[外语类试卷]GMAT（QUANTITATIVE）数学模拟试卷6及答案与解析.doc

1、GMAT（ QUANTITATIVE）数学模拟试卷 6及答案与解析 一、 QUANTITATIVE 1 Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 3 miles to Rock Creek. If he is then n miles from home, what is the range of

2、 possible values for n? （ A） 1n23 （ B） 3n21 （ C） 5n9 （ D） 6n18 （ E） 9n15 2 Amber works 20 days a month at d dollars per day for m months out of the year. Which of the following represents her monthly pay? 3 There are 450 birds at a small zoo. The number of birds is 5 times the number of all the othe

3、r animals combined. How many more birds are there than non-bird animals at the zoo? （ A） 400 （ B） 360 （ C） 270 （ D） 180 （ E） 90 4 If x, y, and z are positive integers, and 4x=5y=6z, then the least possible value of x+y+z is （ A） 15 （ B） 28 （ C） 37 （ D） 42 （ E） 60 5 Three hundred multiples of three a

4、re picked at random, and three hundred multiples of four are picked at random. Approximately what percentage of the six hundred selected numbers are even? （ A） 100% （ B） 75% （ C） 66% （ D） 50% （ E） 33% 6 The incomplete table above shows a distribution of scores for a class of 25 students. If the aver

5、age (arithmetic mean) score for the class is 83, what score is missing from the table? （ A） 75 （ B） 77 （ C） 81 （ D） 84 （ E） 86 7 7 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 da

6、ta 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 sufficient, b

7、ut 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 sufficient.

8、8 What is the value of y? (1) y2+8y+16=0 (2) y 0 9 The integer x is how much greater than 4? (1) (2) 10x=1,000,000 10 In triangle ABC above, if BAD and ADB have measures of 2n, and if ACB has a measure of n, what is the length of side AB? (Figure not necessarily drawn to scale.) (1) n=25 (2) CD=4 11

9、 A dairy farmer has two milk pails, M and P. Milk pail M is 1/3 full. How much milk is in P relative to M? (1) If M is poured into P, P will be full. (2) Milk pail P is smaller than M. 12 Is y between 1 and 2, exclusive? (1) y2 is less than y (2) y2+y is between 1 and 2, exclusive 13 What is the per

10、imeter of the figure above? (Note, figure not necessarily drawn to scale) （ A） 155 （ B） 185 （ C） 220 （ D） 235 （ E） 250 14 In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $846,000 invested

11、in preferred stocks, what is the total amount of money invested in the fund? （ A） $1,974,000 （ B） $2,538,000 （ C） $3,264,000 （ D） $3,826,000 （ E） $4,230,000 15 (32+1)(812+1)(92+1)(32-1)= （ A） 814+1 （ B） 99-1 （ C） 316-1 （ D） 332-1 （ E） 396+1 16 If the area of a circle is 81, then the diameter of the

12、circle is （ A） 9 （ B） 18 （ C） 36 （ D） 9 （ E） 18 17 A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 6 minutes? （ A） 36 （ B） 54 （ C） 108 （ D） 216 （ E） 324 18 （ A） 117,000 （ B） 11,700 （ C） 3,900 （ D） 1,170 （ E） 390 19 In a sa

13、mple of patients at an animal hospital, 30 percent are cats and 60 percent are not dogs. What fraction of those patients who are not cats are dogs? 20 Two dogsled teams raced across a 300-mile course in Wyoming. Team A finished the course in 3 fewer hours than did team B. If team As average speed wa

14、s 5 miles per hour greater than that of team B, what was team Bs average speed, in miles per hour? （ A） 12 （ B） 15 （ C） 18 （ D） 20 （ E） 25 20 The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. Yon have to decide whe

15、ther 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 su

16、fficient, 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 s

17、ufficient. 21 In a club for left-handed people that also admits the ambidextrous, are more than 1/3 of the members ambidextrous? (1) Exactly 50 percent of the male members of the club are ambidextrous. (2) The number of females in the club is exactly 1 fewer than half the number of male members. 22

18、If a0, is b greater than zero? (1) a+b=10 (2) ab=24 23 A truck driver wants to load as many identical cylindrical canisters of olive oil as can fit into the 3- meter 4- meter 9- meter storage space of his truck. How many canisters can he load into the truck? (1) Each canister has a volume of 62,500

19、cubic centimeters. (2) The height of each canister is four times the radius. 24 In the figure above, what is the length of WZ? (Note, figure not necessarily drawn to scale.) (1) xy=64 (2) x2=y2 25 Over the course of a year, a certain house appreciated in value by 10 percent while the house next door

20、 decreased in value by 10 percent as a result of foundation damage. At the end of the year, the reduced price of the second house was what percentage of the increased price of the first house? (1) The amount by which the first house increased in value was half as much as the amount by which the seco

21、nd house decreased in value. (2) At the end of the year, the second house was worth $70,000 more than the first house. 26 Of 40 applicants for a job, 32 had at least 5 years of prior work experience, 24 had advanced degrees, and i6 had at least 5 years of prior work experience and advanced degrees.

22、How many of the applicants had neither 5 years of prior work experience nor advanced degrees? （ A） 0 （ B） 2 （ C） 4 （ D） 8 （ E） 16 27 If a0, and , then b= （ A） (5-a)(3+a) （ B） (3-a)(5+a) （ C） 2a2-15 （ D） -3a2+a-15 （ E） 15-2a2 28 If and represent single digits in the correctly worked computation above

23、, what is the value of times ? （ A） 6 （ B） 10 （ C） 12 （ D） 15 （ E） 18 29 A retailer sells 5 shirts. The first 2 he sells for $64 and $39. If the retailer wishes to sell the 5 shirts for an overall average price of over $50, what must be the minimum average price of the remaining 3 shirts? （ A） $49.0

24、0 （ B） $49.67 （ C） $50.00 （ D） $51.33 （ E） $55.50 30 The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the sec

25、tion of the circle graph representing the manufacturing department takes up 72 of the circle, what percentage of MegaTek employees are in manufacturing? （ A） 20% （ B） 25% （ C） 30% （ D） 35% （ E） 72% 31 If for all integers x and y; then (-5)2= 32 If x, y, and z are positive integers and x2=y2+z2, whic

26、h of the following must be true? .x z .x=y+z . y2+z2 is a positive integer （ A） only （ B） only （ C） only （ D） and only （ E） and only 32 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 t

27、he 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 sufficie

28、nt, 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 suffici

29、ent. 33 If M is a set of five numbers p, q, r, s, and t, is the range of numbers in M greater than 5? (1) The average (arithmetic mean) of p, q, r, s, and t is 5. (2) p-r 5. 34 Of the 3,600 registered voters in Smith County who took part in the county referendum on altering the property tax exemptio

30、n, 2,400 were Democrats and 1,200 were Republicans. What was the total number of female voters who voted in favor of the exemption? (1) The number of female Democrats who voted in favor of the exemption was three times the number of female Republicans who voted in favor of the exemption. (2) The 150

31、 male Republicans who voted in favor of altering the exemption represented 2/5 of all Republicans who voted in favor of altering the exemption. 35 Is the value of x3y-x2y2+xy3 equal to 0? (1) x=0 (2) y=0 36 Is the positive integer y a prime number? (1) 80 y 95 (2) y=3x+1, where x is a positive integ

32、er 37 What is the area of square floor X? (1) The perimeter of the floor is a whole-number multiple of 10. (2) The diagonal of the floor measures . GMAT（ QUANTITATIVE）数学模拟试卷 6答案与解析 一、 QUANTITATIVE 1 【正确答案】 C 【试题解析】 To find the maximum and minimum range for his distance from home, assume that he trav

33、eled either directly toward his home or directly away from his home. The range then is between 12+6-2+3=19 for the maximum, and 12-6+2-3=5 for the minimum, so C is the answer. 2 【正确答案】 B 【试题解析】 The passage states that she works 20 days a month at d dollars per day, so 20 d is her monthly pay. 3 【正确答

34、案】 B 【试题解析】 If the 450 birds are 5 times the number of non-bird animals, then non-birds=450/5=90. 450-90=360 more birds than non-birds at the zoo. 4 【正确答案】 C 【试题解析】 The least common multiple of 4, 5, and 6 is 60, so the numbers are x=15; y=12; z=10; 15+12+10=37. 5 【正确答案】 B 【试题解析】 All multiples of fo

35、ur are even, and half of the multiples of three are even; since they each make up 50% of the 600, the combined percentage is approximately 75%. 6 【正确答案】 A 【试题解析】 If the average score for the class is 83, then the sum of all 25 students scores be 8325=2,075. The sum of the scores for the 22 students

36、for whom we have scores is 368+546+581+355=1,850. So the three students scores must make up the difference between 2,075 and 1,850; 2,075-1,850=225; 225/3=75. 7 【正确答案】 C 【试题解析】 722 is the same thing as (89)2, which is the same as (2232)2, which is the same as (26)(34); consequently, everything facto

37、rs out of the fraction except 52, which equals 25. 8 【正确答案】 A 【试题解析】 alone is sufficient because the equation can be restated as (y+4)(y+4)=0, so y=-4. (2) alone is insufficient because there are infinite negative numbers that meet the condition. 9 【正确答案】 D 【试题解析】 Both (1) and (2) are sufficient, be

38、cause in both cases the answer is that x=6, and therefore x is 2 greater than 4. 10 【正确答案】 B 【试题解析】 alone is insufficient because it offers no information about any lengths in the triangle. (2) alone is sufficient; the crucial principle to remember here is that an exterior angle of a triangle-such a

39、s ADB-is equal to the sum of the remote interior angles of the triangle, in this case triangle BDC. Thus, n+ CBD=2n, or CBD=n. Since sides of a triangle opposite angles of identical degree are of identical length, BD is the same length as CD, or 4. By this same principle, BD and AB are of identical

40、lengths, so AB is also 4. 11 【正 确答案】 E 【试题解析】 alone is insufficient, because M could be the same size as P and 2/3 full to start with, or it could be 1/3 the size of P and empty to start with. (2) alone is insufficient, because it tells us nothing about the relative amounts of milk. If the statement

41、s are combined, there is still no clear answer, because M could be 2/3 the size of P and 1/2 full to start with, or it could be 1/3 the size of P and empty to start with. 12 【正确答案】 D 【试题解析】 alone is sufficient because the only values for y in which y2 is less than y are if y values between 0 and 1,

42、so the answer is “no.“ (2) alone is sufficient because there is no value of y between 1 and 2, exclusive, for which this statement is true the value 1, which is excluded in the question, gives the result 2, which is excluded in statement (2), so the answer is “no.“ 13 【正确答案】 E 【试题解析】 To determine th

43、e length of the unmeasured side, divide the figure into a rectangle with length 65 and a right triangle. If the height of the triangle is 40 and the hypotenuse is 50, then by the Pythagorean theorem the other leg is 30; the top segment of the rectangle is 65 like its opposite side, so the unmeasured

44、 side is 30+65=95. The perimeter is the sum of the sides: 95+40+65+50=250. 14 【正确答案】 E 【试 题解析】 If 846,000 is 1/3 of the total amount in stocks, then 846,0003=2,538,000 invested in stocks. If 2,538,000 is 3/5 of the total, then multiply 2,538,000 times 5/3 to get the total amount in the fund: 4,230,0

45、00. 15 【正确答案】 C 【试题解析】 This question at first appears to be a monster, but you can simplify the statements by reordering them and stating all of the exponential numbers as powers of 3: (32-1)(32+1)(34+1)(38+1). Then, you can scan through the answers and realize that 316-1=(38+1)(38-1)=(38+1)(34+1)(3

46、4-1)=(38+1)(34+1)(32+1)(32-1), which is the same as the statement in the question. 16 【正确答案】 B 【试题解析】 The formula for the area of a circle is r2. Therefore, the radius of this circle is the square root of 81, or 9. The diameter is twice the radius, so 18. 17 【正确答案】 E 【试题解析】 If a standard Veggiematik

47、 can chop 36 carrots in 4 minutes, then it can chop 36/4=9 carrots in 1 minute. 6 machines working for 6 minutes will chop 669 carrots=324 carrots. 18 【正确答案】 B 【试题解析】 Rather than multiplying the numbers out by brute force, try to simplify the statement; it can be restated as: , which is equal to 100

48、,000(0.117), which is equal to 11,700. 19 【正确答案】 E 【试题解析】 For simplicity, assume that there are 100 animals. Of these 30 are cats and 70, therefore, are not cats. If 60 percent of the animals are not dogs, then 40 percent are dogs. If 40 of the noncat animals are dogs, then 4/7 of those patients who

49、 are not cats are dogs. 20 【正确答案】 D 【试题解析】 You could solve this algebraically, or you could just plug the numbers into the statements in the question and see which one fits the facts. If you start from E, 25 mph, then team B will finish the 300-mile course in 12 hours while team A, at 30 mph, will finish the course in 10 hours; this does not meet the 3-hour difference described in the question. If B travels at 20 mph and A travels at 25 mph, then they will finish the course in 15 and 12 ho