1、GRE（ QUANTITATIVE）模拟试卷 27及答案与解析 0 9 19 In year Y, the population of Colorado was approximately half that of New Jersey, and the land area of Colorado was approximately 14 times that of New Jersey. The population density(number of persons per unit of land area)of Colorado in year Y was approximately
2、how many times the population density of New Jersey? 20 In the figure above, line k is parallel to line m. What is the value of y ?y =_ 21 The numbers in data set S have a standard deviation of If a new data set is formed by adding 3 to each number in S, what is the standard deviation of the numbers
3、 in the new data set? （ A） 2 （ B） 3 （ C） 5 （ D） 8 （ E） 15 22 If , which of the following could be the value of y ? （ A） 4 （ B） 1 （ C） -1 （ D） -3 （ E） -5 23 List K consists of the numbers -10, -5, 0, 5, and 10. Which of the following lists of numbers have the same range as the numbers in list K ? Ind
4、icate all such lists. （ A） -15, -1,0, 1, 15 （ B） -7, -4, -2, 1, 13 （ C） 0, 1, 2, 5, 8, 10 （ D） 2, 3, 5, 15, 19, 22 （ E） 4, 5, 6, 24 24 Aishas income in 2004 was 20 percent greater than her income in 200What is the ratio of Aishas income in 2004 to her income in 2003 ? （ A） 1 to 5 （ B） 5 to 6 （ C） 6
5、to 5 （ D） 5 to 1 （ E） 20 to 1 25 Jacobs weekly take-home pay is n dollars. Each week he uses dollars for expenses and saves the rest. At those rates, how many weeks will it take Jacob to save $500, in terms of n ? 26 If t + 3 5, which of the following could be the value of t ? Indicate all such valu
6、es. （ A） -9 （ B） -6 （ C） -2 （ D） 0 （ E） 3 27 The operation is defined for all integers x and y as x y = xy - y. If x and y are positive integers, which of the following CANNOT be zero? （ A） x y （ B） y x （ C） (x-l) y （ D） (x+1) y （ E） x (y- 1) 28 P, Q, and R are three points in a plane, and R does no
7、t lie on line PQ. Which of the following is true about the set of all points in the plane that are the same distance from all three points? （ A） It contains no points. （ B） It contains one point. （ C） It contains two points. （ D） It is a line. （ E） It is a circle. 29 If x all such numbers （ A） a - b
8、 （ B） a2-b2 （ C） ab （ D） a2b （ E） a2b + ab2 37 A flat rectangular picture, represented by the unshaded region in the figure above, is mounted in a flat rectangular frame, represented by the shaded region. The frame is 1 inch wide on all sides. For what value of x, in inches, is the area of the frame
9、 equal to the area of the picture? （ A） 4 （ B） 5 （ C） 6 （ D） 7 （ E） 8 38 Of the people in a certain survey, 58 percent were at most 40 years old and 70 percent were at most 60 years old. If 252 of the people in the survey were more than 40 years old and at most 60 years old, what was the total numbe
10、r of people in the survey? （ A） 1900 （ B） 2100 （ C） 2400 （ D） 2700 （ E） 3000 39 If x0, which of the following is equal to 1.25 percent of x ? 40 Alice earns d dollars and has / percent of what she earns deducted for taxes. How much of what she earns does Alice have left after taxes? （ A） d(1 - 100t)
11、dollars （ B） d(1 -10t)dollars （ C） d(1-t)dollars （ D） d(1 -0.1t)dollars （ E） d(1 -0.01t)dollars 41 A student made a conjecture that for any integer n, the integer An + 3 is a prime number. Which of the following values of n could be used to disprove the students conjecture? Indicate all such values.
12、 （ A） 1 （ B） 3 （ C） 4 （ D） 6 （ E） 7 42 Eight points are equally spaced on a circle. If 4 of the 8 points are to be chosen at random, what is the probability that a quadrilateral having the 4 points chosen as vertices will be a square? （ A） 1/70 （ B） 1/35 （ C） 1/7 （ D） 1/4 （ E） 1/2 42 VARIATION IN TH
13、E AMOUNT OF CAFFEINE IN COMMON BEVERAGES AND DRUGS*Based on 5-ounce cups of coffee, tea, and cocoa; 12-ounce cups of soft drinks; and single doses of drugs. 43 The least amount of caffeine in a 5-ounce cup of drip-brewed coffee exceeds the greatest amount of caffeine in a 5-ounce cup of cocoa by app
14、roximately how many milligrams? （ A） 160 （ B） 80 （ C） 60 （ D） 40 （ E） 20 44 For how many of the 11 categories of beverages and drugs listed in the graph can the amount of caffeine in the given serving size be less than 50 milligrams? _categories 45 Approximately what is the minimum amount of caffein
15、e, in milligrams, consumed per day by a person who daily drinks two 10-ounce mugs of percolated coffee and one 12-ounce cup of a caffeinated soft drink? （ A） 230 （ B） 190 （ C） 140 （ D） 110 （ E） 70 46 Which of the following shows the four types of coffee listed in order according to the range of the
16、amounts of caffeine in a 5-ounce cup, from the least range to the greatest range? （ A） Decaffeinated, instant, percolated, drip-brewed （ B） Decaffeinated, instant, drip-brewed, percolated （ C） Instant, decaffeinated, drip-brewed, percolated （ D） Instant, drip-brewed, decaffeinated, percolated （ E） I
17、nstant, percolated, drip-brewed, decaffeinated 46 ENERGY USED PER METER VERSUS SPEED DURING RUNNING AND WALKING 47 If s is a speed, in miles per hour, at which the energy used per meter during running is twice the energy used per meter during walking, then, according to the graph above, s is between
18、 （ A） 2.5 and 3.0 （ B） 3.0 and 3.5 （ C） 3.5 and 4.0 （ D） 4.0 and 4.5 （ E） 4.5 and 5.0 48 If n = 23, then nn= （ A） 26 （ B） 211 （ C） 218 （ D） 224 （ E） 227 49 Which of the following statements individually provide(s)sufficient additional information to determine the area of triangle ABC above? Indicate
19、 all such statements. （ A） DBC is an equilateral triangle. （ B） ABD is an isosceles triangle. （ C） The length of BC is equal to the length of AD. （ D） The length of BC is 10. （ E） The length of AD is 10. 49 DISTANCE TRAVELED BY A CAR ACCORDING TO THE CARS SPEED WHEN THE DRIVER IS SIGNALED TO STOP*Re
20、action time is the time period that begins when the driver is signaled to stop and ends when the driver applies the brakes.Note: Total stopping distance is the sum of the distance traveled during reaction time and the distance traveled after brakes have been applied. 50 The speed, in miles per hour,
21、 at which the car travels a distance of 52 feet during reaction time is closest to which of the following? （ A） 43 （ B） 47 （ C） 51 （ D） 55 （ E） 59 51 Approximately what is the total stopping distance, in feet, if the car is traveling at a speed of 40 miles per hour when the driver is signaled to sto
22、p? （ A） 130 （ B） 110 （ C） 90 （ D） 70 （ E） 40 52 Of the following, which is the greatest speed, in miles per hour, at which the car can travel and stop with a total stopping distance of less than 200 feet? （ A） 50 （ B） 55 （ C） 60 （ D） 65 （ E） 70 53 The total stopping distance for the car traveling at
23、 60 miles per hour is approximately what percent greater than the total stopping distance for the car traveling at 50 miles per hour? （ A） 0.22 （ B） 0.3 （ C） 0.38 （ D） 0.45 （ E） 0.52 GRE（ QUANTITATIVE）模拟试卷 27答案与解析 1 【正确答案】 C 【试题解析】 In this question, you are asked to compare with 4/3. Recall that if
24、a is a nonzero number, then a-1 = 1/a and = a. Using these rules of exponents, you can see that Thus, , and the correct answer is Choice C. 2 【正确答案】 A 【试题解析】 In this question, you are given that x x, you can conclude that the placeholder in the simplified comparison 1 x represents greater than(). No
25、te that the strategy of simplifying the comparison requires you to consider whether the steps in the simplification are reversible. This is because you must arrive at a conclusion about the initial comparison, not the simplified comparison. If you follow the simplification steps in reverse, you can
26、see that the placeholder in each step remains unchanged: 1 x implies x2 x3 because multiplying by the positive number x2 retains the inequality greater than(). Also, x2 x3 implies x2 + 1 x3 +1. Therefore, Quantity A is greater than Quantity B, and the correct answer is Choice A. 3 【正确答案】 B 【试题解析】 In
27、 this question, you are given that x 0, and you are asked to compare 0.5% of x with x. Recall that of a number is the same as 50% of the number.Therefore, x is equal to 50% of x. Since x 0, it follows that 50% of x is greater than 0.5% of x. The correct answer is Choice B. You could also make the co
28、mparison by rewriting 0.5% of x as a fraction of x and then comparing the result with x. Rewrite 0.5% of x as a fraction of x as follows. Since x 0, it follows that is less than x, and Quantity B is greater than Quantity A. The correct answer is Choice B. 4 【正确答案】 D 【试题解析】 In this question, you are
29、asked to compare the 75th percentiles of the incomes of two groups of college graduates six months after graduation. The only information you are given is that the median income of the group in Quantity A is $3,000 greater than the median income of the group in Quantity B. Recall that the median of
30、a group of numbers is the middle number(or the average of the two middle numbers)when the numbers are listed from least to greatest. The median is also equal to the 50th percentile. The median does not indicate anything about the spread of the numbers in the group. In particular, for each group of i
31、ncomes, you do not know how much greater than the median the 75th percentile of the group of incomes is, nor do you know the relationship between the 75th percentiles of the two groups. Since the relationship between Quantity A and Quantity B cannot be determined, the correct answer is Choice D. 5 【
32、正确答案】 B 【试题解析】 In this question, you are given a graph of the frequency distribution of 50 integer values and are asked to compare the average(arithmetic mean)with the median of the distribution. In general, the median of a group of n values, where n is even, is obtained by ordering the values from
33、least to greatest and then calculating the average(arithmetic mean)of the two middle values. So, for the 50 values shown in the graph, the median is the average of the 25th and 26th values, both of which are equal to 5. Therefore, the median of the 50 values is 5. Once you know that the median of th
34、e 50 values is 5, the comparison simplifies to comparing the average of the 50 values with 5. You can make this comparison without actually calculating the average by noting from the graph that of the 50 values,11 values are 1 unit above 5,16 values are equal to 5,10 values are 1 unit below 5, and13
35、 values are more than 1 unit below 5.Since the part of the distribution that is below 5 contains 23 values-13 of which are more than 1 unit below 5 and the part of the distribution that is above 5 contains 11 values none of which is more than 1 unit above 5 the average(arithmetic mean)of the 50 valu
36、es must be less than 5. The correct answer is Choice B. Alternatively, you can calculate the average of the 50 values as follows. Thus the average of the 50 values, 217/50, or 4.34, is less than the median of the 50 values, 5. The correct answer is Choice B. 6 【正确答案】 B 【试题解析】 In this question, you a
37、re asked to compare the area of triangle PQR with the area of triangle PSR. Note that both triangles are right triangles and that line segment PR is the hypotenuse of both triangles. Recall that the area of a triangle is equal to one-half the product of a base and the height corresponding to the bas
38、e. Also, for any right triangle, the lengths of the two legs of the triangle are a base and the corresponding height. The area of triangle PQR: In the figure, it is given that the length of leg PQ is and the length of leg QR is . Therefore, you can conclude that the area of triangle PQR is , or 5. T
39、he area of triangle PSR: To calculate the area of triangle PSR, you need to know the lengths of the legs PS and RS. From the figure, you know that the length of RS is 3, but you do not know the length of PS. How can you determine the length of PS ? If, in addition to the length of RS, you knew the l
40、ength of hypotenuse PR, you could use the Pythagorean theorem to determine the length of PS. So, to find the length of PS, you first need to find the length of hypotenuse PR. Recall that PR is also the hypotenuse of triangle PQR. The lengths of legs PQ and QR of triangle PQR are and , respectively.
41、By the Pythagorean theorem, Thus, the length of PR is , or 5. Returning to triangle PSR, you now know that the length of hypotenuse PR is 5 and the length of leg RS is 3. Therefore, by the Pythagorean theorem,32 +(PS)2 = 52 9 +(PS)2 = 25(PS)2 = 25-9(RS)2 = 16and the length of PS is 4. Since legs PS
42、and RS have lengths 4 and 3, respectively, the area of triangle PSR is (4)(3), or 6. Recall that you have already determined that the area of triangle PQR is 5. So Quantity B, the area of triangle PSR, is greater than Quantity A, the area of triangle PQR, and the correct answer is Choice B. 7 【正确答案】
43、 A 【试题解析】 In this question, you are asked to compare the sum of the odd integers from 1 to 199 with the sum of the even integers from 2 to 198. Both of these sums involve many integers. How many integers are in each sum? Note that there are 200 integers from 1 to 200, where 100 of them are even and
44、100 of them are odd. The 100 odd integers are precisely the odd integers in Quantity A, whereas the 100 even integers include one more integer, 200, than the even integers in Quantity B. So Quantity A is the sum of 100 integers and Quantity B is the sum of 99 integers. It would be very time-consumin
45、g to write out all the terms in each sum and add them together. Therefore, it is reasonable to find a more efficient way to calculate the sums or to find a way to compare the sums without actually calculating them. To find a more efficient way to calculate the two sums, it is often useful to look fo
46、r ways to rearrange the terms in the sum so that they can be added more easily. You can begin by writing a few terms from the beginning and the end of the sum. For the sum of the 100 odd integers from 1 to 199, you could write 1 +3 + 5 + .+ 195+ 197+ 199You can pair the odd integers in the sum and a
47、dd the two integers in each pair as follows. Note that the sum of the integers in each of the three pairs shown is 200. You can continue pairing terms in the sum in this way until all 100 terms have been rearranged in 50 pairs, where the sum of each pair is 200. It follows that1 +3 + 5 + . + 195 + 1
48、97 + 199 =(1 + 199)+(3+ 197)+(5+ 195)+ . +(99 + 101)= 50(200)= 10,000Now consider the sum of the 99 even integers from 2 to 198. For this sum, you could write2 + 4 + 6 + . + 194+ 196 + 198In this sum, note that the sum of the 1st and 99th terms is 2 + 198 = 200 the sum of the 2nd and 98th terms is 4
49、 + 196 = 200You can continue pairing terms in this way until 98 of the 99 terms in the sum have been rearranged into 49 pairs and the 50th term is unpaired. Note that the unpaired term is 100(the 50th positive even integer). It follows that2 + 4 + . + 98 + 100 + 102 + . + 196 + 198 =(2 + 198)+(4 + 196)+ . +(98 + 102)+ 100= 49(200)+ 100 = 9,900Therefore, Quantity A, 10,000, is greater than Quantity B, 9,900, and the correct answer is Choice A. Alternatively, you can try to compare the two sums without actually calculating them. Recall that Quantity A is the sum of the 10
