【考研类试卷】工商管理硕士入学考试-算术(一)及答案解析.doc

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1、工商管理硕士入学考试-算术(一)及答案解析(总分：225.00，做题时间：90 分钟)一、单项选择题(总题数：45，分数：225.00)1.In how many arrangements can a teacher seat 3 girls and 3 boys in a row of 6 seats if the boys are to have the first, third, and fifth seats?(A) 6 (B) 9(C) 12 (D) 36(E) 720（分数：5.00）A.B.C.D.E.2.If S is the sum of the first n positi

2、ve integers, what is the value of n?(1)S20(2)S2220(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) 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（分数：5.00）A.B.C.D.E.3.Committee X and committee Y, which have no common members, will combine to form Committe

3、e Z. Does Committee X have more members than Committee Y?(1)The average (arithmetic mean) age of the members of Committee X is 25.7 years and the average age of the members of Committee Y is 29.3 years.(2)The average (arithmetic mean) age of the members of Committee Z will be 26.6 years.(A) 条件(1)充分，

4、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) 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（分数：5.00）A.B.C.D.E.4.How many positive integers k are there such that 100k is a factor of (22)(3)(53)?(A) None(B) One(C) TWO(D) Three(E) Four（分数：5.00）A.B.C.D.E.5.It each o

5、f the following fractions were written as a repeating decimal, which would have the longest sequence of different digits?（分数：5.00）A.B.C.D.E.6.In each production lot for a certain toy, 25 percent of the toys are red and 75 percent of the toys are blue. Half the toys are size A and half are size BIf 1

6、0 out of a lot of 100 toys are red and size A, how many of the toys are blue and size B?(A) 15 (B) 25(C) 30 (D) 35(E) 40（分数：5.00）A.B.C.D.E.7.Of the following sums, which is greatest?（分数：5.00）A.B.C.D.E.8.Can the positive integer p be expressed as the product of two integers, each of which is greater

7、than 1?(1)31p37(2)p is odd(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) 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（分数：5.00）A.B.C.D.E.9.If n is an integer, which of the following CANNOT be a factor of 3n+4?(A) 4(B) 5(C) 6(D) 7(E) 8（分数：5.00）A.B.C.D.

8、E.10.Exactly how many bonds does Bob have?(1)Of Bobs bonds，exactly 21 are worth at least$5,000 each.(2)Of Bobs bonds, exactly 65 per cent are worth less than$5,000 each.(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) 条件(1)和条件(2)单独都不充分，条件(1)和条件(

9、2)联合起来也不充分（分数：5.00）A.B.C.D.E.11.If n and p are different positive prime numbers, which of the integers n4, p2, and np has (have) exactly 4 positive divisors?(A) n4only(B) p3only(C) nponly(D) n4andnp(E) p3andnp（分数：5.00）A.B.C.D.E.12. （分数：5.00）A.B.C.D.E.13.If S is an infinite set of real numbers, is th

10、ere a number in S that is less than every other number in S?(1)Every number in S is an integer.(2)Every number in S is positive.(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) 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（分数：5.00）A.B.C.D.E.14.If a 3-di

11、git integer is selected at random from the integers 100 through 199, inclusive, what is the probability that the first digit and the last digit of the integer are each equal to one more than the middle digit?（分数：5.00）A.B.C.D.E.15.How many integers n are there such that rns?(1)s-r=5(2)r and s are not

12、 integers.(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) 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（分数：5.00）A.B.C.D.E.16.3.26If and each represent single digits in the decimal above, what digit does represent?(1)When the decimal is rounded to the n

13、earest tenth, 3.2 is the result.(2)When the decimal is rounded to the nearest hundredth, 3.24 is the result.(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) 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（分数：5.00）A.B.C.D.E.17.A company that ships boxes to

14、 a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for

15、 the coding? (Assume that the order of the colors in a pair does not matter.)(A) 4(B) 5(C) 6(D) 12(E) 24（分数：5.00）A.B.C.D.E.18.Is the integer n a multiple of 140?(1) n is a multiple of 10.(2) n is a multiple of 14.(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(

16、1)充分，条件(2)也充分(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（分数：5.00）A.B.C.D.E.19.In a certain game, a large container is filled with red, yellow, green and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values

17、 of the removed beads is 147,000, how many red beads were removed?(A) 5(B) 4(C) 3(D) 2(E) 0（分数：5.00）A.B.C.D.E.20.Are there exactly 3 distinct symbols used to create the code words in language Q?(1)The set of all code words in language Q is the set of all possible distinct horizonal arrangements of o

18、ne or more symbols, with no repetition.(2)There are exactly 15 code words in language Q.(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) 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（分数：5.00）A.B.C.D.E.21.Raffle tickets numbered consecutively from 101 th

19、rough 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2?（分数：5.00）A.B.C.D.E.22.If x and y are integers and xy=5, then (x+y)2=(A) 13(B) 16(C) 25(D) 26(E) 36（分数：5.00）A.B.C.D.E.23.Is a+b+C+d equal to 4?(1)a, b, c, and d are ea

20、ch positive.(2)The product abcd equals 1.(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) 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（分数：5.00）A.B.C.D.E.24.If , where p and q are nonzero integers, is n an integer?(1)n2 is an integer.(2) （分数：5.00）A.B.C.

21、D.E.25.What is the tens digit of positive integer x?(1)x divided by 100 has a remainder of 30.(2)x divided by 110 has a remainder of 30.(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) 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（分数：5.00）A.B.C.D.E.26.W

22、hich of the following CANNOT be zero?. The sum of 7 consecutive integers. The sum of 10 consecutive even integers. The product of 13 consecutive integers(A) only(B) andonly(C) andonly(D) andonly(E) , , and（分数：5.00）A.B.C.D.E.27.If , x, y, and z are non-negative integers, each less than 3, and (3 3)+x

23、(32)+y(3)+z=34，then+z=(A) 0(B) 1(C) 2(D) 3(E) 4（分数：5.00）A.B.C.D.E.28.If x is an integer, is(x+p)(x+q)an even integer?(1)q is an even integer.(2)p is an even integer.(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) 条件(1)和条件(2)单独都不充分，条件(1)和条件(2)联合

24、起来也不充分（分数：5.00）A.B.C.D.E.29.What is the greatest commom divisor of positive integers m and n?(1)m is a prime number.(2)m and n are consecutive integers.(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) 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（分数：5.0

25、0）A.B.C.D.E.30.If k is an integer greater than 44 and less than 51，then which of the following could be the product of 11 and k?(A) 565(B) 550(C) 500(D) 484(E) 440（分数：5.00）A.B.C.D.E.31.In Township K, of the housing units are equipped with cable television. If of the housing units, including of those

26、 that are equipped with cable television, are equipped with videocassette recorders, what fraction of the housing units have neither cable television nor videocassette recorders?（分数：5.00）A.B.C.D.E.32.In a certain class consisting of 36 students, some boys and some girls, exactly of the boys and exac

27、tly （分数：5.00）A.B.C.D.E.33.If n is a positive integer and k=5.110n, what is the value of k?(1)6,000k500,000(2)k2=2.601109(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) 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（分数：5.00）A.B.C.D.E.34.A necklace is mad

28、e by stringing N individual beads together in the repeating pattern red bead, green bead, white bead, blue bead, and yellow bead. If the necklace design begins with a red bead and ends with a white bead, then N could equal(A) 16(B) 32(C) 41(D) 54(E) 68（分数：5.00）A.B.C.D.E.35.What is the value of the t

29、wo-digit num-ber x?(1)The sum of the two digits is 4.(2)The difference between the two digits is 2.(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) 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（分数：5.00）A.B.C.D.E.36.If Carmen had 12 more tapes, she would

30、 have twice as many tapes as Rafael. Does Carmen have fewer tapes than Rafael?(1)Rafael has more than 5 tapes.(2)Carmen has fewer than 12 tapes.(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) 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（分数：5.00）A.B.C.

31、D.E.37.How many people are directors of both Company K and Company R?(1)There were 17 directors present at a joint meeting of the directors of Company K and Company R, and no directors were absent, (2)Company K has 12 directors and Company R has 8 directors.(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

32、(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) 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（分数：5.00）A.B.C.D.E.38.If P is a set of integers and 3 is in P, is every positive multiple of 3 in P?(1)If x is in P，then x+3 is in P.(2)If x is in p, then x-3 is in p.(A) 条件(1)充分，但条件(2)不充分(B) 条件(2)充分，但

33、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) 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（分数：5.00）A.B.C.D.E.39.What is the greatest possible length of a positive integer less than 1,000?(A) 10(B) 9(C) 8(D) 7(E) 6（分数：5.00）A.B.C.D.E.40.There are between 100 and 110 cards in a collect

34、ion of cards. If they are counted out 3 at a tie, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?(A) 101(B) 103(C) 106(D) 107(E) 109（分数：5.00）A.B.C.D.E.41.If n is an integer between 2 and 100 and if n is also the square of an

35、 integer, what is the value of n?(1)n is the cube of an integer.(2)n is even.(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) 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（分数：5.00）A.B.C.D.E.42.How many integers between 324,700 and 458,600 have tens digi

36、t 1 and units digit 3?(A) 10,300(B) 10,030(C) 1,353(D) 1,352(E) 1,339（分数：5.00）A.B.C.D.E.43.If a, b, and c are integers, is the number 3 (a+b)-c divisible by 3?(1)a+b is divisible by 3.(2)c is divisible by 3.(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

37、件(2)也充分(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（分数：5.00）A.B.C.D.E.44.If n is a positive integer, then n(n+1)(n+2) is(A) even only when n is even(B) even only when n is odd(C) odd whenever n is odd(D) divisible by 3 only when n is odd(E) divisible by 4 whenever n is even（分数：5.00）A.B.C.D.E.45.Xavier,

38、 Y vonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are and , respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?（分数：5.00）A.B.C.D.E.工商管理硕士入学考试-算术(一)答案解析(总分：225.00，做题时间：90 分钟)一、单项选择题(总题数：45，分数：22

39、5.00)1.In how many arrangements can a teacher seat 3 girls and 3 boys in a row of 6 seats if the boys are to have the first, third, and fifth seats?(A) 6 (B) 9(C) 12 (D) 36(E) 720（分数：5.00）A.B.C.D. E.解析：解析 若 3 男孩在 1，3，5 时，则 3 个女孩应在 2，4，6，所以总的安排方式为：2.If S is the sum of the first n positive integers, w

40、hat is the value of n?(1)S20(2)S2220(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) 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（分数：5.00）A.B.C. D.E.解析：解析 当 S20 时，S 的取值范围较大，因此 n 的取值是不确定的，有好几个，所以(1)不充分；根据(2)同样无法得到确定的 n 值；根据(1)+(2)可得 S 的取值范围为3.Committee

41、X and committee Y, which have no common members, will combine to form Committee Z. Does Committee X have more members than Committee Y?(1)The average (arithmetic mean) age of the members of Committee X is 25.7 years and the average age of the members of Committee Y is 29.3 years.(2)The average (arit

42、hmetic mean) age of the members of Committee Z will be 26.6 years.(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) 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（分数：5.00）A.B.C. D.E.解析：解析 (1)不充分，因为(1)只是给出了两个委员会成员的各自平均年龄，而没有给出年龄与成员数目之间的关系，所以无法判断两个委员会的成员的多少

43、；(2)同理不能说明哪一个委员会的成员多；(1)+(2)充分，设 X 委员会的人数为 m，Y 委员会的人数为 n，则 Z 委员会的人数为 m+n，根据题意可得：4.How many positive integers k are there such that 100k is a factor of (22)(3)(53)?(A) None(B) One(C) TWO(D) Three(E) Four（分数：5.00）A.B.C.D.E. 解析：解析 (2) 2(3)(53)=(25)2(3)(5)=10035，要使 100k 是(2) 2(3)(53)的一个因子，则 k 应为35 的一个因子

44、。因为 35 共有 1，3，5，15 四个正整数因子，所以共有四个这样的 k 值。5.It each of the following fractions were written as a repeating decimal, which would have the longest sequence of different digits?（分数：5.00）A.B.C.D.E. 解析：解析 五个选项中的数都是无限循环小数，很明显 和 的循环节只有一位；而 和的循环节有两位，他们分别以 0.18 和 0.41 循环；6.In each production lot for a certain

45、 toy, 25 percent of the toys are red and 75 percent of the toys are blue. Half the toys are size A and half are size BIf 10 out of a lot of 100 toys are red and size A, how many of the toys are blue and size B?(A) 15 (B) 25(C) 30 (D) 35(E) 40（分数：5.00）A.B.C.D. E.解析：解析 由题意可知，在这 100 个玩具中红色的玩具有 25 个，蓝色的

46、玩具有 75 个，根据 100 个玩具中 10 个是红色 A 型，可推知红色 B 型玩具是 15 个，而 B 型共 50 个，所以蓝色 B 型有 35 个。7.Of the following sums, which is greatest?（分数：5.00）A. B.C.D.E.解析：解析 (D)选项的值明显小于(E)选项的值；在(A) ，(B)，(C)和(E)这四个选项中分母的值大小排序为：(B)(C)(E)(A) 。在分子大小都一样的情况下，分母小的分式的值大，所以(A) 选项8.Can the positive integer p be expressed as the product

47、 of two integers, each of which is greater than 1?(1)31p37(2)p is odd(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) 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（分数：5.00）A. B.C.D.E.解析：解析 本题的正确答案为(A) 。由(1)可得 p 的取值可以为 32，33，34，35，36，这五个整数都可表示成两个大于 1 的整数

48、的乘积的形式，所以(1)充分；因为奇数既可能是质数也可能是合数，所以(2)不充分。9.If n is an integer, which of the following CANNOT be a factor of 3n+4?(A) 4(B) 5(C) 6(D) 7(E) 8（分数：5.00）A.B.C. D.E.解析：解析 一般采用排除法来解此类数字规律题。(A) 当 n=0 时，4 是 3n+4 的因子；(B)当 n=7 时，5是 3n+4 的因子；(C)无论 n 取何值，3n+4 都不可能有 6 这个因子；而(D)中当 n 取 1 时 3n+4 可以被 7 整除；(E)中当 n 取 4

49、时 3n+4 可被 8 整除。10.Exactly how many bonds does Bob have?(1)Of Bobs bonds，exactly 21 are worth at least$5,000 each.(2)Of Bobs bonds, exactly 65 per cent are worth less than$5,000 each.(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) 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（分数：5.00）A.B.C. D.E.解析：解析 很明显，(1)和(2)单独都不充分；根据(1)+(2)可得 21 张价值在 5,000 美元以