the exact value of either one. The median of the 95 measurements is the middle measurement when the measurements are listed in increasing order. The middle measurement is the 48th measurement. From the h
15、istogram, you can see that the measurement interval 1-5 contains the first 15 measurements, and the measurement interval 6-10 contains the next 35 measurements(that is, measurements 16 through 50). Therefore, the median is in the measurement interval 6-10 and could be 6, 7, 8, 9, or 10. Estimating t
16、he average of the 95 measurements is more complicated. Since you are asked to compare the average and the median, not necessarily to calculate them, you may ask yourself if you can tell whether the average is greater than or less than the median. Note that visually the measurements in the first thre
17、e measurement intervals are symmetric around the measurement interval 6-10, so you would expect the average of the measurements in just these three measurement intervals to lie in the 6-10 measurement interval. The 30 measurements in the remaining four measurement intervals are all greater than 10,
18、some significantly greater than 10. Therefore, the average of the 95 measurements is greater than the average of the measurements in the first three measurementintervals, probably greater than 10. At this point it seems likely that the average of the 95 measurements is greater than the median of the
19、 95 measurements. It turns out that this is true. To actually show that the average must be greater than 10, you can make the average as small as possible and see if the smallest possible average is greater than 10. To make the average as small as possible, assume that all of the measurements in eac
20、h interval are as small as possible. That is to say, all 15 measurements in the measurement interval 1-5 are equal to 1, all 35 measurements in the measurement interval 6-10 are equal to 6, etc. Under this assumption, the average of the 95 measurements isThe value of the smallest possible average,1,
21、015/95, is greater than 10. Therefore, since the average of the 95 measurements is greater than 10 and the median is in the measurement interval 6-10, it follows that the average is greater than the median, and the correct answer is Choice A 3 【正确答案】 D 【试题解析】 One way to approach this question is to
22、plug in numbers for the variables and see what the relationship between the two quantities is for each of the numbers you plug in. If you plug in x = 2, you see that Quantity A is 3x+1= 33 or 27, and Quantity B is 4x = 42, or 16. In this case, Quantity A is greater than Quantity B. If you plug in x
23、= 3, you see that Quantity A is 3x+1 = 34, or 81, and Quantity B is 4x= 43, or 64. In this case, Quantity A is greater than Quantity B. If you plug in x = 4, you see that Quantity A is 3x+1 = 35 or 243, and Quantity B is 4x = 44, or 256. In this case, Quantity B is greater than Quantity A. Since for
24、 x = 2 and for x= 3, Quantity A is greater than Quantity B, and for x= 4, Quantity B is greater than Quantity A, it follows that the relationship between the two quantities cannot be determined. The correct answer is Choice D. Since both quantities are algebraic expressions, another way to approach
25、this problem is to set up a placeholder relationship between the two quantities and simplify it to see what conclusions you can draw. For any value of x, the value of 3x is positive, so dividing by 3x does not change any inequality that could be put in the placeholder. Since each step in this simpli
26、fication is reversible, this reduces the problem to comparing 3 with ;(4/3)x. You can see that because 4/3 is greater than 1, the value of(4/3)x becomes greater as x becomes larger. In particular, it is greater than 3 for large enough values of x.For the smallest value of x, x = 2, the relationship
27、is(4/3)2= 16/9 3. Since for x = 2, Quantity A is greater than Quantity B and for large values of x, Quantity B is greater than Quantity A, it follows that the relationship between the two quantities cannot be determined. The correct answer is Choice D. 4 【正确答案】 A 【试题解析】 In this question you are aske
28、d to compare the area of rectangle A and the area of rectangle B. Since the information given relates the dimensions of both rectangle A and rectangle B to the corresponding dimensions of rectangle C, you can try to use the relationships to make the desired comparison. If l represents the length of
29、rectangle C and w represents its width, then the length and width of rectangles A and B can be translated into algebraic expressions as follows. The length of rectangle A is 10 percent greater than the length of rectangle C, or 1.1l. The width of rectangle A is 10 percent less than the width of rect
30、angle C, or 0.9w. The length of rectangle B is 20 percent greater than the length of rectangle C, or 1.2l. The width of rectangle B is 20 percent less than the width of rectangle C, or 0.8w. In terms of l and w, the area of rectangle A is(1.1l)(0.9w), or 0.99lw. In terms of l and w, the area of rect
31、angle B is(1.2l)(0.8w), or 0.96lw. Since 0.99lw is greater than 0.96lw, Quantity A is greater than Quantity B, and the correct answer is Choice A. 5 【正确答案】 B 【试题解析】 You are given that the distribution of random variable X is normal and that the values 650 and 850 are at the 60th and 90th percentiles
32、 of the distribution, respectively. Both of the values 650 and 850 are greater than the mean of the distribution. If you draw a rough sketch of the graph of the normal distribution, the sketch could look something like the one below. Note that it is not necessary to know the exact location of 650 an
33、d 850, just that both values are above the mean. To say that the value 650 is at the 60th percentile of the distribution means, graphically, that 60 percent of the area between the normal curve and the horizontal axis lies to the left of the vertical line segment at 650. To say that 850 is at the 90
34、th percentile of the distribution means that 90 percent of the area between the normal curve and the horizontal axis lies to the left of the vertical line segment at 850. The value 750 is halfway between 650 and 850. However, because the curve is decreasing in that interval, the area between 650 and
35、 750 is greater than the area between 750 and 850. Since the value at the 75th percentile should divide in half the area between the value at the 60th percentile(650)and the value at the 90th percentile(850), this value is closer to 650 than to 850. Thus you can conclude that Quantity A, the value a
36、t the 75th percentile of the distribution of X, is less than Quantity B. The correct answer is Choice B. 6 【正确答案】 C 【试题解析】 Set S consists of all integers from 1 to 80, except those that are equal to the square of an integer. So, Quantity A, the number of integers in set S, is equal to the number of
37、positive integers that are less than 81 minus the number of positive integers less than 81 that are equal to the square of an integer. Clearly, there are 80 positive integers that are less than 81. One way to determine the number of positive integers less than 81 that are squares of integers is by n
38、oticing that 81 is equal to 92 and concluding that the squares of the integers from 1 to 8 are all positive integers that are less than 81. You can also draw this conclusion by squaring each of the positive integers, beginning with 1, until you get to an integer n such that n2 is greater than or equ
39、al to 81. Either way, there are 8 positive integers less than 81 that are squares of integers. Therefore, the number of integers in set S is 80 - 8, or 72, which is equal to Quantity B. So Quantity A is equal to Quantity B, and the correct answer is Choice C. 7 【正确答案】 C 【试题解析】 To determine the numbe
40、r of different combinations of 3 of the remaining candidates that the manager has to choose from, you first have to know the number of remaining candidates. Since you know that the manager has already chosen 3 of the 11 candidates to be on the team, it is easy to see that there are 8 remaining candi
41、dates. Now you need to count how many different combinations of 3 objects can be chosen from a group of 8 objects. If you remember the combinations formula, you know that the number of combinations is (which is denoted symbolically as or ). You can then calculate the number of different combinations
42、 of 3 of the remaining candidates as follows. The correct answer is Choice C. 8 【正确答案】 C 【试题解析】 To determine which of the graphs is the correct answer, you first need to determine all values of x that satisfy the inequality. To do that you need to simplify the inequality until you isolate x. You can
43、 begin by multiplying both sides of the inequality by 3 to obtain(3)(2 - 5x) -(6x - 5). Note that when you multiply by 3, the right-hand side of the inequality becomes -(6x - 5), not -6x - 5. The rest of the simplification is as follows. Note that when an inequality is multiplied(or divided)by a neg
44、ative number, the direction of the inequality reverses. The graphs in the answer choices are number lines on which only the number 0 is indicated. Therefore, you do not need to locate 1/9 on the number line; it is nough to know that 1/9 is a positive number. Choice C is the only choice in which the
45、shaded part of the line is equal to or greater than a positive number. Therefore, the correct answer is Choice C. 9 【正确答案】 B 【试题解析】 A quick inspection of the answer choices shows that it is not necessary to solve the equation 1 + x + x2 + x3 = 60 for x to answer this question. You are being asked to
46、 express the average of the four quantities x, x2, x3, and x4 in terms of x. To express this average in terms of x, you need to add the 4 quantities and divide the result by 4; that is, .The only information given in the question is that the sum of the 4 quantities, 1 +x+ x2+ x3, is 60, so you need
47、to think of a way to use this information to simplify the expression .Note that the numerator of the fraction is a sum of 4 quantities, each of which has an x term raised to a power. Thus, the expression in the numerator can be factored as x + x2+ x3+ x4= x(1+ x + x2+ x3). By using the information i
48、n the question, you can make the following simplification. Therefore, the correct answer is Choice B. 10 【正确答案】 E 【试题解析】 Since OPQR is a parallelogram, line segments PQ and OR have the same length and the same slope. Therefore, in the figure above, PQM and ORN arc congruent right triangles. From the
49、 coordinates of P and Q, the lengths of the legs of triangle PQM are PM = 8 - 2 = 6 and QM = 6-4 = 2. Thus, the lengths of the legs ON and RN of triangle ORN are also 6 and 2, respectively. So the coordinates of point R are(6, 2). The correct answer is Choice E. 11 【正确答案】 A 【试题解析】 One way to approach this problem is to realize that the value of the constant k is the same for all circles. Therefore, you can pick a specific circle and substitute the circumference and the area of that particular circle into the formula and calculate the value of k. Say, for example, that you pick a circle
