1、GRE（ QUANTITATIVE）综合模拟试卷 18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 A construction company will produce identical metal supports in the shape of a right triangle with legs of length 3 fe
3、et and 4 feet. The three sides of each triangular support are to be constructed of metal stripping. If the company has a total of 6,000 feet of metal stripping and there is no waste of material in the construction of the supports, what is the greatest possible number of supports that the company can
4、 produce? （ A） 428 （ B） 500 （ C） 545 （ D） 600 （ E） 1,000 8 What is the area of triangle ABC shown above? （ A） 18 （ B） 20 （ C） 12 （ D） 18 （ E） 36 9 The volume V of a right circular cylinder is V =r2h, where r is the radius of the base and h is the height of the cylinder. If the volume of a right circ
5、ular cylinder is 45 and its height is 5, what is the circumference of its base? （ A） 3 （ B） 9 （ C） 3 （ D） 6 （ E） 9 10 In the figure above, if the square inscribed in the circle has an area of 16, what is the area of the shaded region? （ A） 2-1 （ B） 2-4 （ C） 4-2 （ D） 4-4 （ E） 8-4 11 The radius of cir
6、cle A is r, and the radius of circle B is r. What is the ratio of the area of circle A to the area of circle B ? （ A） 1 to 4 （ B） 3 to 4 （ C） 4 to 3 （ D） 9 to 16 （ E） 16 to 9 12 A flat, rectangular flower bed with an area of 2,400 square feet is bordered by a fence on three sides and by a walkway on
7、 the fourth side. If the entire length of the fence is 140 feet, which of the following could be the length, in feet, of one of the sides of the flower bed? Indicate all such lengths. A 20 B 30 C 40 D 50 E 60 F 70 G 80 H 90 13 The quadrants of the xy-plane are shown in the figure above. In the xy-pl
8、ane, line m(not shown)has a positive slope and a positive x- intercept. Line m intersects which of the quadrants? Indicate all such quadrants. （ A） Quadrant I （ B） Quadrant II （ C） Quadrant III （ D） Quadrant IV 14 In the figure above, if , what is the value of r ?r =_ 15 The graph above shows the di
9、stribution of three different flavors of hard candies cherry, lemon, and lime in a candy jar. If all the lemon candies are removed and no other candies are added or removed, what fraction of the remaining candies in the jar will be lime candies? 16 R is a list of 15 consecutive integers, and T is a
10、list of 21 consecutive integers. The median of the integers in list R is equal to the least integer in list T. If the two lists are combined into one list of 36 integers, how many different integers are on the combined list? （ A） 25 （ B） 27 （ C） 28 （ D） 32 （ E） 36 17 From the 5 points A, B, C, D, an
11、d E on the number line above, 3 different points are to be randomly selected. What is the probability that the coordinates of the 3 points selected will all be positive? 18 In a distribution of 850 different measurements, x centimeters is at the 73rd percentile. If there are 68 measurements in the d
12、istribution that are greater than y centimeters but less than x centimeters, then y is approximately at what percentile in the distribution? （ A） 45th （ B） 50th （ C） 55th （ D） 60th （ E） 65th 19 Each of the following linear equations defines y as a function of x for all integers x from 1 to 100. For
13、which of the following equations is the standard deviation of the y-values corresponding to all the x-values the greatest? （ A） y=x/3 （ B） y = x/2+ 40 （ C） y = x （ D） y = 2x + 50 （ E） y = 3x-20 20 For a certain distribution, the measurement 12.1 is 1.5 standard deviations below the mean, and the mea
14、surement 17.5 is 3.0 standard deviations above the mean. What is the mean of the distribution? （ A） 13.8 （ B） 13.9 （ C） 14.0 （ D） 14.1 （ E） 14.2 21 Set A has 50 members and set B has 53 members. At least 2 of the members in set A are not in set B. Which of the following could be the number of member
15、s in set B that are not in set A ? Indicate all such numbers. A 3 B 5 C 13 D 25 E 50 F 53 22 The figure above shows the probability distribution of a continuous random variable X. For each of the five intervals shown, the figure gives the probability that the value of X is in that interval. What is
16、the probability that 1 X 4 ? 23 The populations of the five most populous cities in the United States in April 2000 are listed in the table above. The total population of the United States in April 2000 was 281,422,000. Based on the data shown, the population of the three most populous cities combin
17、ed was what percent of the total population of the United States in April 2000 ?Give your answer to the nearest whole percent._% 24 *For each year, the work time, in hours, required to pay for a food item is the average price of the food item divided by the average hourly wage for rank-and-file manu
18、facturing workers. The work time in the graph is given in minutes.In 1997, at the rates shown in the graph, the work time required to pay for which of the following food items was greatest? （ A） 10 pounds of bread （ B） 5 gallons of milk （ C） 3 pounds of coffee （ D） 20 pounds of sugar （ E） 5 dozen eg
19、gs 25 If the average hourly wage of the rank-and-file manufacturing worker in 1919 was $0.55, which of the following is closest to the average price of 1/2 gallon of milk in 1919? （ A） $0.80 （ B） $0.65 （ C） $0.50 （ D） $0.35 （ E） $0.20 GRE（ QUANTITATIVE）综合模拟试卷 18答案与解析 1 【正确答案】 A 【试题解析】 Note that Quan
20、tity B, $80, is the average of the 4 donations. The average of 2 of the 4 donations, $90 and $60, is $75. Since $75 is less than $80, it follows that Quantity A, the average of the other 2 donations, is greater than Quantity B. Therefore the correct answer is Choice A. This explanation uses the foll
21、owing strategy. Strategy 8: Search for a Mathematical Relationship 2 【正确答案】 D 【试题解析】 Of the 20 oldest employees, 18 are in the 55-64 age-group, and 21 are in the 45-54 age-group. Therefore the youngest of the 20 employees is in the 45-54 age-group, and the oldest is in the 55-64 age-group. The young
22、est of the 20 employees could be 45 years old and the oldest could be 64 years old. In this case, the range of their ages would be 64 - 45, or 19 years. On the other hand, the youngest could be 54 years old and the oldest could be 55 years old, so the range of their ages would be 1 year. Because the
23、re are cases where the range is greater than 11 years and cases where it is less than 11 years, the correct answer is Choice D. This explanation uses the following strategies. Strategy 11: Divide into Cases Strategy 13: Determine Whether a Conclusion Follows from the Information Given 3 【正确答案】 C 【试题
24、解析】 Quantity A is 1+2 + 3 + 4 + 5 + 6 + 7, or 28. The median of the first 7 positive integers is the middle number when they are listed in order from least to greatest, which is 4. So Quantity B is(7)(4), or 28. Thus the correct answer is Choice C. This explanation uses the following strategy. Strat
25、egy 8: Search for a Mathematical Relationship 4 【正确答案】 A 【试题解析】 The two-digit positive integers are the integers from 10 to 99. There are 90 such integers. In 9 of these integers, namely, 11, 22, 33,., 99, the units digit and tens digit are equal. Hence, Quantity A, the number of two-digit positive
26、integers for which the units digit is not equal to the tens digit, is 90-9, or 81. Since Quantity B is 80, the correct answer is Choice A. This explanation uses the following strategy. Strategy 11: Divide into Cases 5 【正确答案】 B 【试题解析】 By the rules of probability, you can conclude that the probability
27、 that event H will not occur is 1 - s. Also, the fact that G and H are independent events implies that G and “not H“ are independent events. Therefore the probability that G will occur and H will not occur is r(1-s). Similarly, the probability that H will occur and G will not occur is s(l - r). So Q
28、uantity A, the probability that either G will occur or H will occur, but not both, is r(1-s)+ s(1-r)= r + s- 2rs, which is less than Quantity B, r + s-rs. Thus the correct answer is Choice B. This explanation uses the following strategy. Strategy 1: Translate from Words to an Arithmetic or Algebraic
29、 Representation 6 【正确答案】 B 【试题解析】 There are 4 numbers in S and 5 numbers in T, so the total number of possible products that can be formed using one number in each set is(4)(5), or 20. However, some of these products have the same value; for example,(1)(8)=(4)(2). Therefore, Quantity A, the number o
30、f different possible values of the product xy, is less than Quantity B, 20. Thus the correct answer is Choice B. This explanation uses the following strategy. Strategy 8: Search for a Mathematical Relationship 7 【正确答案】 B 【试题解析】 Since each support is in the shape of a right triangle with legs of leng
31、th 3 feet and 4 feet, the length of the third side of the support is , or 5 feet. The total length of the stripping of each support is therefore 3 + 4 + 5, or 12 feet. The company has 6,000 feet of metal stripping available. So, with no waste, the greatest possible number of supports that can be pro
32、duced is 6,000/12, or 500. The correct answer is Choice B.This explanation uses the following strategy.Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation 8 【正确答案】 D 【试题解析】 The triangle is a 30-60-90 triangle, so the ratio of the lengths of the legs is 1 to . Since the leng
33、th of the shorter leg, AB, is 6, it follows that the length of the longer leg, AC, is 6 . The area of the triangle is therefore , or 18 . The correct answer is Choice D.This explanation uses the following strategies.Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation Str
34、ategy 8: Search for a Mathematical Relationship 9 【正确答案】 D 【试题解析】 You are given that the volume of the right circular cylinder is 45 and the height is 5. It follows that r2h= 45, or r2h= 45. Since h = 5 and r2h= 45, it follows that r2= 9, or r = 3. Therefore the circumference of the circular base is
35、 2r = 2(3)= 6, and the correct answer is Choice D. This explanation uses the following strategy. Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation 10 【正确答案】 B 【试题解析】 It is clear from the figure that the area of the shaded region is 1/4 of the difference between the area o
36、f the circle and the area of the square. You are given that the area of the square is 16, so each side has length 4.You can find the area of the circle if you know the radius of the circle. If you draw a diagonal of the square, as shown in the figure below, you can see that the diagonal is also a di
37、ameter of the circle. Note that the diagonal divides the square into two isosceles right triangles with legs of length 4. By the Pythagorean theorem applied to one of the right triangles, the length of the diagonal is equal to , or 4 . Thus the radius of the circle is r = , and the area of the circl
38、e is r2=(2 )2=8. Therefore the area of the shaded region is , or 2-4. The correct answer is Choice B.This explanation uses the following strategies.Strategy 4: Translate from a Figure to an Arithmetic or Algebraic RepresentationStrategy 6: Add to a Geometric FigureStrategy 8: Search for a Mathematic
39、al Relationship 11 【正确答案】 E 【试题解析】 Circle A has radius r, so its area is r2. Circle B has radius , so its area is . Therefore the ratio of the area of circle A to the area of circle B is r2 to , which is the same as the ratio 1 to 9/16, which is the same as the ratio 16 to 9.The correct answer is Ch
40、oice E.This explanation uses the following strategy.Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation 12 【正确答案】 B， C， E 【试题解析】 You know that the area of the rectangular flower bed is 2,400 square feet. So if the flower bed is a feet long and b feet wide, then ab = 2,400.
41、If the side of the flower bed that is bordered by the walkway is one of the sides that are b feet long, then the total length of the three sides of the flower bed bordered by the fence is 2a + b feet. Since you are given that the total length of the fence is 140 feet, it follows that 2a + b = 140. S
42、ince ab = 2,400, you can substitute for b in the equation 2a + b=140 to get the equation 2a + = 140. It follows that 2a2 + 2,400 = 140a, or a2 - 70a + 1,200 = 0.When you solve this equation for a(either by factoring or by using the quadratic formula), you get a = 30 or a = 40. If a = 30, then b = =
43、80; if a = 40, then b = = 60. So the possible lengths of the sides are 30, 40, 60, and 80. Thus the correct answer consists of Choices B, C, E, and G.This explanation uses the following strategies.Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation Strategy 8: Search for a
44、Mathematical Relationship 13 【正确答案】 A， C， D 【试题解析】 Since line m has a positive x-intercept, it must cross the x-axis to the right of the origin; and since the slope of line m is positive, the line must slant upward and to the right. Consequently, the line must have a negative y-intercept. The figure
45、 below shows a typical line that satisfies these conditions. In the figure, the line intersects quadrants I, III, and IV. Thus the correct answer consists of Choices A, C, and D.This explanation uses the following strategy.Strategy 6: Add to a Geometric Figure 14 【正确答案】 112.5 【试题解析】 From the figure,
46、 note that r + s must equal 180. Therefore . Since you are also given in the question that , you can conclude that . Thus r = = 112.5, and the correct answer is 112.5.This explanation uses the following strategy.Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation 15 【正确答
47、案】 D 【试题解析】 If the lemon candies are removed, then 85% of the original number of candies will remain. Of these, the fraction of lime candies will be 25/85, or 5/17. The correct answer is Choice D. This explanation uses the following strategy. Strategy 4: Translate from a Figure to an Arithmetic or A
48、lgebraic Representation 16 【正确答案】 C 【试题解析】 The median of the numbers in list R is the middle number when the numbers are listed in order from least to greatest, that is, the 8th number. Since the median of the numbers in list R is equal to the least integer in list T, the 8 greatest integers in R ar
49、e the 8 least integers in T, and the number of different integers in the combined list is 15 + 21-8, or 28. The correct answer is Choice C. This explanation uses the following strategy. Strategy 8: Search for a Mathematical Relationship 17 【正确答案】 A 【试题解析】 Of the 5 points, 3 have positive coordinates, points C, D, and E. The probability that the first point selected will have a positive coordinate is 3/5. Since the second point selected must be different from the first point, there are 4 remaining points to select from, of which 2 are points with positive
