1、工商管理硕士入学考试-算术(二)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. （分数：5.00）A.B.C.D.E.2.How many two-digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?(A) None(B) One(C) TWO(D) Three(E) Four（分数：5.00）A.B.C.D.E.3. （分数：5.00）A.B.C.D.E.4.C
2、REATE YUUR OWN SUNDAE 12 Ice Cream Flavors 10 Kind of Candies 8 Liquid Toppings 5 Kinds of Toppings With or Without Whipped cream If a customer makes exactly one selection from each of the five categories shown in the table above, what is the greatest possible number of different ice cream sundaes t
3、hat a customer can create?(A) 9,600 (B) 4,800(C) 2,400 (D) 800(E) 400（分数：5.00）A.B.C.D.E.5.How many integers between 100 and 150, inclusive, can be evenly divided by neither 3 nor 5?(A) 33(B) 28(C) 27(D) 25(E) 24（分数：5.00）A.B.C.D.E.6.Is the positive integer n equal to the square of an integer?(1)For e
4、very prime number p, if p is a divisor of n, then so is p2.(2) （分数：5.00）A.B.C.D.E.7.Ben and Ann are among 7 contestants from which 4 semifinalists are to be selected. Of the different possible selections, how many contain neither Ben nor Ann?(A) 5 (B) 6(C) 7 (D) 14(E) 21（分数：5.00）A.B.C.D.E.8. （分数：5.0
5、0）A.B.C.D.E.9.All of the following have the same number of distinct prime factors EXCEPT(A) 20(B) 21(C) 24(D) 30(E) 45（分数：5.00）A.B.C.D.E.10.If x and y are integers, is xy+1 divisible by 3?(1)When x is divided by 3, the remainder is 1.(2)When y is divided by 9, the remainder is 8.(A) 条件(1)充分，但条件(2)不充
6、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.11.How many positive prime numbers are less than the integer n?(1)14n20(2)13n17(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(
7、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.12.What is the remainder when the positive integer x is divided by 2?(1)x is an odd integer.(2)x is a multiple of 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，条件(2)也充分(E) 条
8、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.13.If the sum of the first n positive integers is S，what is the sum of the first n positive even integers, in terms of S?(A) （分数：5.00）A.B.C.D.E.14.A computer is programmed to generate a list of multiples of prime numbers 2,3 and 5, as shown belo
9、w:Program 1List multiples of 2 Program 2List multiples of 3 Program 3List multiples of 5 How many integers less than 100 will appear on all of the lists of programs produced above?(A) None (B) 1(C) 3 (D) 5(E) An infinite number of integers（分数：5.00）A.B.C.D.E.15.How many of the integers between 25 and
10、 45 are even?(A) 21(B) 20(C) 11(D) 10(E) 9（分数：5.00）A.B.C.D.E.16.When the integer n is divided by 6, the remainder is 3. Which of the following is NOT a multiple of 6?(A) n-3 (B) T+3(C) 2n (D) 3n(E) 4n（分数：5.00）A.B.C.D.E.17.For any integer n greater than 1, denotes the product of all the integers from
11、 1 to n, inclusive. How many prime nunbers are there between and （分数：5.00）A.B.C.D.E.18.If the two-digit integers M and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of M and N?(A) 181 (B) 165 (C) 121(D) 99 (E) 44（分数：5.00）A.B.C.D.E.19.If when
12、a certain mteger x is divided by 5 the remainder is 2, then each of the following could also be an integer（分数：5.00）A.B.C.D.E.20.Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If the slips are then drawn one at a tim
13、e without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?(A) Three(B) Four(C) Five(D) Six(E) Seven（分数：5.00）A.B.C.D.E.21.Which of the following procedures is always equivalent to adding 5 given numbers and then dividing the sum by 5? Mul
14、tiplying the 5 numbers and then finding the 5 th root of the product. Adding the 5 numbers, doubling the sum, and then moving the decimal point one place to the left. Ordering the 5 numbers numerically and then selecting the middle number.(A) None(B) only(C) only(D) only(E) and（分数：5.00）A.B.C.D.E.22.
15、What is the probability that events A and B both occur?(1)The probability that event A occurs is 0.8.(2)The probability that event B occurs is 0.6.(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
16、.C.D.E.23.What is the units digit of (13)4(17)2(29)3?(A) 9(B) 7(C) 5(D) 3(E) 1（分数：5.00）A.B.C.D.E.24.If k and n are integers, is n divisible by 7?(1)n-3=2k(2)2k-4 is divisible by 7.(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
17、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.25.If the sum of a set of ten different positive prime numbers is an even number, which of the following prime numbers CANNOT be in the set?(A) 2(B) 3(C) 5(D) 7(E) 11（分数：5.00）A.B.C.D.E.26.A certain alloy contains only lead, copper, and tin. How many pounds of
18、tin are contained in 56 pounds of the alloy?(1)By weight the alloy is lead and （分数：5.00）A.B.C.D.E.27.Is the positive integer x an even number?(1)If z is divided by 3, the remainder is 2.(2)If x is divided by 5, the remainder 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
19、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.28.If n=p+r, where n, p, and r are positive integers and n is odd, does p equal 2?(1)p and r are prime numbers.(2)r2(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
20、(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.29.Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio is expressed as a decimal, is （分数
21、：5.00）A.B.C.D.E.30.If the average (arithmetic mean) of 5 positive temperatures is 32 degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be（分数：5.00）A.B.C.D.E.31.Coins are to be put into 7 pockets so that each pocket contains at least one coin. At mo
22、st 3 of the pockets are to contain the same number of coins, and no two of the remaining pockets are tO contain an equal number of coins. What is the least possible number of coins needed for the pockets?(A) 7(B) 13(C) 17(D) 22(E) 28（分数：5.00）A.B.C.D.E.32.If x and y are positive integers and x is a m
23、ultiple of y，is y=2?(1)y1(2)x+2 is a multiple of y.(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.33.There are 4 card-processing machines in an office. The fastest of these machines proce
24、sses x cards in 7 hours and the slowest processes x cards in 8 hours. Which of the following could NOT be the average time per machine for each of the 4 machines to process x cards?(A) 7.2(B) 7.3(C) 7.5(D) 7.6(E) 7.7（分数：5.00）A.B.C.D.E.34.How many two-element subsets of 1, 2, 3, 4are there that do no
25、t contain the pair of elements 2 and 4?(A) One (B) TWO (C) Four(D) Five (E) Six（分数：5.00）A.B.C.D.E.35. （分数：5.00）A.B.C.D.E.36.The pages of a report are numbered consecutively from 1 to 10. If the sum of the page numbers up to and including page number z of the report is equal to one more than the sum
26、of the page numbers following page number x, then x=(A) 4(B) 5(C) 6(D) 7(E) 8（分数：5.00）A.B.C.D.E.37.If x, y, and z are single-digit integers and 100(x)+1,000(y)+10(z)=N, what is the units digit of the number N?(A) 0(B) 1(C) x(D) y(E) z（分数：5.00）A.B.C.D.E.38.If n is a positive integer, is the value of
27、b-a at least twice the value of 3n-2n?(1)a=2n+1 and b=3n+1(2)n=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 least possible product of 4 different integers, each of which has
28、a value between -5 and 10, inclusive?(A) -5040(B) -3600(C) -720(D) -600(E) -120（分数：5.00）A.B.C.D.E.40.For any positive integer n, n1, the “length“ of n is the number of positive primes (not necessarily distinct) whose product is n. For example, the length of 50 is 3 since 50=(2)(5)(5)Which of the fol
29、lowing integers has length 3?(A) 3(B) 15(C) 60(D) 64(E) 105（分数：5.00）A.B.C.D.E.41.If r=23527 and s=22325, which of the following is equal to the greatest common divisor of r and s?(A) 25 (B) 225(C) 2352 (D) 2357(E) 2332527（分数：5.00）A.B.C.D.E.42.If n is a positive integer and k+2=3n, which of the follo
30、wing could NOT be a value of K?(A) 1(B) 4(C) 7(D) 25(E) 79（分数：5.00）A.B.C.D.E.43.When the integer k is divided by 12, the remainder is 3. Which of the following, when divided by 12, will have a remainder of 6? 2k 6k 4k+6(A) only (B) only(C) only (D) andonly(E) , , and（分数：5.00）A.B.C.D.E.44.An even num
31、ber x divided by 7 give some quotient plus a remainder of 6. Which of the following, when added to x, gives a sum which must be divisible by 14?(A) 1 (B) 3 (C) 7(D) 8 (E) 13（分数：5.00）A.B.C.D.E.45.All trainees in a certain aviator training program must take both a written test and a flight test, If 70
32、 percent of the trainees passed the written test, and 80 percent of the trainees passed the flight test, what percent of the trainees passed both tests?(1)10 percent of the trainees did not pass either test.(2)20 percent of the trainees passed only the flight test.(A) 条件(1)充分，但条件(2)不充分(B) 条件(2)充分，但条
33、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.工商管理硕士入学考试-算术(二)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. （分数：5.00）A.B. C.D.E.解析：解析 由上面的加法算式可知，个位向十位进了一位，十位向百位进了一位，所以根据加法原则，可得到如下的式子：3+1=10+=62.How many two-digit
34、whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?(A) None(B) One(C) TWO(D) Three(E) Four（分数：5.00）A.B.C.D. E.解析：解析 被 10 除时余 1，被 6 除时也余 1 的两位数就是被 10 和 6 的最小公倍数除也余 1 的数，10和 6 的最小公倍数是 30，而被 30 除余 1 的两位数有 3 个，即为 31，61 和 91，所以被 10 除时余数为 1，被 6 除时余数也为
35、 1 的两位整数也是 3 个。3. （分数：5.00）A. B.C.D.E.解析：解析 本题的正确答案为(A) 。根据题意可得：4st=8tu，也即 s=2u，s 的值与 t 无关，而由 u 的大小决定，所以(1)充分，而(2)不充分。4.CREATE YUUR OWN SUNDAE 12 Ice Cream Flavors 10 Kind of Candies 8 Liquid Toppings 5 Kinds of Toppings With or Without Whipped cream If a customer makes exactly one selection from ea
36、ch of the five categories shown in the table above, what is the greatest possible number of different ice cream sundaes that a customer can create?(A) 9,600 (B) 4,800(C) 2,400 (D) 800(E) 400（分数：5.00）A. B.C.D.E.解析：解析 由表格可知，该顾客在第一类中有 种选法，在第二类中有 种选法，在第三类中有 种选法，在第四类中有 种选法，在第五类中有 种选法，所以一共的选法为这五类不同选法的组合数：
37、5.How many integers between 100 and 150, inclusive, can be evenly divided by neither 3 nor 5?(A) 33(B) 28(C) 27(D) 25(E) 24（分数：5.00）A.B.C. D.E.解析：解析 用 100 到 150 之间的所有数减去能被 3 整除的数，再减去能被 5 整除的数，最后再加上既能被 3 整除，又能被 5 整除的数即为所求：100 和 150 之间包括 100 和 150 共有 51 个数，能被 3 整除的数的个数为 17 个；能被 5 整除的数的个数为 个；既能被 3 整除又能
38、被 5 整除的数的个数为6.Is the positive integer n equal to the square of an integer?(1)For every prime number p, if p is a divisor of n, then so is p2.(2) （分数：5.00）A.B. C.D.E.解析：解析 (1)不充分，因为 p2有可能等于 n，也有可能不等于 n；(2)充分，因为 是整数，则 n就是整数7.Ben and Ann are among 7 contestants from which 4 semifinalists are to be sele
39、cted. Of the different possible selections, how many contain neither Ben nor Ann?(A) 5 (B) 6(C) 7 (D) 14(E) 21（分数：5.00）A. B.C.D.E.解析：解析 7 人中若不包括 B 和 A 则剩下 5 人，因此本题也即为求从 5 人中选出 4 人的可能性有多少种，根据组合的基本概念可知共有8. （分数：5.00）A.B.C. D.E.解析：解析 若第一站为从 A 到 E，则该销售代表有两种可选择的道路：(1)AECFA(2)AEFCA根据题目表格中的数据可知两条道路的费，用分别为：(
40、1)=7+2+4+3=16 美元(2)=7+6+4+3=20 美元由上分析可知在道路 1 的花费最低为 16 美元。9.All of the following have the same number of distinct prime factors EXCEPT(A) 20(B) 21(C) 24(D) 30(E) 45（分数：5.00）A.B.C.D. E.解析：解析 在做此题时考生一定要注意题目要求的不同质因子的个数，所以可用质因子数求解公式来解此题：20=225，所以 20 的不同因子数为两个(2 和 5)21=37，所以 21 的不同因子数为两个(3 和 7)24=233，所以
41、24 的不同质因子数为两个(2 和 3)30=235，所以 30 的不同质因子数为为三个(2，3 和 5)45=325，所以 45 的不同质因子数为两个(3 和 5)10.If x and y are integers, is xy+1 divisible by 3?(1)When x is divided by 3, the remainder is 1.(2)When y is divided by 9, the remainder is 8.(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)
42、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 因为 xy+1 能否被 3 整除，不但取决于 x 的值，而且还取决于 y 的值，所以(1)和(2)单独都很明显不充分；根据(1)+(2)可得：x=3m+1，y=9n+8，其中 m，n 是整数。把这两个式子代入 xy+1 可得：xy+1=(3m+1)(9n+8)+1=27mn+24m+9n+84-1=3(9mn4-8m+3n+3)因此 xy+1 能被 3 整除，所以(1)+(2)充分。11.How many po
43、sitive prime numbers are less than the integer n?(1)14n20(2)13n17(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 因为在 14 与 20 之间有质数 17，所以当 n 取 15，16，17 时，比 n 小的质数有2，3，5，7，11，13，共 6 个
44、；而当 n 取 18，19 时，比 n 小的质数有 2，3，5，7，11，13，17，共有 7个，所以(1)不充分；因为 13 与 17 之间没有质数，所以当 n 的取值在 13 与 17 之间时，小于它的质数的个数是一定的，因此(2)充分。12.What is the remainder when the positive integer x is divided by 2?(1)x is an odd integer.(2)x is a multiple of 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
45、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) 。因为偶数都是 2 的倍数，所以当 x 是偶数被 2 除时，其余数为0，所以(1)充分；(2)不充分，因为 3 的倍数即有可能被 2 整除(如 6)，也有可能不能被 2 整除(如 9)。13.If the sum of the first n positive integers is S，what is the sum of the first n positive
46、 even integers, in terms of S?(A) （分数：5.00）A.B.C. D.E.解析：解析 前 n 个正整数的和为：S=1+2+3+n前 n 个正偶数的和为：2+4+6+2n=2(1+2+3+n)=2S14.A computer is programmed to generate a list of multiples of prime numbers 2,3 and 5, as shown below:Program 1List multiples of 2 Program 2List multiples of 3 Program 3List multiples
47、of 5 How many integers less than 100 will appear on all of the lists of programs produced above?(A) None (B) 1(C) 3 (D) 5(E) An infinite number of integers（分数：5.00）A.B.C. D.E.解析：解析 此题目也即问在小于 100 的整数中有多少数同时是 2，3，5 的倍数。因为 2，3，5 互质，所以小于 100 的 2，3，5 的公倍数为 30，60，90。15.How many of the integers between 25
48、and 45 are even?(A) 21(B) 20(C) 11(D) 10(E) 9（分数：5.00）A.B.C.D. E.解析：解析 25 与 45 之间的偶数形成一个首项为 26，末项为 44，公差为 2 的等差数列，所以可以按等差数列的公式 an=a1+(n-1)d，来求其偶数的个数：16.When the integer n is divided by 6, the remainder is 3. Which of the following is NOT a multiple of 6?(A) n-3 (B) T+3(C) 2n (D) 3n(E) 4n（分数：5.00）A.B
49、.C.D. E.解析：解析 根据题意可设 n=6k+3，其中 k 为整数，则五个选项的值可分别表示为：6k，6(k+1)，6(2k+1)，6(k+1)+3，6(4k+2)。由以上数据可知 3n 不是 6 的倍数。17.For any integer n greater than 1, denotes the product of all the integers from 1 to n, inclusive. How many prime nunbers are there between and （分数：5.00）A. B.C.D.E.解析：解析 由题意可得：18.If the two-digit integers M and N are positive and have the same digits, but in reverse order, which of the following CA
