1、GMAT（ QUANTITATIVE）数学模拟试卷 4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 In the figure above, is AB BC? (Note: Figure not necessarily drawn to scale.) (1) AB CD (2) (AD-AB) (AD-BC) 2 A box contains 90 jelly beans, of which some are orange, some are purple, and some are black. How man
6、y black jelly beans are in the box? (1) There are 27 orange jelly beans. (2) There are twice as many purple jelly beans as orange jelly beans. 3 Is 3x greater than 100? (1) 9x=36 (2) 4 How many more dogs than cats are in the veterinarians office? (1) There is a total of 30 dogs and cats in the offic
7、e. (2) The number of cats is the square root of the number of dogs. 5 If p is a positive integer, and p0, is an integer? (1) p is an even number (2) p is a multiple of 3 6 A certain prosthodontist specializes in implanting gold and silver teeth in his patients mouths. He charges $650 for a gold toot
8、h and $325 for a silver tooth. If his total fees for implanting gold and silver teeth last week were $15,925 in total, and he implanted five more gold teeth than silver teeth, how many teeth in total did he implant over the week? （ A） 31 （ B） 32 （ C） 33 （ D） 34 （ E） 35 7 What is the ratio of 3/7 to
9、the product 3(7/3)? （ A） 3:7 （ B） 1:3 （ C） 3:21 （ D） 1:7 （ E） 3:49 8 If the average (arithmetic mean) of a and b is 110, and the average of b and c is 160, what is the value of a-c? （ A） -220 （ B） -100 （ C） 100 （ D） 135 （ E） It cannot be determined from the information given. 9 A travel company want
10、s to charter a plane to the Bahamas. Chartering the plane costs $8,000. So far, 18 people have signed up for the trip. If the company charges $300 per ticket, how many more passengers must sign up for the trip before the company can make any profit on the charter? （ A） 7 （ B） 9 （ C） 13 （ D） 27 （ E）
11、45 10 If x2+9x-3=3x2+2x(4-x), then x2= （ A） 2 （ B） 3 （ C） 4 （ D） 9 （ E） 16 11 The pilot of a small aircraft with a 40-gallon fuel tank wants to fly to Cleveland, which is 480 miles away. The pilot recognizes that the current engine, which can fly only 8 miles per gallon, will not get him there. By h
12、ow many miles per gallon must the aircrafts fuel efficiency be improved to make the flight to Cleveland possible? （ A） 2 （ B） 4 （ C） 12 （ D） 40 （ E） 160 12 A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 14% microphotonics; 24% home electronics; 15% f
13、ood additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics re
14、search? （ A） 8 （ B） 10 （ C） 18 （ D） 36 （ E） 52 12 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 whether the data given in the statements are sufficient for answering the question. Using the d
15、ata 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 sufficient, but statement (2) alone is not sufficient. . Statement (2) ALONE is sufficient, bu
16、t 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 sufficient. 13 If x+y=36, what is the value of xy? (1) y-x=14 (2) y=2x+3 14 A hotdog vendor s
17、old $45 worth of hotdogs at lunchtime Tuesday. Each hotdog cost $1.50. What percentage of his days stock of hotdogs did the vendor sell at lunchtime? (1) The vendor started the day with 120 hotdogs. (2) The vendor sold twice as many hotdogs at dinnertime as he sold at lunchtime. 15 For real numbers
18、a, b, and c, is ab=bc+3? (1) ab=3b (2) b+3=c 16 What is the number of male employees at the factory? (1) If the factory were to hire 150 more employees and 2/3 of them were female, the ratio of male to female employees would be 8:3. (2) The factory has at least twice as many male employees as female
19、 employees, and it employs at least 150 females. 17 An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 46.5 meters. How many times did
20、the ball bounce? （ A） 5 （ B） 6 （ C） 7 （ D） 8 （ E） 9 17 A newspaper polled 1,000 likely voters about which of the following issues, if any, played an important role in their decision-making process for an upcoming election: education, crime, and/or taxes. Of the voters surveyed, a total of 495 named
21、education, 490 named crime, and 440 named taxes. In the figure above, the overlapping areas between two circles represent the people who named only those two items; the overlapping area between the three circles represents those people who named all three issues. 18 What percentage of those polled n
22、amed only education or only crime but no other issue? （ A） 25.5% （ B） 31.5% （ C） 39% （ D） 55% （ E） 98.5% 19 How many of the 1,000 people polled responded “none of the above“ to the questions? （ A） 140 （ B） 110 （ C） 80 （ D） 20 （ E） 0 20 The equation relates the values of two linked currencies, where
23、R is the value in dollars of one currency and S is the value in dollars of the other currency. Which of the following equations can be used to convert dollar values from the R currency to the S currency? 21 If x is a positive number and 1/2 the square root of x is the cube root of x, then x= （ A） 64
24、 （ B） 32 （ C） 16 （ D） 4 （ E） 1 22 If Josh, Doug, and Brad have a total of $72 among them, and Josh has three times as much money as Brad but only three-fourths as much as Doug, how much money does Doug have? （ A） $8 （ B） $9 （ C） $27 （ D） $32 （ E） $36 23 The flat triangular lot depicted above is avai
25、lable for development. If 150 meters, what is the area of the lot in square meters? 24 For any numbers w and z, wz=w3z(8-w2). If both z and wz are positive numbers, which of the following could be a value of w? （ A） 9 （ B） 3 （ C） 0 （ D） -2 （ E） -9 25 26 Last years receipts from the sale of greeting
26、cards during the week before Mothers Day totaled $189 million, which represented 9 percent of total greeting card sales for the year. Total greeting card sales for the year totaled how many million dollars? （ A） 17,010 （ B） 2,100 （ C） 1,890 （ D） 1,701 （ E） 210 27 What is the value of 5x2-1.9x-3.7 fo
27、r x=-0.3? （ A） -4.72 （ B） -3.82 （ C） -3.58 （ D） -2.68 （ E） 0.57 27 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 whether the data given in the statements are sufficient for answering the ques
28、tion. 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 sufficient, but statement (2) alone is not sufficient. . Statement (2) ALONE
29、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 sufficient. 28 Two cyclists are racing up a mountain at different constant r
30、ates. Cyclist A is now 50 meters ahead of cyclist B. How many minutes from now will cyclist A be 150 meters ahead of cyclist B? (1) 5 minutes ago, cyclist A was 200 meters behind cyclist B. (2) Cyclist A is moving 25% faster than cyclist B. 29 Is integer x divisible by 48? (1) x is divisible by 16.
31、(2) x is divisible by 12. 30 Is ? (1) x 20 (2) x 5 31 The figure above shows the shape of a brick patio. If arc AB is a semicircle and ABCD is a square, what is the perimeter of the patio ? (1) The radius of the semicircle described by arc AB is 4. (2) The perimeter of the square ABCD is 32. 32 A ca
32、ll to Rosies Psychic Hotline costs $5.99 for the first 2 minutes and $1.99 for each additional minute. Stuart called the hotline for x minutes, where x is an integer. How many minutes long was the call? (1) The total charge for the call was $11.96. (2) The charge for the last 3 minutes of the call w
33、as $0.01 less than half the total cost of the call. 33 If Z is represented by the decimal 0. W7, what is the digit W? 34 If a cube has a volume of 125, what is the surface area of one side? （ A） 5 （ B） 25 （ C） 50 （ D） 150 （ E） 625 35 An investor bought 200 shares of stock in ABCD company in 1990. By
34、 1992, the investment was worth only 2/3 of its original value. By 1995, the 200 shares were worth only 1/2 of their value in 1990. By what percent did the value of the investment drop from 1992 to 1995? 36 In the rectangular quadrant system shown above, which quadrant, if any, contains no point (x,
35、y) that satisfies the equation x2-2y=3? （ A） none （ B） （ C） （ D） （ E） 37 Which of the following cannot be the median of five positive integers a, b, c, d, and e? （ A） a （ B） d+e （ C） b+c+d （ D） (b+c+d)/3 （ E） (a+b+c+d+e)/5 GMAT（ QUANTITATIVE）数学模拟试卷 4答案与解析 一、 QUANTITATIVE 1 【正确答案】 B 【试题解析】 Statement
36、(1) tells us nothing about the relationship of AB to BC, so the answer cannot be A or D. Statement (2), however, tells us that AB must be a smaller number than BC. This gives us sufficient information to answer the question in the negative, so the answer is B. Note that it does not matter whether th
37、e answer to a Data Sufficiency question is yes or no; it only matters that you have sufficient data to answer the question. 2 【正确答案】 C 【试题解析】 alone is not sufficient, because there could be 6 or 60 black jelly beans in the jar. (2) alone is not sufficient, because there could be 1 orange and 2 purpl
38、es, or 20 oranges and 40 purples. But (1) and (2) together tell us there are 27 orange jelly beans, 54 purple jelly beans, and therefore 9 black jelly beans. 3 【正确答案】 D 【试题解析】 To be able to answer this question, we need to know a numerical value for x, because any numerical value will give a value f
39、or 3x that is either greater or less than 100. (1) gives the value of 4 for x, so it is sufficient (3x=81; it is not greater). (2) can be restated as 100 3x, so 3x cannot be greater than 100, and (2) is sufficient to answer the question. 4 【正确答案】 C 【试题解析】 Statement (1) alone is insufficient because
40、it does not give the breakdown between dogs and cats of the 30 animals. Statement (2) alone is insufficient because the pair of numbers described could be 2 and 4, 3 and 9, 4 and 16, and so on. When the two statements are combined, however, there is only one pair of numbers that can match both state
41、ments: 5 and 25. That is sufficient information to answer the question. 5 【正确答案】 A 【试题解析】 One way to verify this is to plug in even numbers; the results soon show that the result is always half of p plus 1/2, which is never an integer. You could also simplify the equation to , and since an even numb
42、er plus 1 is always an odd number, dividing the sum by 2 will never produce an integer. So statement (1) alone is sufficient. Statement (2) results in integers if p is an odd multiple of 3, but in non-integers if p is an even multiple of 3, so this statement alone is not sufficient. 6 【正确答案】 A 【试题解析
43、】 It is probably easiest to approach this question by plugging in the available answers and seeing which one works. If it was 31 teeth (answer A), for example, then we know that the doctor implanted 18 gold and 13 silver. 18$650+13$325=$15,925, so A is the answer. 7 【正确答案】 E 【试题解析】 can be restated a
44、s 7. If you multiply 7 times both numbers to get rid of the fraction in 3/7, you get 3 and 49. 8 【正确答案】 B 【试题解析】 Restate both statements as equations: a+b=220 and b+c=320. Subtract the second equation from the first and you get a+b-b-c=220-320=a-c=-100. 9 【正确答案】 B 【试题解析】 $8,000 divided by $300 per p
45、erson means that the company must book 26.67 passengers to make a profit, so in practice this means 27 passengers. 27 required minus 18 already booked means that the company must find 9 more passengers. 10 【正确答案】 D 【试题解析】 The statement 3x2+2x(4-x) can be restated as x2+8x. Thus, the original equatio
46、n can be restated as x=3, so x2=9. 11 【正确答案】 B 【试题解析】 For an aircraft with a 40-gallon tank to fly 480 miles, it must average at least 480/40=12 miles per gallon. 12-8=4. 12 【正确答案】 D 【试题解析】 First, determine what percentage of the budget is devoted to basic astrophysics: 14+24+15+29+8=90, so 10% is l
47、eft over for astrophysics. There are 360 in a circle, so multiply the 10% by 360/100 and you get 36. 13 【正确答案】 D 【试题解析】 alone is sufficient; add the two equations together and you get 2y=50, so y=25 and x=11. (2) alone is sufficient, because if you plug the equation into the question, you get x+2x+3
48、=36, or 3x=33, so x=11 and y=25. 14 【正确答案】 A 【试题解析】 From the information given in the passage, we can determine that the vendor sold 30 hotdogs at lunchtime. To determine the percentage of the total stock sold, we need to know the total stock of hotdogs. (1) provides this number, while (2) does not,
49、 so the answer is A. 15 【正确答案】 C 【试题解析】 To answer this question, the statements have to prove either that the equation above is true or that it cannot be true. (1) alone is insufficient; it allows the equation to be restated as 3b=bc+3, which could be true or not true depending on the values of b and c. (2) alone is insufficient; it allows the equation to be restated as ab=b2+3b+3, which could be true or not true depending on the values of a and b. If the two are combined, the equation can be restated as 3b=b2+3b+3, which can be
