GRE-练习六及答案解析.doc

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1、GRE-练习六及答案解析(总分：30.00，做题时间：90 分钟)一、General Math Strateg(总题数：12，分数：15.00)（分数：3.00）A.B.C.D.A.B.C.D.A.B.C.D.1.If 5x + 13 = 31, what is the value of （分数：1.00）A.B.C.D.E.2.If a + 2b = 14 and 5a + 4b = 16, what is the average (arithmetic mean) of a and b? (A) 1.5 (B) 2 (C) 2.5 (D) 3 (E) 3.5（分数：1.00）A.B.C.D

2、.E.3.In the figure at the right, ABCD is a square and AED is an equilateral triangle. If AB = 2, what is the area of the shaded region?（分数：1.00）A.B.C.D.E.4.In the figure below, vertex Q of square OPQR is on a circle with center O. If the area of the square is 8, what is the area of the circle?（分数：1.

3、00）A.B.C.D.E.5.In writing all of the integers from 1 to 300, how many times is the digit 1 used? (A) 60 (B) 120 (C) 150 (D) 160 (E) 180（分数：1.00）A.B.C.D.E.6.In the figure below, if the radius of circle O is 10, what is the length of diagonal AC of rectangle OABC?（分数：1.00）A.B.C.D.E.7.At Leos Lumberyar

4、d, an 8-foot long wooden pole costs $3.00. At this rate, what is the cost, in cents, of a pole that is 16 inches long? (A) 0.5 (B) 48 (C) 50 (D) 64 (E) 96（分数：1.00）A.B.C.D.E.8.In the figure below, three circles of radius 1 are tangent to one another. What is the area of the shaded region between them

5、?（分数：1.00）A.B.C.D.E.Questions 14-15 refer to the following definition.a, b represents the remainder when a is divided by b.（分数：2.00）A.B.C.D.A.B.C.D.9.In 1999, Diana read 10 English books and 7 French books. In 2000, she read twice as many French books as English books. If 60% of the books! that she

6、read during the two years were French, how many books did she read in 2000? (A) 16 (B) 26 (C) 32 (D) 39 (E) 48（分数：1.00）A.B.C.D.E.10.In the figure below, equilateral triangle ABC is inscribed in circle O, whose radius is 4. Altitude BD is extended until it intersects the circle at E. What is the leng

7、th of DE?（分数：1.00）A.B.C.D.E.二、Discrete Quantitativ(总题数：15，分数：15.00)11.If x and y are integers such that x3 = y2, which of the following could not be the value of y? (A) -1 (B) 1 (C) 8 (D) 16 (E) 27（分数：1.00）A.B.C.D.E.12.For what value of x is 82x-4 = 16x? (A) 2 (B) 3 (C) 4 (D) 6 (E) 8（分数：1.00）A.B.C.D

8、.E.13.Alison is now three times as old as Jeremy, but 5 years ago, she was 5 times as old as he was. How old is Alison now? (A) 10 (B) 12 (C) 24 (D) 30 (E) 36（分数：1.00）A.B.C.D.E.14.Judy plans to visit the National Gallery once each month in 2001 except in July and August when she plans to go three ti

9、mes each. A single admission costs $3.50, a pass valid for unlimited visits in any 3-month period can be purchased for $18, and an annual pass costs $60.00. What is the least amount, in dollars, that Judy can spend for her intended number of visits? (A) 72 (B) 60 (C) 56 (D) 49.5 (E) 48（分数：1.00）A.B.C

10、.D.E.15.If an object is moving at a speed of 36 kilometers per hour, how many meters does it travel in one second? (A) 10 (B) 36 (C) 100 (D) 360 (E) 1000（分数：1.00）A.B.C.D.E.16.What is a divided by a% of a?（分数：1.00）A.B.C.D.E.17.If x% of y is 10, what is y?（分数：1.00）A.B.C.D.E.18.In the figure at the rig

11、ht, WXYZ is a square whose sides are 12. AB, CD, EF, and GH are each 8, and are the diameters of the four semicircles. What is the area of the shaded region?（分数：1.00）A.B.C.D.E.19.If 12a + 3b = 1 and 7b - 2a = 9, what is the average (arithmetic mean) of a and b? (A) 0.1 (B) 0.5 (C) l (D) 2.5 (E) 5（分数

12、：1.00）A.B.C.D.E.20.If 120% of a is equal to 80% of b, which of the following is equal to a + b? (A) 1.5a (B) 2a (C) 2.5a (D) 3a (E) 5a（分数：1.00）A.B.C.D.E.21.If w widgets cost c cents, how many widgets can you get for d dollars?（分数：1.00）A.B.C.D.E.22.What is the largest prime factor of 255? (A)5 (B) 15

13、 (C) 17 (D)51 (E)255（分数：1.00）A.B.C.D.E.23.If c is the product of a and b, which of the following is the quotient of a and b?（分数：1.00）A.B.C.D.E.24.On a certain French-American committee, of the members are men, a and of the men are Americans. If of the committee members are French, what fraction of t

14、he members are American women?（分数：1.00）A.B.C.D.E.25.Evan has 4 times as many books as David and 5 times as many as Jason. If Jason has more than 40 books, what is the least number of books that Evan could have? (A) 200 (B) 205 (C) 210 (D) 220 (E) 240（分数：1.00）A.B.C.D.E.GRE-练习六答案解析(总分：30.00，做题时间：90 分钟

15、)一、General Math Strateg(总题数：12，分数：15.00)（分数：3.00）A.B. C.D.解析：If you dont see how to do this, use TACTIC 2: trust the diagram. Estimate the measure of each angle: for example, a = 45, b = 70, c = 30, and d = 120. So c + d (150) is considerably greater than a + b (115). Choose B.*In fact, d by itself

16、is equal to a + b (an exterior angle of a triangle is equal to the sum of the opposite two interior angles). So c+da+b.A.B. C.D.解析：From the figure, it appears that x and y are equal, or nearly so. However, the given information states that BC CD, but this is not clear from the diagram. Use TACTIC 3:

17、 when you draw the figure on your scrap paper, exaggerate it. Draw it with BC much greater than CD. Now it is clear that y is greater.*Since BC CD. central angle 1 is greater than central angle 2, which means that x y.A.B.C. D.解析：Use TACTIC 8. Systematically list all the factors of 30, either indivi

18、dually or in pairs: 1, 30; 2, 15; 3, 10; 5, 6. Of the 8 factors, 4 are even and 4 are odd.1.If 5x + 13 = 31, what is the value of （分数：1.00）A.B.C. D.E.解析：Use TACTIC 6: dont do more than you have to. In particular, dont solve for x.*2.If a + 2b = 14 and 5a + 4b = 16, what is the average (arithmetic me

19、an) of a and b? (A) 1.5 (B) 2 (C) 2.5 (D) 3 (E) 3.5（分数：1.00）A.B.C. D.E.解析：Use TACTIC 6: dont do more than is necessary. You do not need to solve this system of equations; we dont need to know the values of a and b, only their average. Adding the two equations, we get 6a + 6b = *3.In the figure at th

20、e right, ABCD is a square and AED is an equilateral triangle. If AB = 2, what is the area of the shaded region?（分数：1.00）A.B.C.D.E. 解析：Use TACTIC 5: subtract to find the shaded area. The area of the square is 4. The area of the equilateral triangle (see Section 14-J) is*4.In the figure below, vertex

21、Q of square OPQR is on a circle with center O. If the area of the square is 8, what is the area of the circle?（分数：1.00）A.B.C. D.E.解析：Use TACTICS 2 and 4. On your scrap paper, extend line segments OP and OR.*Square OPQR, whose area is 8, takes up most of quarter-circle OXY. So the area of the quarter

22、-circle is certainly between 11 and 13. The area of the whole circle is 4 times as great: between 44 and 52. Check the five choices: they are approximately 25, 36, 50, 100, 200. The answer is clearly C.*Another way to use TACTIC 4 is to draw in line segment OQ.*Since the area of the square is 8, eac

23、h side is *, and diagonal OQ is * 4. But OQ is also a radius, so the area of the circle is 16.5.In writing all of the integers from 1 to 300, how many times is the digit 1 used? (A) 60 (B) 120 (C) 150 (D) 160 (E) 180（分数：1.00）A.B.C.D. E.解析：Use TACTIC 8. Systematically list the numbers that contain th

24、e digit 1, writing as many as you need to see the pattern. Between 1 and 99 the digit 1 is used 10 times as the units digit (1, 11, 21 91) and 10 times as the tens digit (10, 11, 12,.,19) for a total of 20 times. From 200 to 299, there are 20 more (the same 20 preceded by a 2). From 100 to 199 there

25、 are 20 more plus 100 numbers where the digit 1 is used in the hundreds place. So the total is 20 + 20 + 20 + 100 = 160.6.In the figure below, if the radius of circle O is 10, what is the length of diagonal AC of rectangle OABC?（分数：1.00）A.B.C.D. E.解析：Use TACTIC 2. Trust the diagram: AC, which is cle

26、arly longer than OC, is approximately as long as radius OE.*Therefore, AC must be about 10. Check: the choices. They are approximately 1.4, 3.1, 7, 10, and 14. The answer must be 10.*The answer is 10. Use TACTIC 4: copy the diagram on your scrap paper and draw in diagonal OB.*Since the two diagonals

27、 of a rectangle are equal, and diagonal OB is a radius,OA = OB = 10.7.At Leos Lumberyard, an 8-foot long wooden pole costs $3.00. At this rate, what is the cost, in cents, of a pole that is 16 inches long? (A) 0.5 (B) 48 (C) 50 (D) 64 (E) 96（分数：1.00）A.B.C. D.E.解析：This is a relatively simple ratio pr

28、oblem, but use TACTIC 7 and make sure you get the units right. To do this you need to know that there are 100 cents in a dollar and 12 inches in a foot.*8.In the figure below, three circles of radius 1 are tangent to one another. What is the area of the shaded region between them?（分数：1.00）A.B.C.D. E

29、.解析：Use TACTIC 4 and add some lines: connect the centers of the three circles to form an equilateral triangle whose sides are 2.*Now use TACTIC 5 and find the shaded area by subtracting the area of the three sectors from the area of the triangle. The area of the triangle is*(see Section 14-J). Each

30、sector is one sixth of a circle of radius 1. Together they form one half of such a circle, so their total area is *. Finally subtract: the shaded area is *Questions 14-15 refer to the following definition.a, b represents the remainder when a is divided by b.（分数：2.00）A. B.C.D.解析：Column A: When 10 3 (

31、1000) is divided by 3,the quotient is 333 and the remainder is 1.Column B: 105 is divisible by 5, so theremainder is 0.Column A is greater.A. B.C.D.解析：Column A: since c d, the quotient when c is divided by d is 0, and the remainder is c.Column B: when d is divided by c the remainder must be less tha

32、n c.So Column A is greater.9.In 1999, Diana read 10 English books and 7 French books. In 2000, she read twice as many French books as English books. If 60% of the books! that she read during the two years were French, how many books did she read in 2000? (A) 16 (B) 26 (C) 32 (D) 39 (E) 48（分数：1.00）A.

33、B.C.D.E. 解析：Use TACTIC 1: draw a picture representing a pile of books or a bookshelf.*In the two years the number of French books Diana read was 7 + 2x and the total number of books was 17 + 3x. Then 60% or*In 2000, Diana read 16 English books and 32 French books, a total of 48 books.10.In the figur

34、e below, equilateral triangle ABC is inscribed in circle O, whose radius is 4. Altitude BD is extended until it intersects the circle at E. What is the length of DE?（分数：1.00）A.B.C. D.E.解析：Use TACTIC 5: to get DE, subtract OD from radius OE, which is 4. Draw AO (TACTIC 4). Since AOD is a 30-60-90 rig

35、ht triangle, OD is 2 (one half of OA). So, DE = 4 - 2 = 2.*二、Discrete Quantitativ(总题数：15，分数：15.00)11.If x and y are integers such that x3 = y2, which of the following could not be the value of y? (A) -1 (B) 1 (C) 8 (D) 16 (E) 27（分数：1.00）A.B.C.D. E.解析：Test each choice until you find the correct answe

36、r. Could y = -1 ? Is there an integer x such that x3 = (-1)2 = 1? Yes, x = 1. Similarly, if y = 1, x = 1. Could y = 8? Is there an integer x such that x3 = (8)2 = 64? Yes, x=4. Could y = 16? Is there an integer x such that x3 = 162 = 256? No, 63 = 216, which is too small; and 73 = 343, which is too

37、big. The answer is D.12.For what value of x is 82x-4 = 16x? (A) 2 (B) 3 (C) 4 (D) 6 (E) 8（分数：1.00）A.B.C.D. E.解析：Use the laws of exponents to simplify the equation, and then solve it: 8 2x-4 = 16x* (23)2x-4= (24)x * 3(2x - 4) = 4x* 6x- 12 =4x* 2x= 12*x=6.13.Alison is now three times as old as Jeremy,

38、 but 5 years ago, she was 5 times as old as he was. How old is Alison now? (A) 10 (B) 12 (C) 24 (D) 30 (E) 36（分数：1.00）A.B.C.D. E.解析：Use TACTIC 1: backsolve starting with C. If Alison is now 24, Jeremy is 8, and 5 years ago, they would have been 19 and 3, which is more than 5 times as much. Eliminate

39、 A, B, and C, and try a bigger value. If Alison is now 30, Jeremy is 10, and 5 years ago, they would have been 25 and 5. Thats it; 25 is 5 times 5.*If Jeremy is now x, Alison is 3x, and 5 years ago they were x - 5 and 3x - 5, respectively. Now, solve:*14.Judy plans to visit the National Gallery once

40、 each month in 2001 except in July and August when she plans to go three times each. A single admission costs $3.50, a pass valid for unlimited visits in any 3-month period can be purchased for $18, and an annual pass costs $60.00. What is the least amount, in dollars, that Judy can spend for her in

41、tended number of visits? (A) 72 (B) 60 (C) 56 (D) 49.5 (E) 48（分数：1.00）A.B.C.D. E.解析：Judy intends to go to the Gallery 16 times during the year. Buying a single admission each time would cost 16 $3.50 = $56, which is less than the annual pass. If she bought a 3-month pass for June, July, and August,

42、she would pay $18 plus $31.50 for 9 single admissions (9 $3.50), for a total expense of $49.50, which is the least expensive option.15.If an object is moving at a speed of 36 kilometers per hour, how many meters does it travel in one second? (A) 10 (B) 36 (C) 100 (D) 360 (E) 1000（分数：1.00）A. B.C.D.E.

43、解析：*Use TACTIC 1: Test choices starting with C:100 meters/second = 6000 meters/minute= 360,000 meters/hour = 360 kilometers (hour.Not only is that too big, it is too big by a factor of 10. The answer is 10.16.What is a divided by a% of a?（分数：1.00）A.B. C.D.E.解析：*Use TACTICS 2 and 3: replace a by a nu

44、mber, and use 100 since the problem involves percents. 100 + (100% of 100) = 100 + 100 = 1. Test each choice; which one equals 1 when a = 100. Both A and B:*.Eliminate Choices C, D, and E, and test A and B with another value for a. 50(50% of 50)=50(25)=2.Now, only B works *17.If x% of y is 10, what

45、is y?（分数：1.00）A.B.C. D.E.解析：Pick easy-to-use numbers. Since 100% of 10 is 10, let x = 100 and y = 10. When x = 100, Choices C and E are each 10. Eliminate Choices A, B, and D, and try some other numbers: 50% of 20 is 10. Of Choices C and E, only C = 20 when x = 50.18.In the figure at the right, WXYZ

46、 is a square whose sides are 12. AB, CD, EF, and GH are each 8, and are the diameters of the four semicircles. What is the area of the shaded region?（分数：1.00）A.B.C. D.E.解析：If you dont know how to solve this, you must use TACTIC 4 and guess after eliminating the absurd choices. Which choices are absu

47、rd? Certainly, A and B, both of which are negative. Also, since Choice D is about 94, which is much more than half the area of the square, it is much too big. Guess between Choice C (about 43) and Choice E (about 50). If you remember that the way to find shaded areas is to subtract, guess C.*The are

48、a of the square is 122 = 144. The area of each semicircle is 8, one-half the area of a circle of radius 4. So together the areas of the semicircles is 3219.If 12a + 3b = 1 and 7b - 2a = 9, what is the average (arithmetic mean) of a and b? (A) 0.1 (B) 0.5 (C) l (D) 2.5 (E) 5（分数：1.00）A.B. C.D.E.解析：Add

49、 the two equations:*Do not waste time solving for a and b.20.If 120% of a is equal to 80% of b, which of the following is equal to a + b? (A) 1.5a (B) 2a (C) 2.5a (D) 3a (E) 5a（分数：1.00）A.B.C. D.E.解析：Since 120% of 80 = 80% of120,1et a = 80 and b = 120. Then a + b = 200, and 200 + 80 = 2.5.21.If w widgets cost c cents, how many widgets can you get for d d