[外语类试卷]GMAT（QUANTITATIVE）数学模拟试卷1及答案与解析.doc

1、GMAT（ QUANTITATIVE）数学模拟试卷 1及答案与解析 一、 QUANTITATIVE 0 Solve the problem and indicate the best of the answer choices given. NUMBERS: All numbers used are real numbers. FIGURES: A figure accompanying a problem-solving question is intended to provide information useful in solving the problem. Figures are

2、 drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale. Straight lines may sometimes appear jagged. All figures lie in a plane unless otherwise indicated. The following data sufficiency problems consist of a question and two statements,

3、labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning

4、 of counterclockwise), you must indicate whether . Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. . Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. . BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. . EAC

5、H statement ALONE is sufficient. . Statements (1) and (2) TOGETHER are NOT sufficient. 1 A hiker in a national forest stopped at a ranger station to add water to her canteen. How many ounces of water were in the canteen when she arrived at the ranger station? (1) The hiker added 24 ounces to the can

6、teen at the ranger station. (2) After the hiker added water to the canteen, the canteen was 75 percent full. 2 If b a, then a is what percent of b? (1) a=4 (2) b=4a 3 If all apples at a certain grocery store are equally priced, and all pears at the same grocery store are equally priced, what is the

7、same price of a pear? (1) Eight pears cost eighty cents more than eight apples. (2) Ten apples cost twenty cents more than eight pears. 4 If each of the segments marked on the board above is of equal length, and if x and y represent the indicated lines on the board, then what is the distance between

8、 x and y? (There are twelve inches in a foot). (1) The board is five feet long. (2) x is 18 inches from the nearest end of the board. 5 Any decimal that has a finite number of nonzero digits is a terminating decimal. For example, 16, 12.43, and 0.26 are all terminating decimals. If a and b are posit

9、ive integers and the ratio a/b is expressed as a decimal, is a/b a terminating decimal? (1) b=5 (2) 70 a 80 6 A company, Chauncy Co., has an annual travel budget of $55,000. The accounting department estimates that transportation expenses Will increase 5 percent in the coming year, and nontransporta

10、tion travel expenses will increase by 15 percent in the coming year. Last year, Chauncy Co. spent $19,500 on transportation-related expenses, and $35,000 on nontransportation travel expenses. If the annual travel budget does not increase this year, and if the accounting departments estimates are cor

11、rect, how far over the annual travel budget will expenses be this year? （ A） Expenses will not go over the budget. （ B） $5O0 （ C） $4,225 （ D） $5,725 （ E） $60,725 7 A hiker walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hou

12、r, but she walked one mile per hour faster than on the first day. On the third day she walked the same number of hours as on the first day but at the same speed as on the second day. How many miles in total did she walk? （ A） 24 （ B） 44 （ C） 58 （ D） 60 （ E） 62 8 9 （ A） 0.0125 （ B） 0.025 （ C） 0.1 （ D

13、） 0.25 （ E） 0.625 10 The promoters of the Springfield music festival estimated a 50 percent increase in ticket sales from last year, but because of bad weather, ticket sales actually decreased by 25 percent from last years level. What percent of the projected ticket sales were the actual ticket sale

14、s? （ A） 45 （ B） 50 （ C） 55 （ D） 65 （ E） 75 11 If the average (arithmetic mean) of x and y is 40, and z-x=60, what is the average of y and z? （ A） 20 （ B） 50 （ C） 65 （ D） 70 （ E） 140 12 When Greenville State University decided to move its fine arts collection to a new library, it had to package the c

15、ollection in 20-inch by 20-inch by 15-inch boxes. If the university pays $0.50 for every box, and if the university needs 3.6 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes? （ A） $255 （ B） $275 （ C） $510 （ D） $1,250 （ E） $2,550 12 The fo

16、llowing data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathe

17、matics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether . Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. . Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. . BOTH statemen

18、ts TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. . EACH statement ALONE is sufficient. . Statements (1) and (2) TOGETHER are NOT sufficient. 13 If n is a positive integer and m=6.2510n what is the value of n? (1) 500 m 5,000 (2) m 6,250 14 If p+q=400 and p q, is p+q r+s? (1) p+

19、r+s=600 (2) q+r 400 15 If n is an integer, and n0, is a positive integer? (1) n2=25 (2) 5n=25 16 Over the weekend, a shoe store sold 1/3 of the shoes in its stock. The average price of the shoes sold was $60 per pair. What was the total revenue from shoe sales over the weekend for this shoe store? (

20、1) When the store closed on Sunday night, 600 pairs of shoes were still in stock. (2) The store began the weekend with 900 pairs of shoes. 17 Ajar contains 30 coins, of which 20 are nickels and 10 are dimes. If 7 coins are removed, how many nickels are left? (1) More nickels are removed than dimes.

21、(2) The remaining coins in the jar are worth $1.55. 18 If for all numbers q, r, s, and t, then （ A） -3 （ B） -1 （ C） 1 （ D） 4/3 （ E） 4 19 A certain tire company can produce tires at a cost of $22,500 per batch plus $9 per tire. The company can sell tires to the wholesaler at a cost of $20 per tire. I

22、f a batch of 15,000 tires is produced and sold, what is the companys profit per tire? （ A） $9.00 （ B） $9.50 （ C） $11.00 （ D） $13.50 （ E） $20.00 20 Of the following, which is most nearly equal to but not greater than ? （ A） 3.7 （ B） 3.8 （ C） 3.9 （ D） 4.0 （ E） 4.1 21 A moving company charges a flat ra

23、te of $550 for loading its trucks and an additional $20 per 1/5 mile for moves within the city. How much would a move of 2.8 miles within the city cost? （ A） $690 （ B） $790 （ C） $830 （ D） $880 （ E） $1,010 22 Donna is a mountain biking enthusiast. One Saturday, she spent the morning biking up an uphi

24、ll trail at an average speed of 20 kilometers per hour, and then returned by the same route in the afternoon at an average speed of 25 kilometers per hour. If the downhill trip in the afternoon took 3/4 of an hour less than the uphill trek in the morning, how many kilometers did Donna ride each way?

25、 （ A） 50 （ B） 55 （ C） 65 （ D） 70 （ E） 75 23 If x, y, and w are nonzero numbers and x-y=w, which of the following is equal to 1? 24 If 12 percent of x is 30 percent of 480, then x is （ A） 144 （ B） 640 （ C） 960 （ D） 1,200 （ E） 1,440 24 The following data sufficiency problems consist of a question and

26、two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in Jul

27、y or the meaning of counterclockwise), you must indicate whether . Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. . Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. . BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is s

28、ufficient. . EACH statement ALONE is sufficient. . Statements (1) and (2) TOGETHER are NOT sufficient. 25 Is the triangle depicted above equilateral? (Figure not necessarily drawn to scale.) (1) x+y+z=180 (2) y=z 26 If w+x+y=42, what is the value of wxy? (1) x and y are consecutive odd integers (2)

29、w=2x 27 What is the value of integer x? (1) x is a positive integer (2) 17x18 28 What is the value of x-y? (1) (x-y)2=25 (2) 4x=4(y+3) 29 A farmer sells buckets of onions for $2, buckets of potatoes for $4, and buckets of squash for $5. How many buckets of squash did the farmer sell? (1) The farmer

30、sold one bucket of onions. (2) In total, the farmer sold 7 buckets of produce for $33. 30 If x dollars are invested at 12 percent for one year and y dollars are invested at 8 percent for one year, the annual income from the 8 percent investment will exceed the annual income from the 12 percent inves

31、tment by $64. If $5,000 is the total amount invested between x and y, how much is invested at 12 percent? （ A） $1,680 （ B） $1,997 （ C） $3,003 （ D） $3,320 （ E） $3,500 31 If and xy=4, then 7y+2x= 32 In the flat triangular surface depicted above, if feet, what is the area of the surface in square feet?

32、 (Figure not necessarily drawn to scale.) 33 Which of the following is equal to x24 for all positive values of x? （ A） x12+x12 （ B） (-x12)-2 （ C） (x6)6 （ D） (x2)(x3)(x4) （ E） (x72)1/3 34 A particular rocket car can travel for sustained periods at a maximum speed of 240 miles per hour. How many minut

33、es would it take this rocket car to travel 86 miles? （ A） 2.8 （ B） 18 1/2 （ C） 21 1/2 （ D） 22 （ E） 24 35 The square root of 800 is between which of the following integers? （ A） 21 and 25 （ B） 24 and 28 （ C） 27 and 31 （ D） 30 and 34 （ E） 33 and 37 36 36 If x is an integer and y=4x+3, which of the fol

34、lowing cannot be a divisor of y? （ A） 5 （ B） 6 （ C） 7 （ D） 9 （ E） 23 37 A real estate developer has bought 1,872 acres of land on which to build a new neighborhood. He plans to zone the area for roads, common area, and housing plots on a ratio of 2:3:8, respectively. If a planned lake will take up 1

35、6 acres of the common area, how many acres of the common area will be left over for the clubhouse and golf course? （ A） 128 （ B） 144 （ C） 416 （ D） 432 （ E） 450 GMAT（ QUANTITATIVE）数学模拟试卷 1答案与解析 一、 QUANTITATIVE 1 【正确答案】 E 【试题解析】 is insufficient because it says only that there was space for 24 ounces i

36、n the canteen, it does not give information about how much was in the canteen initially. (2) is insufficient because it tells neither how much was in the canteen nor how much was added. If the statements are combined, the information is still insufficient because there is no way to tell how large th

37、e canteen is, so there is no way to tell what part of the 75 percent the 24 ounces constitutes. 2 【正确答案】 B 【试题解析】 alone is insufficient because it gives no value for b. (2) alone is sufficient, because it gives the relationship between a and b, so that we know that a is 1/4=25 percent of b. 3 【正确答案】

38、 C 【试题解析】 alone is insufficient because it does not give the price of either item. (2) alone is insufficient because it does not give the price of either item. If the statements are combined, you can determine that the addition of two apples increased the value of the bundle of apples as opposed to

39、the bundle of pears by $1.00, so each apple must be worth $0.50. From (1), we know that each pear costs $0.10 more than each apple, so each pear is worth $0.60. 4 【正确答案】 D 【试题解析】 alone is sufficient; there are 10 segments on the board, and the board is 5 feet=60 inches long, so each segment is six i

40、nches; there are four segments between x and y, so the distance is 24 inches. (2) alone is sufficient; x is three segments from the near end of the board, so each segment is 18/3 inches=6 inches long; there are four segments between x and y, so the distance is 24 inches. 5 【正确答案】 A 【试题解析】 alone is s

41、ufficient because any positive integer divided by 5 will have a remainder of either 0, 1, 2, 3, or 4, which translate into terminating decimals of either 0.0, 0.2, 0.4, 0.6, or 0.8; therefore, if b=5, then a/b has to be a terminating decimal. (2) alone is insufficient because it does not give the va

42、lue for b;, if, for example, b=5, then any of the numbers in that range would result in terminating decimals, but if b=3, then 71/3=23.666666666 6 【正确答案】 D 【试题解析】 The total travel expenses in the coming year will be $19,5001.05=$20,475 and $35,0001.15=$40,250, so $60,725 in total. $60,725 in expense

43、s minus $55,000 in budget means excess expenses of $5,725. 7 【正确答案】 E 【试题解析】 If she walked 18 miles on the first day at 3 mph, she walked for 6 hours. Following the question, we know that on the second day she walked for 5 hours at 4 mph to cover 20 miles, and on the third day she walked for 6 hours

44、 at 4 mph to cover 24 miles. The sum of 18, 20, and 24 is 62. 8 【正确答案】 B 【试题解析】 16+64 can be rewritten as 16(1+4); the square root of (165) is . 9 【正确答案】 D 【试题解析】 10 【正确答案】 B 【试题解析】 If last years sales were S, the projected sales were 1.5S, and actual sales were 0.75S. 0.75S/1.5S=0.5=50%. 11 【正确答案】

45、D 【试题解析】 To get the average of y and z, you need to find half of the sum of y+ z. To obtain that number, first restate the first statement as an equation: x+y=80. Add that equation to z-x=60, so that x+y+z-x=80+60=y+z=140. The average of y and z is 140/2=70. 12 【正确答案】 A 【试题解析】 The boxes mentioned ar

46、e 202015 cubic inches=6,000 cubic inches each. 3,060,000 divided by 6,000 equals 510 boxes. 510$0.50 per box=$255. 13 【正确答案】 A 【试题解析】 alone is sufficient because the only value for m that meets the stated conditions is 625, which means that n=2. (2) alone is insufficient because m could be equal to

47、6.25, 62.5, or 625. 14 【正确答案】 A 【试题解析】 alone is sufficient because we know from the question that p 200, because p is less than q and p+q=400, so if p+r+s=600, then r+s 400, so it is greater than p+q and the answer is “yes.“ (2) alone is insufficient, because the statement could be consistent with e

48、ither a “yes“ or “no“ answer to the question, since it does not tell us the values for any of the variables. 15 【正确答案】 B 【试题解析】 Statement (1) alone is insufficient, since n could be either 5 or -5, so the equation could be either positive or negative. Statement (2) alone is sufficient because it onl

49、y has one solution, n=5, in which case the equation above equals 25, which is a positive integer. 16 【正确答案】 D 【试题解析】 Since we know the average price per pair of shoes sold, all we need to determine is the number of pairs of shoes sold. Statement (1) provides this answer, because we can determine that if 2/3 of the original stock is 600, then the original stock was 900; 1/3 of 900 is 300 pairs of shoes; 300$60=$18,000. Statement (2) is also sufficient because 1/3 of 900 is 300; 300$60=$18,000. 17 【正确答案】 B 【试题解析】 From the question, we