1、工商管理硕士入学考试-代数及答案解析(总分：270.00，做题时间：90 分钟)一、单项选择题(总题数：54，分数：270.00)1.If x+y+z0, is z1?(1)zx+y+1(2)x+y+10（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分2.What is the 1st term in sequence S?(1)The 3 rd term
2、in S is 2. (2)The 2 nd term in S is twice the 1 st, and the 3 rd term is three times the 2 nd.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分3.If Pat bought a tennis shirt with matching shorts, what was
3、the cost of the shirt?(1)The total cost of the shirt and shorts was $20.(2)The ratio of the cost of the shirt to the cost of the shorts was 2:3.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分4.If x, y, a
4、nd z are positive integers and 3x=4y=7z, then the least possible value of x+y+z is（分数：5.00）A.33B.40C.49D.61E.(E) 845.A man drove his automobile d1 kilometers at the rate of r1 kilometers per hour and an additional d2 kilometers at the rate of r2 kilometers per hour. In terms of d1, d2, r1, r2, what
5、was his average speed, in kilometers per hour, for the entire trip?（分数：5.00）A.B.C.D.E.6.Vandas Butcher Shop sells packages of ground turkey and ground beef. Is the price for a pound of ground turkey less than that for a pound of ground beef?(1)The price for a package of ground turkey is 30 percent g
6、reater than the price for a package of ground beef.(2)A package of ground turkey weighs 25 percent more than a package of ground beef.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分7. （分数：5.00）A.B.C.D.E.
7、8.On a scale that measures the intensity of a certain phenomenon, a reading of n+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n. On that scale, the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a r
8、eading of 3?（分数：5.00）A.5B.50C.105D.510E.(E) 810-3109.If x=0.rstu, where r, s, t, and u each represent a nonzero digit of x, what is the value of x?(1)r=3s=2t=6u(2)The product of r and u is equal to the product of s and t.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合
9、起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分10. （分数：5.00）A.B.C.D.E.11.If s1, s2, s3is the sequence such that sn for all positive integers n, then the product of the first 10 terms of this sequence is（分数：5.00）A.B.C.D.E.12.If C is the temperature in degrees Celsins and F is the te
10、mperature in degrees Fahrenheit, then the relationship between temperatures on the two scales is expressed by the equation 9C=5(F-32). On a day when the temperature extremes recorded at a certain weather station differed by 45 degrees on the Fahrenheit scale, by how many degrees did the temperature
11、extremes differ on the Celsius scale?（分数：5.00）A.B.13C.25D.45E.(E) 8113. （分数：5.00）A.B.C.D.E.14.Are all of the numbers in a certain list of 15 numbers equal?(1)The sum of all of the numbers in the list is 60.(2)The sum of any 3 numbers in the list is 12。（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C
12、.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分15.An infinite sequence of positive integers is called an “alpha sequence“ if the number of even integers in the sequence is finite. If S is an infinite sequence of positive integers, is S an alpha sequen
13、ce?(1)The first ten integers in S are even.(2)An infinite number of integers in S are Odd.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分16.x-y=32x=2y+6The system of equations above has how many solution
14、s?（分数：5.00）A.NoneB.Exactly oneC.Exactly twoD.Exactly threeE.(E) Infinitely many17.For a light that has an intensity of 60 candies at its source, the intensity in candles, S, of the light at a point d feet from the source is given by the formula , where k is a constant. If the intensity of the light
15、is 30 candles at a distance of 2 feet from the Source, What is the intensity of the light at a distance of 20 feet from the source?（分数：5.00）A.B.C.D.E.18.When an object is dropped, the number of feet N that it falls is given by the formula （分数：5.00）A.B.C.D.E.19.If represents one of the operations +,-
16、, and, is k(1+m)=(k1)+(km) for all numbers k, 1 and m?(1)k1 is not equal to 1k for some numbers k.(2)represents subtraction.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分20.If x and y are positive integ
17、ers, is xy?(1)x3y(2) （分数：5.00）A.B.C.D.E.21.The operation * is defined as follows： .What is the value of (6)*(4)?（分数：5.00）A.B.C.D.E.22. （分数：5.00）A.B.C.D.E.23.A rectangular circuit board is designed to have width 叫 inches, perimeter p inches, and area k square inches. Which of the following equations
18、must be true?（分数：5.00）A.2+p+k=0B.2-pw4+2k=0C.2+pw+2k=0D.2-p-2k=0E.(E) 22-pw+2k=024.In a certain sequence, the first term is 1, and each successive term is 1 more than the reciprocal of the term that immediately precedes it. What is the fifth term of the sequence?（分数：5.00）A.B.C.D.E.25. （分数：5.00）A.B.C
19、.D.E.26.The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feet below the top of the tank, the concentration is 3 （分数：5.00）A.B.C.D.E.27.A plane traveled k miles in the first 96 minutes of flight time. If it completed the remaining 300
20、 miles of the trip in t minutes, what was its average speed, in miles per hour, for the entire trip?（分数：5.00）A.B.C.D.E.28.Mr. Kramer, the losing candidate in a two-candidate election, received 942, 568 votes, which was exactly 40 percent of all the votes castApproximately what percent of the remaini
21、ng votes would he need to have received in order to have won at least 50 percent of all the votes cast?（分数：5.00）A.10%B.12%C.15%D.17%E.(E) 20%29.For all real numbers , the operation *is defined by the equation （分数：5.00）A.B.C.D.E.30.If y3 and （分数：5.00）A.B.C.D.E.31.A certain used-book dealer sells pape
22、rback books at 3 times dealers cost and hardback books at 4 times dealers cost. Last week the dealer sold a total of 120 books, each of which had cost the dealer$1. If the gross profit (sales revenue minus dealers cost) on the sale of all of these books was$300, how many of the books sold were paper
23、 backs?（分数：5.00）A.40B.60C.75D.90E.(E) 10032.If , then （分数：5.00）A.B.C.D.E.33.If rs=rs+r+s, then for what value of s is rs equal to r for all values of r?（分数：5.00）A.-1B.0C.1D.E.(E) r34.What is the maximum capacity in cups of a pail that contains only sand and is filled to three fourths of its capacity
24、?(1)If one cup of sand were added to the pail, it would be filled to seven eighths of its capacity.(2)If two cups were removed from the pail, it would be filled to one half of its capacity.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1
25、)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分35.In a certain formula, p is directly proportional to s and inversely proportional to r. If p=1 when r=-0.5 and s=2，what is the value of p in terms of r and s?（分数：5.00）A.B.C.D.E.36.If xy=-6, what is the value of xy(x+y)?(1)x-y=5(2)xy2=18（分数：5.00）A.条件(1)充分，但条件(2)不充分B
26、.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分37.In the expression above, a, b, and c are different numbers and each is one of the numbers 2, 3, or 5. What is the least possible value of the expression?（分数：5.00）A.B.C.D.E.38.The onl
27、y contents of a parcel are 25 photographs and 30 negatives. What is the total weight, in ounces, of the parcels contents?(1)The weight of each photograph is 3 times the weight of each negative.(2)The total weight of 1 of the photographs and 2 of the negatives is （分数：5.00）A.B.C.D.E.39.If xyz and y-x5
28、, where x is an even integer and y and z are odd integers, what is the least possible value of z-x?（分数：5.00）A.6B.7C.8D.9E.(E) 1040.A certain theater has 100 balcony seats. For every$2 increase in the price of a balcony seat above$10, 5 fewer seats will be sold. If a11 the balcony seats are sold when
29、 the price of each seat is$10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is$1,360?（分数：5.00）A.$12B.$14C.$16D.$17E.(E) $1841.The function * is defined by the equation （分数：5.00）A.B.C.D.E.42.If x, y and z are non-zero numbers such that 1yx
30、and xy=z, which of the following cannot be true?（分数：5.00）A.yzB.y=zC.z=xD.xzE.(E) z043.If denotes a mathematical operation, does xy=yx for all x and y?(1)For all z and y, xy=2(x2+y2)(2)For all y, 0y=2y2（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也
31、充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分44. （分数：5.00）A.B.C.D.E.45.On a certain 10-question test, each question after the first question is worth 2 points more than the previous question. If the greatest number of points that can be scored on the test is 100, how many points is the eighth questi
32、on worth?（分数：5.00）A.9B.14C.15D.19E.(E) 3346.If the successive tick marks shown on the number line above are equally spaced and if x and y are the numbers designating the end points of intervals as shown, what is the value of y?（分数：5.00）A.B.C.D.E.47.On the day of the performance of a certain play, ea
33、ch ticket that regularly sells for less than$10,00 is sold for half price plus $0.50, and each ticket that regularly sells for$10.00 or more is sold for half price plus$1.00. On the day of the performance, a person purchases a total of y tickets, of which x regularly sell for $9.00 each and the rest
34、 regularly sell for $12.00 each. What is the amount paid, in dollars, for the y tickets?(A) 7y-2x (B) 12x-7y（分数：5.00）A.B.C.D.E.48.A certain fraction is equivalent to . If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to （分数：5.00）A.B.C.
35、D.E.49.The cost C of manufacturing a certain product can be estimated by the formula C=0, 03rst2, where r and 8 are the amounts, in pounds, of the two major ingredients and t is the production time in hours. If r is increased by 50 percent, s is increased by 20 percent，and t is decreased by 30 perce
36、nt, by approximately what percent will the estimated cost of manufacturing the product change?（分数：5.00）A.40%increaseB.12%increaseC.4%increaseD.12%decreaseE.(E) 24%decrease50.If x=y2, what is the value of y-x?(1)x=4(2)x+y=2（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联
37、合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分51.What is the value of x2-y2?(1)x+y=2x(2)x+y=0（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分52.Is x3 equal to 125?(1)x4(2)x6（分数：5.00）A.
38、条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分53.What percent of the employees of Company X are technicians?(1)Exactly 40 percent of the men and 55 percent of the women employed by Company X are technicians.(2)At
39、Company X, the ratio of the number of technicians to the number of nontechnicians is 9 to 11.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分54.For a group of n people, k of whom are of the same sex, the
40、expression （分数：5.00）A.B.C.D.E.工商管理硕士入学考试-代数答案解析(总分：270.00，做题时间：90 分钟)一、单项选择题(总题数：54，分数：270.00)1.If x+y+z0, is z1?(1)zx+y+1(2)x+y+10（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分 C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分解析：解析 (1)不充分，因为无法判断 x+y
41、是否大于 0；由 x+y+z2.What is the 1st term in sequence S?(1)The 3 rd term in S is 2. (2)The 2 nd term in S is twice the 1 st, and the 3 rd term is three times the 2 nd.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分 D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联
42、合起来也不充分解析：解析 (1)不充分，因为不知道第三项与第一项之间有何种关系；(2)不充分，因为(2)中虽然给出了数列 S 的前三项之间的关系，但没给出具体值，所以也无法求出数列 S 的首项是多少；根据(1)+(2)可得，数列 S 的首项为第三项的*，即数列 S 的首项为*，所以(1)+(2)充分。3.If Pat bought a tennis shirt with matching shorts, what was the cost of the shirt?(1)The total cost of the shirt and shorts was $20.(2)The ratio of
43、 the cost of the shirt to the cost of the shorts was 2:3.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分 D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分解析：解析 设衬衫的价格为 x 美元，短裤的价格为 y 美元，由(1)可得：x+y=20；由(2)可得 3x=2y；因此很明显(1)和(2)单独都求不出 x 的值，(1)+(2)可得到一个二元一次
44、方程组，从而可求出 y=8 美元，所以(1)+(2)充分。4.If x, y, and z are positive integers and 3x=4y=7z, then the least possible value of x+y+z is（分数：5.00）A.33B.40C.49D.61 E.(E) 84解析：解析 若要使 x，y 和 z 都是整数且满足 3x=4y=7z，则 x 应能被 4 和 7 整除，y 应能被 3 和 7 整除，同理 z 要能被 3 和 4 整除，又因为 3，4，7 为互质数，所以 x，y 和 z 的最小值分别为 47=28，37=21和 34=12。由此可知
45、x+y+z 的最小值为：28+21+12=615.A man drove his automobile d1 kilometers at the rate of r1 kilometers per hour and an additional d2 kilometers at the rate of r2 kilometers per hour. In terms of d1, d2, r1, r2, what was his average speed, in kilometers per hour, for the entire trip?（分数：5.00）A. B.C.D.E.解析：解析
46、 总的平均速度等于总路程除以总时间，这个人开车所行驶的总路程为 d1+d2，开车所用的总时间为*，所以其总的平均速度为：*6.Vandas Butcher Shop sells packages of ground turkey and ground beef. Is the price for a pound of ground turkey less than that for a pound of ground beef?(1)The price for a package of ground turkey is 30 percent greater than the price for
47、 a package of ground beef.(2)A package of ground turkey weighs 25 percent more than a package of ground beef.（分数：5.00）A.条件(1)充分，但条件(2)不充分B.条件(2)充分，但条件(1)不充分C.条件(1)和(2)单独都不充分，但条件(1)和条件(2)联合起来充分 D.条件(1)充分，条件(2)也充分E.(E) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合起来也不充分解析：解析 (1)中因不知道一袋火鸡和一袋牛肉各自的重量是多少，所以求不出是一磅火鸡贵还是一
48、磅牛肉贵，因此(1)不充分；(2)因不知道一袋火鸡和一袋牛肉的价格，所以(2)也不充分；设一袋牛肉的价格为 a，重量为 b，则一磅牛肉的价格为*，根据(1)+(2)可得一磅火鸡的价格为*，所以(1)+(2)充分。7. （分数：5.00）A.B.C. D.E.解析：解析 *8.On a scale that measures the intensity of a certain phenomenon, a reading of n+1 corresponds to an intensity that is 10 times the intensity corresponding to a rea
49、ding of n. On that scale, the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3?（分数：5.00）A.5B.50C.105 D.510E.(E) 810-310解析：解析 由 n+1 所对应的强度是 n 的 10 倍可推知 8 所对应的强度是 3 所对应的强度的 105倍，9.If x=0.rstu, where r, s, t, and u each represent a nonzero digit of x, what is the value of x?(1)r=3s=2t=6u(2)The product of r and u is equal to the product of s
