1、工商管理硕士入学考试-数学机考-(一)及答案解析(总分：250.00，做题时间：90 分钟)一、问题求解题(总题数：50，分数：250.00)1.Two cars left the same town traveling in the same direction. Car A traveled 40 miles per hour and left at 3:20. Car B traveled 50 miles per hour and left at 4:40. At what time will car B catch up with car A?(A) 10:00 (B) 9:00 (
2、C) 8:40(D) 7:20 (E) 6:10（分数：5.00）A.B.C.D.E.2.The width of a rectangle is 6 cm less than the length. If the perimeter of the rectangle is 48 cm, what is the length of the rectangle in centimeters?(A) 48 (B) 15 (C) 12(D) 9 (E) 6（分数：5.00）A.B.C.D.E.3.A child withdraws from his piggy bank 10% of the orig
3、inal sum in the bank. If he must add 90 to bring the amount in the bank back up to the original sum, what was the original sum in the bank?(A) $1.00 (B) $1.90 (C) $8.10(D) $9.00 (g) $9.90（分数：5.00）A.B.C.D.E.4.A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and
4、with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?（分数：5.00）A.B.C.D.E.5.For how many integers n is 2n=n2?(A) None (B) One (C) Two(D) Three (E) More than three（分数：5.00）A.B.C.D.E.6.Last year, an appliance store sold a
5、n average (arithmetic mean) of 42 microwave ovens per month. In the first 10 months of this year, the store has sold an average (arithmetic mean) of only 20 microwaves per month. What was the average number of microwaves sold per month during the entire 22-month period?(A) 21 (B) 30 (C) 31(D) 32 (E)
6、 44（分数：5.00）A.B.C.D.E.7.The enrollments at College X and College Y both grew by 8 percent from 1980 to 1985. If the enrollment at College X grew by 800 and the enrollment at College Y grew by 840, the enrollment at College Y was how much greater than the enrollment at College X in 1985?(A) 400 (B) 4
7、60 (C) 500(D) 540 (E) 580（分数：5.00）A.B.C.D.E.8.Joe works two part time jobs. One week Joe worked 8 hours at one job, earning $150, and 4.5 hours at other job, earning $90. What were his average hourly earnings for the week?(A) $8.00 (B) $9.60 (C) $16.00(D) $19.20 (E) $32.00（分数：5.00）A.B.C.D.E.9.A numb
8、er of bricks were purchased to build a fireplace, at a cost of 40 cents each, but only （分数：5.00）A.B.C.D.E.10. （分数：5.00）A.B.C.D.E.11.If the areas of the three different sized faces of a rectangular solid are 6, 8, and 12, then what is the volume of the solid?(A) 576 (B) 288 (C) 144(D) 48 (E) 24（分数：5.
9、00）A.B.C.D.E.12.The sum of four consecutive odd positive integers is always(A) an odd number(B) divisible by 4(C) a prime number(D) a multiple of 3(E) greater than 24（分数：5.00）A.B.C.D.E.13.A painter has painted one-third of a rectangular wall which is ten feet high. When she has painted another 75 sq
10、uare feet of wall, she will be three-quarters finished with the job. What is the length (the horizontal dimension) of the wall?(A) 18 feet (B) 12 feet (C) 10 feet(D) 9 feet (E) 6 feet（分数：5.00）A.B.C.D.E.14. （分数：5.00）A.B.C.D.E.15.Sam and Jessica are invited to a dance. If there are 7 men and 7women in
11、 total at the dance, and one woman and one man are chosen to lead the dance, what is the probability that Sam and Jessica will NOT be chosen to lead the dance?（分数：5.00）A.B.C.D.E.16.If a = 1 and （分数：5.00）A.B.C.D.E.17.A group of store managers must assemble 280 displays for an upcoming sale. If they a
12、ssemble 25 percent of the displays during the first hour and 40 percent of the remaining displays during the second hour, how many of the displays will not have been assembled by the end of the second hour?(A) 70 (B) 98 (C) 126(D) 168 (E) 182（分数：5.00）A.B.C.D.E.18.The figure above is a regular hexago
13、n with center H, The shaded area is a parallelogram that shares three vertices with the hexagon; its fourth vertex is the center of the hexagon. If the length of one side of the hexagon is 8 centimeters, what is the area of the unshaded region?（分数：5.00）A.B.C.D.E.19.If n is an integer between 0 and 1
14、00, then any of the following could be 3n+3 EXCEPT(A) 300 (B) 297 (C) 208(D) 63 (E) 6（分数：5.00）A.B.C.D.E.20.The contents of a certain box consist of 14 apples and 23 oranges. How many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples?(A) 3 (B) 6
15、(C) 14(D) 17 (E) 2O（分数：5.00）A.B.C.D.E.21.Jerome wrote each of the integers 1 through 20, inclusive, on a separate index card. He placed the cards in a box, then drew cards one at a time randomly from the box, without returning the cards he had already drawn to the box. In order to ensure that the su
16、m of all the cards he drew was even, how many cards did Jerome have to draw?(A) 19 (B) 12 (C) 11(D) 10 (E) 3（分数：5.00）A.B.C.D.E.22.Ron can type five forms of a test in 4 hours. Joan can type the same five forms in 6 hours. If they work together, how many hours would it take them to type ten forms of
17、a test?（分数：5.00）A.B.C.D.E.23.Cans of tennis balls were purchased for the tournament at a cost of $1. 90 per can. Only （分数：5.00）A.B.C.D.E.24.If r and s are integers and rs+r is odd, which of the following must be even?(A) r (B) s (C) r+s(D) rs-r (E) r2+s（分数：5.00）A.B.C.D.E.25. （分数：5.00）A.B.C.D.E.26.On
18、 the number line above, the segment from 0 to 1 has been divided into fifths, as indicated by the large tick marks, and also into sevenths, as indicated by the small tick marks. What is the least possible distance between any two of the tick marks?（分数：5.00）A.B.C.D.E.27.Together, Andrea and Brian wei
19、gh p pounds; Brian weighs 10 pounds more than Andrea. Brian and Andreas dog, Cubby, weighs pounds more than Andrea. In terms of p. what is Cubbys weight in pounds?（分数：5.00）A.B.C.D.E.28.A four-character password consists of one letter of the alphabet and three different digits between 0 and 9, inclus
20、ive. The letter must appear as the second or third character of the password. How many different passwords are possible?(A) 5,040 (B) 18,720 (C) 26,000(D) 37,440 (E) 52,000（分数：5.00）A.B.C.D.E.29.How many minutes will it take to completely fill a water tank with a capacity of 3,750 cubic feet if the w
21、ater is being pumped into the tank at the rate of 800 cubic feet per minute and is being drained out of the tank at the rate of 300 cubic feet per minute?(A) 3 min. 36 see. (B) 6 minutes(C) 7 min. 30 sec. (D) 8 minutes(E) 1,875 minutes（分数：5.00）A.B.C.D.E.30.A $500 investment and a $1, 500 investment
22、have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1, 500 investment have?（分数：5.00）A.B.C.D.E.31.A first-grade teacher use ten flash cards, numbered 1 through 10, to teach her
23、students to order numbers correctly. She has students choose four flash cards randomly, then arrange the cards in ascending order. One day, she removes the cards numbered “2“ and “4“ from the deck of flash cards. On that day, how many different correct arrangements of four randomly selected cards ar
24、e possible?(A) 70 (B) 210 (C) 336(D) 840 (E) 1,680（分数：5.00）A.B.C.D.E.32.A laborer is paid $8 per hour for an 8-hour day and （分数：5.00）A.B.C.D.E.33.If triangle AOB is equilateral, O is the center of the semicircle ABC, and the radius of semicircle ABC is 6, what is the length to BC?（分数：5.00）A.B.C.D.E.
25、34.John budgeted 50% of his take-home pay for household expense, 20% for transportation, 15% for a retirement fund, and the remaining $240 for recreation. How much of his take home pay did he budget for household expenses?(A) $500 (B) $800 (C) $1,000(D) $1,200 (E) $240（分数：5.00）A.B.C.D.E.35.A group o
26、f 20 friends formed an investment club, with each member contributing an equal amount to the general fund. The club then invested the entire fund, which amounted to d dollars, in Stock X. The value of the stock subsequently increased 40 percent, at which point the stock was sold and the proceeds div
27、ided evenly among the members. In terms of d, how much money did each member of the club receive from the sales (Assume that transaction fees and other associated costs were negligible).（分数：5.00）A.B.C.D.E.36.In a certain flower shop, which stocks four types of flowers, there are as many violets as c
28、arnations, and （分数：5.00）A.B.C.D.E.37.If x is an even integer and y is an odd integer, then which of the following is an even integer?(A) x2+y (B) x2-y(C) (x2)(y) (D) x+y(E) x-y（分数：5.00）A.B.C.D.E.38.A student conducts an experiment in biology lab and discovers that the ratio of the number Of insects
29、in a given population having characteristic X to the number of insects in the population not having characteristic X is 5:3, and that of the insects having characteristic X are male insects. What proportion of the total insect population are male insects having the characteristic X?（分数：5.00）A.B.C.D.
30、E.39.A certain grocery purchased x pounds of produce for p dollars per pound. If y pounds of the produce had to be discarded due to spoilage and the grocery sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the produce?(A) (x-y)s-xp(B) (x-y)p-ys
31、(C) (s-p)y-xp(D) xp-ys(E) (x-y)(s-p)（分数：5.00）A.B.C.D.E.40.Jolene began building a picket fence by planting stakes in a row; the stakes were evenly spaced. After planting the first 10 stakes, Jolene measured the length of the row and found that the row was 27 feet long. She continued the row by plant
32、ing another 10 stakes, then measured the length of the entire row. How many feet long was the row of stakes Jolene had planted?(A) 37 (B) 54 (C) 57(D) 60 (E) 81（分数：5.00）A.B.C.D.E.41.A student had an average of 86 for three tests. If the students highest test score was 2a, what was the average of the
33、 students two lowest scores?(A) 129-2a (B) 258-2a(C) 129-a (D) 258+2a(E) 258-a（分数：5.00）A.B.C.D.E.42.Last year, a certain public transportation system sold an average (arithmetic mean) of 41,000 tickets per day on weekdays (Monday through Friday) and an average of 18,000 tickets per day on Saturday a
34、nd Sunday. Which of the following is closest to the total number of tickets sold last year?(A) 1 million (B) 1.25 million(C) 10 million (D) 12.5 million(E) 125 million（分数：5.00）A.B.C.D.E.43.A business firm reduces the number of hours its employees work from 40 hours per week to 36 hours per week whil
35、e continuing to pay the same amount of money. If an employee earned x dollars per hour before the reduction in hours, how much does he earn per hour under the new system?（分数：5.00）A.B.C.D.E.44.On Monday, a certain animal shelter housed 55 eats and dogs. By Friday, exactly of the eats and （分数：5.00）A.B
36、.C.D.E.45.The product of three consecutive integers must be. Divisible by 3. Divisible by 5. Divisible by 6(A) only(B) only(C) and only(D) and only(E) , , and （分数：5.00）A.B.C.D.E.46.Paul is standing 180 yards due north of point P, Franny is standing 240 yards due west of point P. What is the shortest
37、 distance between Franny and Paul?(A) 60 yards (B) 300 yards(C) 420 yards (D) 900 yards(E) 9,000 yards（分数：5.00）A.B.C.D.E.47.To fill a number of vacancies, an employer must hire 3 programmers from among 6 applicants, and 2 managers from among 4 applicants.What is the total number of ways in which she
38、 can make her selection?(A) 1,490 (B) 132 (C) 120(D) 6O (E) 23（分数：5.00）A.B.C.D.E.48.The Binary Ice Cream Shoppe sells two flavors, vanilla and chocolate. On Friday, the ratio of vanilla cones sold to chocolate cones sold was 2 to 3. If the store had sold 4 more vanilla cones, the ratio of vanilla co
39、nes sold to chocolate cones sold would have been 3 to 4. How many vanilla cones did the store sell on Friday?(A) 32 (B) 35 (C) 42(D) 48 (E) 54（分数：5.00）A.B.C.D.E.49.A salesman makes a profit of 25% on all sales. How many fax machines will he have to sell for $375 each to make a total commission of at
40、 least $ 500?(A) 4 (B) 5 (C) 6(D) 15 (E) 20（分数：5.00）A.B.C.D.E.50.A salesperson works 50 weeks each year and makes an average (arithmetic mean) of 100 sales per week. If each sale is worth an average (arithmetic mean) of $1,000, then what is the total value of sales made by the salesperson in a year?
41、(A) $50,000 (B) $100,000(C) $500,000 (D) $1,000,000(E) $5,000,000（分数：5.00）A.B.C.D.E.工商管理硕士入学考试-数学机考-(一)答案解析(总分：250.00，做题时间：90 分钟)一、问题求解题(总题数：50，分数：250.00)1.Two cars left the same town traveling in the same direction. Car A traveled 40 miles per hour and left at 3:20. Car B traveled 50 miles per hour
42、 and left at 4:40. At what time will car B catch up with car A?(A) 10:00 (B) 9:00 (C) 8:40(D) 7:20 (E) 6:10（分数：5.00）A. B.C.D.E.解析：2.The width of a rectangle is 6 cm less than the length. If the perimeter of the rectangle is 48 cm, what is the length of the rectangle in centimeters?(A) 48 (B) 15 (C)
43、12(D) 9 (E) 6（分数：5.00）A.B. C.D.E.解析：3.A child withdraws from his piggy bank 10% of the original sum in the bank. If he must add 90 to bring the amount in the bank back up to the original sum, what was the original sum in the bank?(A) $1.00 (B) $1.90 (C) $8.10(D) $9.00 (g) $9.90（分数：5.00）A.B.C.D. E.解析
44、：4.A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?（分数：5.00）A.B.C. D.E.解析：5.For how many integers n is 2n=n2?(A) None (B
45、) One (C) Two(D) Three (E) More than three（分数：5.00）A.B.C. D.E.解析：6.Last year, an appliance store sold an average (arithmetic mean) of 42 microwave ovens per month. In the first 10 months of this year, the store has sold an average (arithmetic mean) of only 20 microwaves per month. What was the avera
46、ge number of microwaves sold per month during the entire 22-month period?(A) 21 (B) 30 (C) 31(D) 32 (E) 44（分数：5.00）A.B.C.D. E.解析：7.The enrollments at College X and College Y both grew by 8 percent from 1980 to 1985. If the enrollment at College X grew by 800 and the enrollment at College Y grew by 8
47、40, the enrollment at College Y was how much greater than the enrollment at College X in 1985?(A) 400 (B) 460 (C) 500(D) 540 (E) 580（分数：5.00）A.B.C.D. E.解析：8.Joe works two part time jobs. One week Joe worked 8 hours at one job, earning $150, and 4.5 hours at other job, earning $90. What were his aver
48、age hourly earnings for the week?(A) $8.00 (B) $9.60 (C) $16.00(D) $19.20 (E) $32.00（分数：5.00）A.B.C.D. E.解析：9.A number of bricks were purchased to build a fireplace, at a cost of 40 cents each, but only （分数：5.00）A.B. C.D.E.解析：10. （分数：5.00）A.B.C.D. E.解析：11.If the areas of the three different sized fac
49、es of a rectangular solid are 6, 8, and 12, then what is the volume of the solid?(A) 576 (B) 288 (C) 144(D) 48 (E) 24（分数：5.00）A.B.C.D.E. 解析：12.The sum of four consecutive odd positive integers is always(A) an odd number(B) divisible by 4(C) a prime number(D) a multiple of 3(E) greater than 24（分数：5.00）A.B. C.D.E.解析：13.A painter has painted one-third of a rectangular wall which is ten feet high. When she has painted another 75 square feet of wall, she will be three-quarters finished with the job. What is the length (the horizontal dimension) of the wall?(A) 18
