[外语类试卷]GMAT（QUANTITATIVE）数学模拟试卷2及答案与解析.doc

1、GMAT（ QUANTITATIVE）数学模拟试卷 2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 If x is an integer, is an integer? (1) 18 x 54 (2) x is a multiple of 18 2 If a 0 and b 0, is (1) a=b-2 (2) 3 The figure above shows the shape of a flowerbed. If arcs WZ and XY are semicircles and WXYZ is a squa

6、re, what is the area of the flowerbed? (1) The perimeter of square WXYZ is 24. (2) The diagonal 4 A total of 72 passengers are on a ship, and they go out on an excursion in boats R and Q. How many of the ships passengers are female? (1) There are 13 females on boat Q. (2) There are equal numbers of

7、women on boats R and Q. 5 In the xy plane, is the point (4, -2) on the line l? (1) Point (1, 1) is on line l. (2) The equation x=2-y describes line l. 6 A type of extra-large SUV averages 12.2 miles per gallon (mpg) on the highway, but only 7.6 mpg in the city. What is the maximum distance, in miles

8、, that this SUV could be driven on 25 gallons of gasoline? （ A） 190 （ B） 284.6 （ C） 300 （ D） 305 （ E） 312 7 The ratio of 2 quantifies is 5 to 6. If each of the quantities is increased by 15, what is the ratio of these two new quantifies? （ A） 5:6 （ B） 25:27 （ C） 15:16 （ D） 20:21 （ E） It cannot be de

9、termined from the information given. 8 （ A） （ B） 8 （ C） 9 （ D） 10 （ E） 9 In an animal behavior experiment, 50 tagged white pigeons and 200 tagged gray pigeons were released from a laboratory. Within one week, 88 percent of the white pigeons and 80.5 percent of the gray pigeons had returned to the la

10、boratory. What percent of the total number of pigeons returned to the laboratory? （ A） 80.5 （ B） 82 （ C） 82.5 （ D） 85 （ E） 86.5 10 In the circular region shown above, sections A and B represent 3/8 and 5/11, respectively, of the area of the circular region. Section C represents what fractional part

11、of the area of the circular region? 11 At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 250-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $200? （ A） 1,108 （ B） 2,100 （ C） 2,108 （ D） 2,124 （ E） 2,256 11 The follow

12、ing 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 mathemati

13、cs 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 statements T

14、OGETHER are sufficient, but NEITHER statement ALONE is sufficient. . EACH statement ALONE is sufficient. . Statements (1) and (2) TOGETHER are NOT sufficient. 12 What was the percent decrease in the price of MegaTek (MGTK) stock during the market decline of March 1, 2001, to March 1, 2002? (1) The p

15、rice of MGTK was $56.20 on March 1, 2001. (2) The price of the stock on January 1, 2002, was only one-quarter of its price as of March 1, 2001. 13 Gregs long-distance telephone plan charges him $0.50 for the first 4 minutes of a call, and $0.07 per minute for each subsequent minute. Greg made a call

16、 to Carrie for x minutes, where x is an integer. How many minutes long was Gregs call? (1) The last 7 minutes of Gregs call cost $0.22 less than the first 7 minutes of the call. (2) The call did not cost more than $1.05. 14 If x and y are both positive numbers, is x greater than 75% of y? (1) 5x 4y+

17、1 (2) x=6 15 Is xyz=1? (1) x(yz)=1 (2) 5z=0 16 What is the average (arithmetic mean) of x and y? (1) The average of x+3 and y+5 is 14. (2) The average of x, y, and 16 is 12. 17 One day a car rental agency rented 2/3 of its cars, including 3/5 of its cars with CD players. If 3/4 of its cars have CD p

18、layers, what percent of the cars that were not rented had CD players? （ A） 10% （ B） 35% （ C） 45% （ D） 66.7% （ E） 90% 18 If x is 20 percent greater than 88, then x= （ A） 68 （ B） 70.4 （ C） 86 （ D） 105.6 （ E） 108 19 A farmer with 1,350 acres of land had planted his fields with corn, sugar cane, and tob

19、acco in the ratio of 5:3:1, respectively, but he wanted to make more money, so he shifted the ratio to 2:4:3, respectively. How many more acres of land were planted with tobacco under the new system? （ A） 90 （ B） 150 （ C） 270 （ D） 300 （ E） 450 20 （ A） 18 （ B） 33 （ C） 36 （ D） 42 （ E） 45 21 What is th

20、e perimeter of a square with area ? 22 If a three-digit number is selected at random from the integers 100 to 999, inclusive, what is the probability that the first digit and the last digit of the integer will both be exactly two less than the middle digit? （ A） 1:900 （ B） 7:900 （ C） 9:1,000 （ D） 1:

21、100 （ E） 7:100 23 Which of the following inequalities is equivalent to -4 x 8? （ A） |x-1| 7 （ B） |x+2| 6 （ C） |x+3| 5 （ D） |x-2| 6 （ E） None of the above 24 （ A） 416 （ B） 224 （ C） 188 （ D） 104 （ E） 56 25 Three different lumberjacks can chop W amount of wood in 30 minutes, 45 minutes, and 50 minutes

22、according to their different levels of skill with the axe. How much wood, in terms of W, could the two fastest lumberjacks chop in 2 hours? 25 The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide wh

23、ether 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 of counterclockwise), you must indicate whether . Statement (1) ALONE is s

24、ufficient, 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. . EACH statement ALONE is sufficient. . Statements (1) and (2) TOGETHER are NOT

25、sufficient. 26 In what year was Edward born? (1) In 1988, Edward turned 17 years old. (2) Edwards sister Lisa, who is 14 months older than Edward, was born in 1970. 27 Is rs=rx-2? (1) r is an odd number (2) x=s+2 28 A CEO is building an extra-wide garage in which to park his limousines. The garage i

26、s x feet wide, and at least 2 feet of space is required between each two cars and between the cars and the walls. Will all 9 limousines fit in the garage? (1) The average width of the limousines is the square root of x. (2) x=100. 29 If q+r+s=45, what is the value of qr? (1) q=r=s (2) q-r-s=-15 30 I

27、s the triangle depicted above isosceles? (Figure not necessarily drawn to scale.) (1) 180-(a+c)=60 (2) a=2b-c 31 Last year Jackie saved 5% of her annual salary. This year, she made 10% more money than last year, and she saved 8% of her salary. The amount saved this year was what percent of the amoun

28、t she saved last year? （ A） 56% （ B） 76% （ C） 158% （ D） 176% （ E） 188% 32 The table above shows the one-way driving distance, in miles, between four cities: P, Q, R, and S. For example, the distance between P and Q is 144 miles. If the round trip between S and Q is 16 miles further than the round tr

29、ip between S and R, and the round trip between S and R is 24 miles less than the round trip between S and P, what is the value of X? （ A） 174 （ B） 182 （ C） 186 （ D） 348 （ E） 364 33 If 35 percent of 400 is 20 percent of x, then x= （ A） 200 （ B） 350 （ C） 700 （ D） 900 （ E） 1,400 34 (23-1)(23+1)(26+1)(2

30、12+1)= （ A） (224-1) （ B） (224-1) （ C） (248-1) （ D） (296+1) （ E） 26(212-1) 35 To be considered for “movie of the year,“ a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academys 765 members. What is the smallest number of top-10 lists a film can appear on and s

31、till be considered for “movie of the year?“ （ A） 191 （ B） 192 （ C） 193 （ D） 212 （ E） 213 36 In a sample of associates at a law firm, 30 percent are second-year associates, and 60 percent are not first-year associates. What percentage of the associates at the law firm have been there for more than tw

32、o years? （ A） 10 （ B） 20 （ C） 30 （ D） 40 （ E） 50 37 Which of the following fractions has the greatest value? GMAT（ QUANTITATIVE）数学模拟试卷 2答案与解析 一、 QUANTITATIVE 1 【正确答案】 C 【试题解析】 alone is insufficient, because if x=36, then the answer is “yes,“ but if x=37, then the answer is “no.“ (2) alone is insuffi

33、cient, because if x=36, then the answer is “yes,“ but if x=180, then the answer is “no.“ If the statements are combined, however, then the only value of x that meets all the conditions is 36, for which the answer is “yes.“ 2 【正确答案】 D 【试题解析】 alone is sufficient because it tells us that b is a larger

34、number than a, which means that the answer to the question must be “no.“ (2) alone is sufficient; the statement can be simplified to 5a=4b, which means that b is larger than a, so the answer to the question must be “no.“ 3 【正确答案】 D 【试题解析】 alone is sufficient; if the perimeter of the square is 24, th

35、en the length of each side is 24/4=6, and the radius of each of the semicircles is 6/2=3. The area of the square is 66=36, and since the formula for the area of a circle is r2, the area of the semicircles is 21/2(33)=9; 36+9 is the area of the flowerbed. (2) alone is sufficient; the side of a square

36、 is the diagonal divided by (this is derived from the Pythagorean theorem), so the sides are equal to 6; by following the same process used with statement (1), we can determine the area of the flowerbed. 4 【正确答案】 C 【试题解析】 alone is insufficient because it gives no information about the number of fema

37、les on boat R. (2) alone is insufficient because it does not give the number of women on either boat. If the statements are combined, we see that there are 13 women on each boat, or 26 in all. 5 【正确答案】 B 【试题解析】 alone is insufficient because it offers information about only one point on the line. (2)

38、 alone is sufficient, because the line it describes includes the point (4, -2). 6 【正确答案】 D 【试题解析】 The SUV will reach its maximum distance only if driven only on the highway; 2512.2=305. 7 【正确答案】 E 【试题解析】 With no idea of what the quantifies actually are, there is no way to tell how adding 15 to each

39、of them will affect their ratio; for example, if the quantities were 5 and 6, the new ratio would be 20:21, but if the quantities were 10 and 12, the ratio would be 25:27. 8 【正确答案】 C 【试题解析】 9 【正确答案】 B 【试题解析】 88% of 50 is 44, and 80.5% of 200 is 161.44+161=205. 205/250 total pigeons=0.82=82%. 10 【正确答

40、案】 A 【试题解析】 Section C is equal to 1-(3/8+5/11)=1-(33/88+40/88)=15/88. 11 【正确答案】 B 【试题解析】 You should start with the 250-packs, because that is the best value, with each hot dog costing less than 10 cents. Rounding 22.95 to 23 for simplicity, you can determine that you can afford 8 of the 250-packs, f

41、or a total of $183.60. The 20-packs are the next best value at around 15 cents per hot dog, so with the remaining $16.40 you can buy 5 of the 20-packs for $15.25, leaving $1.15. $1.15 isnt enough for an 8-pack, so the total number of hot dogs is 8250+520=2,100. 12 【正确答案】 E 【试题解析】 alone is insufficie

42、nt because it gives only the value at the starting point of the period in question. (2) alone is insufficient because the price as of January 1, 2002, is irrelevant to the question. Combining the two statements yields no new insights. 13 【正确答案】 C 【试题解析】 alone is insufficient; we know that the first

43、7 minutes cost $0.50+3$0.07=$0.71; the least the last 7 minutes could cost is 7$0.07=$0.49, which is exactly $0.22 less than the first 7 minutes, so we know that the last 7 minutes did not include the first 4 minutes, but that is all we can tell. (2) alone is insufficient, because the call could hav

44、e lasted any length of time under 12 minutes (12 minutes=$1.06, 11 minutes=$0.99). If the two are combined, the only value that meets all the conditions is 11 minutes. 14 【正确答案】 A 【试题解析】 states that x is greater than 80 percent of y (the easiest way to confirm this is to plug in numbers), so the que

45、stion is answered in the affirmative and (1) alone is sufficient. (2) is insufficient without providing any information about the relative value of y, so the answer is A. 15 【正确答案】 B 【试题解析】 alone is insufficient, because x, y, and z could be (1, 1, 1) or (1, 1, 0) or other values, which give differe

46、nt answers to the question. (2) alone is sufficient, because if z=0, it does not matter what the values are for x and y ; xyz=01. 16 【正确答案】 D 【试题解析】 alone is sufficient; the statement could be restated to say that x+y+3+5=142, or x+y=20; therefore, the average of x and y is 10. (2) alone is sufficie

47、nt; the statement could be restated as x+y+16=123, or x+y=20; therefore, the average of x and y is 10. 17 【正确答案】 E 【试题解析】 One way to approach this problem is to think of the fractions as actual cars. Since the given denominators are 3, 4, and 5, imagine that there are 60 cars. In this case, the agen

48、cy rented 40 cars (2/3), 45 of the total cars have CD players (3/4), and 27 of its cars with CD players were rented (3/5 of 3/4). From these numbers, we can determine that 20 cars in total were not rented, and 18 cars with CD players were not rented. 18 out of 20 is 90 percent. 18 【正确答案】 D 【试题解析】 20

49、 percent of 88 is 17.6. 88+17.6=105.6. 19 【正确答案】 D 【试题解析】 The numbers in both sets of ratios add up to 9, so you can look at each of the ratios in terms of ninths of 1,350. In the original planting system, tobacco accounted for 1/9 of the total, so 1,350/9=150. In the new system, tobacco accounts for 3/9, or 450. 450-150=300. 20 【正确答案】 E 【试题解 析】 The statement can be restated as 12+15+18=45. 21 【正确答案】 C 【试题解析】 The area of a square is the square of its sides, so one of the sides of this square is . The perimeter of a square is