GRE-练习七及答案解析.doc

1、GRE-练习七及答案解析(总分：30.00，做题时间：90 分钟)一、Quantitative Compari(总题数：2，分数：15.00)a, b, and c are the measures of the anglesof isosceles triangle ABCx, y, and z are the measures of the anglesof right triangle XYZLine k goes through (1,1) and (5,2).Line m is perpendicular to k.（分数：9.00）A.B.C.D.A.B.C.D.A.B.C.D.A

2、B.C.D.A.B.C.D.A.B.C.D.A.B.C.D.A.B.C.D.A.B.C.D.O is the center of the circle of radius 6.OXYZ is a square.The number of square inches in the surface area of a cube is equal to the number of cubic inches in its volume.（分数：6.00）A.B.C.D.A.B.C.D.A.B.C.D.A.B.C.D.A.B.C.D.A.B.C.D.二、Data Interpretation (总题数

3、6，分数：15.00)UQuestions 1-2/U refer to the following graphs.Vitamin C Content of Foodsinterpretation questions, each pair referring to a different set of graphs. However, to illustrate the variety of questions that can be asked, in this exercise set, for some of the graphs there is only one question

4、and for some there are three questions.（分数：2.00）(1).What is the ratio of the amount of Vitamin C in 500 grams of orange to the amount of Vitamin C in 500 grams of orange juice? A. 4:7 B. 1:1 C. 7:4 D. 2:1 E. 4:1（分数：1.00）A.B.C.D.(2).How many grams of tomato would you have to eat to be certain of gett

5、ing more vitamin C than you would get by eating 100 grams of raw broccoli? A. 300B. 500C. 750D. 1200E. 1650（分数：1.00）A.B.C.D.Questions 3-5 refer to the following graphs.（分数：3.00）(1).If there were 10,000,000 college students in 1975, how many more male students were there than female students? A. 800,

6、000 B. 1,600,000 C. 2,400,000 D. 4,600,000 E. 5,400,000（分数：1.00）A.B.C.D.(2).In 1975 what percent of female college students were at least 25 years old? A. 14%B. 30%C. 45% D. 69%E. 76%（分数：1.00）A.B.C.D.(3).If the total number of students enrolled in college was 40% higher in 1995 than in 1975, what is

7、 the ratio of the number of male students in 1995 to the number of male students in 1975? A. 5:6 B. 6:7 C. 7:6 D. 6:5 E. 7:5（分数：1.00）A.B.C.D.Questions 6-8 refer to the following graph.（分数：3.00）(1).If 1,000,000 vehicles were stolen in 1994, how many were stolen in 1996? A. 889,000 B. 906,000 C. 940,0

8、00 D. 1,094,000 E. 1,100,000（分数：1.00）A.B.C.D.(2).By what percent did the number of vehicles stolen decrease from 1997 to 1998? A. 7.4%B. 8.0%C. 8.4% D. 12.0%E. 19.4%（分数：1.00）A.B.C.D.(3).To the nearest percent, by what percent did the population of the United States increase from 1994 to 1998? A. 1%B

9、 2%C. 3%D. 4%E. 5%（分数：1.00）A.B.C.D.Questions 9-10 refer to the following graph.（分数：2.00）(1).What percent of underweight adult females perceive themselves to be underweight? A. 5%B. 22%C. 38%D. 50%E. 70%（分数：1.00）A.B.C.D.(2).The members of which of the four groups had the least accurate perception of

10、 their body weight? A. Underweight B. Normal weight C. Moderately overweight D. Severely overweight E. It cannot be determined from the information given in the graph.（分数：1.00）A.B.C.D.Questions 11-12 refer to the tables at the bottom of the page.Residents of New York City pay both New York State and

11、 New York City tax.Residents of New York State who live and work outside of New York City pay only New York State tax.（分数：2.00）(1).In 1979 how much tax would a resident of New York State who lived and worked outside New York City have paid on a taxable income of $16,100? A. $34B. $110C. $352 D. $970

12、E. $1322（分数：1.00）A.B.C.D.(2).In 1979, how much more total tax would a resident of New York City who had a taxable income of $36,500 pay, compared to a resident of New York City who had a taxable income of $36,000? （分数：1.00）A.B.C.D.Questions 13-14 refer to the following tables.Years of Life Expectanc

13、y at Birth(Life expectancy in years)（分数：3.00）(1).For how many of the countries listed in the graphs is it true that the life expectancy of a female born in 1955 was higher than the life expectancy of a male born in 1990? A. NoneB. IC. 2D. 3E. 4（分数：1.00）A.B.C.D.(2).By sex and nationality, who had the

14、 greatest increase in life expectancy between 1955 and 1990? A. A Korean female B. A Korean male C. A Costa Rican female D. A Costa Rican male E. A Norwegian female（分数：1.00）A.B.C.D.(3).Question 15 refers to the following graph.（分数：1.00）A.B.C.D.GRE-练习七答案解析(总分：30.00，做题时间：90 分钟)一、Quantitative Compari(总

15、题数：2，分数：15.00)a, b, and c are the measures of the anglesof isosceles triangle ABCx, y, and z are the measures of the anglesof right triangle XYZLine k goes through (1,1) and (5,2).Line m is perpendicular to k.（分数：9.00）A.B. C.D.解析：This can easily be solved in less than a minute by adding, but in only

16、 5 seconds by thinking! Use TACTIC 5: dont calculate; compare. Each of the three numbers in Column B is greater than the corresponding number in Column A.A.B.C.D. 解析：Use TACTIC 1. When x = 1, the columns are equal; when x = 2, they arent. *Use TACTIC 3 * This is a much easier comparison, x2 could eq

17、ual 1, but doesnt have to. The answer is Choice D.A. B.C.D.解析：You can easily calculate each of the times by dividing 7 by 6 in Column A, and 6 by 7 in Column B. However, it is easier to just observe that the time in Column A is more than one hour, whereas the time in Column B is less than one hour.A

18、B. C.D.解析：Use TACTIC 3*Since it is given that cd 0, so is 2cd.*If you cant expand (c + d)2, use TACTIC 1. Replace c and d with numbers satisfying cd 0. Column A Column B CompareEliminateLet c = 1and d = -1(1 +-1)2 =012 + (-1)2 =1+1=2B isgreaterA and CLet c = 3and d = -5(3 +-5)2=(-2)2 = 432 + (-5)2

19、9 + 25 = 34B isgreaterBoth times Column B was greater: choose B.A.B.C. D.解析：The average of 3 numbers is their sum divided by 3. Since in any triangle the sum of the measures of the 3 angles is 180 KEY FACT J 1 , the average in each column is equal to 180 + 3 = 60. *Use TACTIC 1. Pick values for the

20、 measures of the angles. For example, in isosceles ABC choose 70, 70, 40; in right XYZ, choose 30, 60, 90. Each average is 60. Choose C.A.B. C.D.解析：Since b 0, 6b is negative, whereas b 6 is positive.*Use TACTIC 1. Replace b with numbers satisfying b 0. Column A Column B Compare EliminateLet b = -16(

21、1) = -6 (-1)6 = 1 B is greaterA and CLet b = -26(-2) = -12(-2)6 = 64 B is greaterBoth times Column B was greater: choose B.A.B. C.D.解析：Again, use TACTIC 5: dont calculate the two areas; compare them. The circle in Column A has a radius of 17, and so its diameter is 34. Since the circle in Column B

22、has a larger diameter, its area is greater.A. B.C.D.解析：Again, use TACTIC 5: dont calculate either slope. Quickly, make a rough sketch of line k, going through (1,1) and (5,2), and draw line m perpendicular to it. * Line k has a positive slope (it slopes upward), whereas line m has a negative slope (

23、it slopes downward). Column A is greater. Note: the slope of k is* and the slope of m is -4. See Section 14-N for all the facts you need to know about slopes. *If you dont know this fact about slopes, use TACTIC 6. The answer cannot be Choice D, and if two lines intersect, their slopes cannot be equ

24、al, so eliminate Choice C. Guess Choices A or B.A.B.C.D. 解析：Every sixth integer is a multiple of 6 and every ninth integer is a multiple of 9, so in a large interval there will be many more multiples of 6. But in a very small interval, there might be none or possibly just one of each. *Use TACTIC 1.

25、 Let x = 1. Between 100 and 101 there are no multiples of 6 and no multiples of 9. Eliminate Choices A and B. Choose a large number for x: 100, for example. Between 100 and 200 there are many more multiples of 6 than there are multiples of 9. Eliminate Choice C.O is the center of the circle of radiu

26、s 6.OXYZ is a square.The number of square inches in the surface area of a cube is equal to the number of cubic inches in its volume.（分数：6.00）A.B.C. D.解析：* Since 2y = 0, y = 0. *Use TACTIC 4. Could y = 0? In each equation, if y = 0, then x = -5. So, y can equal 0. Eliminate Choices A and B, and eithe

27、r guess between Choices C and D or try to continue. Must y = 0? Yes, when you have two linear equations in two variables, there is only one solution, so nothing else is possible.A. B.C.D.解析：The arithmetic is annoying and time-consuming, but not difficult. However, you can avoid the arithmetic, if yo

28、u know KEY FACT A24:If 0x 1 and n 1, then x n x.*A.B. C.D.解析：The area of the shaded region is the area of quarter-circle AOB minus the area of the square. Since r = OA = 6, the area of the quarter-circle is *OY, the diagonal of the square, is 6 (since it is a radius of the. circle), so OZ, the side

29、of the square, is *KEY FACT J8. So the area of the square is*Finally, the area of the shaded region is 9 - 18, which is approximately 10. *The solution above requires several steps. See Sections 14-J, K, L to review any of the facts used. If you cant reason through this, you still should be able to

30、answer this question correctly. Use TACTIC 6. The shaded region has a definite area, which is either 12, more than 12, or less than 12. Eliminate D. Also, the area of a curved region almost always involves , so assume the area isnt exactly 12. Eliminate Choice C. You can now guess between Choices A

31、and B, but if you trust the diagram and know a little bit you can improve your guess. If you know that the area of the circle is 36, so that the quarter-circle is 9 or about 28, you can estimate the shaded region. Its well less than half of the quarter-circle, so less than 14 and probably less than

32、12. Guess Choice B.A.B.C. D.解析：Use TACTIC 4. Could the edge be 6? Test it. If each edge is 6, the area of each face is 6 6 = 36, and since a cube has 6 faces, the total surface area is 6 36 = 216. The volume is 63 = 216. So the columns could be equal. Eliminate Choices A and B. If you have a sense t

33、hat this is the only cube with this property, choose C. In fact, if you had no idea how to do this, you might use TACTIC 6, assume that there is only one way, eliminate Choice D, and then guess C. The direct solution is simple enough if you know the formulas. The area is 6e2 and the volume is e3: 6e

34、2 = e3 *6 = e.A.B.C.D. 解析：There are several ways to do this. Use TACTIC 1: plug in a number for x. If x = 2, Column A is 2, which is slightly more than 6, and Column B is 2 2 = 4. Column A is greater: eliminate Choices B and C. Must Column A be greater? If the only other number you try is x = 3, you

35、ll think so, because 32 = 9, but 3 9. But remember, x does not have to be an integer: 3.92 15, whereas 3.9 4, which is a little over 12.*Use TACTIC 4. Could x = x 2? Yes, if x = . Must x = ? No.*Use TACTIC 3. Divide each side by x: Now Column A is and Column B is x. Which is bigger, or x? We cannot

36、tell.A.B.C.D. 解析：Use TACTIC 4. Could the area of ABC = 3? Since the height is 6, the area would be 3 only if the base were *Could BC = 1 ? Sure (see the figure). Must the base be 1? Of course not. *二、Data Interpretation (总题数：6，分数：15.00)UQuestions 1-2/U refer to the following graphs.Vitamin C Content

37、 of Foodsinterpretation questions, each pair referring to a different set of graphs. However, to illustrate the variety of questions that can be asked, in this exercise set, for some of the graphs there is only one question and for some there are three questions.（分数：2.00）(1).What is the ratio of the

38、 amount of Vitamin C in 500 grams of orange to the amount of Vitamin C in 500 grams of orange juice? A. 4:7 B. 1:1 C. 7:4 D. 2:1 E. 4:1（分数：1.00）A.B.C. D.解析：According to the graph on the left, there are approximately 70 milligrams of vitamin C in 100 grams of orange and 40 milligrams in the same amou

39、nt of orange juice. This is a ratio of 70:40 = 7:4. Since the question refers to the same amount of orange and orange juice (500 grams), the ratio is unchanged.(2).How many grams of tomato would you have to eat to be certain of getting more vitamin C than you would get by eating 100 grams of raw bro

40、ccoli? A. 300B. 500C. 750D. 1200E. 1650（分数：1.00）A.B.C.D.解析：From the graph on the right, you can see that by eating 100 grams of raw broccoli, you could receive as much as 165 milligrams of vitamin C. Since 100 grams of tomato could have as little as 10 milligrams of vitamin C, you would have to eat

41、1650 grams of tomato to be sure of getting 165 milligrams of vitamin C.Questions 3-5 refer to the following graphs.（分数：3.00）(1).If there were 10,000,000 college students in 1975, how many more male students were there than female students? A. 800,000 B. 1,600,000 C. 2,400,000 D. 4,600,000 E. 5,400,0

42、00（分数：1.00）A. B.C.D.解析：From the top graph, we see that in 1975, 54% (35% + 19%) of all college students were male, and the other 46% were female. So there were 5,400,000 males and 4,600,000 femalesa difference of 800,000.(2).In 1975 what percent of female college students were at least 25 years old?

43、 A. 14%B. 30%C. 45% D. 69%E. 76%（分数：1.00）A.B. C.D.解析：In 1975, of every 100 college students, 46 were female32 of whom were less than 25 years old, and 14 of whom were 25 years old and over. So, 14 of every 46 female students were at least 25 years old. Finally, *(3).If the total number of students e

44、nrolled in college was 40% higher in 1995 than in 1975, what is the ratio of the number of male students in 1995 to the number of male students in 1975? A. 5:6 B. 6:7 C. 7:6 D. 6:5 E. 7:5（分数：1.00）A.B.C. D.解析：From the two graphs, we see that in 1975 54% (35% + 19%) of all college students were male,

45、whereas in 1995 the corresponding figure was 45% (28% + 17%). For simplicity, assume that there were 100 college students in 1975, 54 of whom were male. Then in 1995, there were 140 college students, 63 of whom were male (45% of 140 = 63). So the ratio of the number of male students in 1995 to the n

46、umber of male students in 1975 is 63:54 = 7:6.Questions 6-8 refer to the following graph.（分数：3.00）(1).If 1,000,000 vehicles were stolen in 1994, how many were stolen in 1996? A. 889,000 B. 906,000 C. 940,000 D. 1,094,000 E. 1,100,000（分数：1.00）A.B. C.D.解析：From 1994 to 1996 there was a 9.4% decrease in

47、 the number of vehicles stolen. Since 9.4% of 1,000,000 = 94,000, the number of vehicles stolen in 1996 was 1,000,000 - 94,000 = 906,000. If you cant solve problems such as this, you have to guess. But since the number of stolen vehicles is clearly decreasing, be sure to eliminate Choices D and E fi

48、rst.(2).By what percent did the number of vehicles stolen decrease from 1997 to 1998? A. 7.4%B. 8.0%C. 8.4% D. 12.0%E. 19.4%（分数：1.00）A.B.C. D.解析：For simplicity, assume that 1000 vehicles were stolen in 1994. By 1997, the number had decreased by 12.0% to880 (12% of 1000 = 120, and 1000 - 120 = 880);

49、by 1998, the number had decreased 19.4% to 806 (19.4% of 1000 = 194 and 1000 - 194 = 806). So from 1997 to 1998, the number of vehicles stolen decreased by 74 from 880 to 806. This represents a decrease of*(3).To the nearest percent, by what percent did the population of the United States increase from 1994 to 1998? A. 1%B. 2%C. 3%D. 4%E. 5%（分数：1.00）A.B.C.D.