1、工商管理硕士入学考试-算术(三)及答案解析(总分：170.00，做题时间：90 分钟)一、单项选择题(总题数：34，分数：170.00)1.The positive integer n is divisible by 25. If is greater than 25, which of the following could be the value of （分数：5.00）A.B.C.D.E.2.If a is a positive integer, and if the units digit of a2 is 9 and the units digit of (a+1)2 is 4,
2、what is the units digit of (a+2)2?(A) 1(B) 3(C) 5(D) 7(E) 9（分数：5.00）A.B.C.D.E.3.The average (arithmetic mean) of 3 different positive integers is 100 and the largest of these 3 integers is 120, what is the least possible value of the smallest of these 3 integers?(A) 1(B) 10(C) 61(D) 71(E) 80（分数：5.00
3、）A.B.C.D.E.4.How many integers 72 greater than 10 and less than 100 are there such that, if the digits of n are reversed, the resulting integer is n+9?(A) 5(B) 6(C) 7(D) 8(E) 9（分数：5.00）A.B.C.D.E.5. （分数：5.00）A.B.C.D.E.6.If n is an integer, is an integer?(1) is an integer.(2) （分数：5.00）A.B.C.D.E.7.A ja
4、r contains only x black balls and y white balls. One ball is drawn randomly from the jar and is not replaced. A second ball is then drawn randomly from the jar. What is the probability that the first ball drawn is black and the second ball drawn is white?（分数：5.00）A.B.C.D.E.8.What is the least positi
5、ve integer that is divisible by each of the integers 1 through 7, inclusive?(A) 420 (B) 840(C) 1,260 (D) 2,520(E) 5,040（分数：5.00）A.B.C.D.E.9.If a and b are positive integers, what is the value of a+b?（分数：5.00）A.B.C.D.E.10.How many factors of 60 are greater than （分数：5.00）A.B.C.D.E.11.Set S consists of
6、 n distinct positive integers, none of which is greater than 12. What is the greatest possible value of n if no two integers in S have a common factor greater than 1?(A) 4(B) 5(C) 6(D) 7(E) 11（分数：5.00）A.B.C.D.E.12.If the product of the integers , x, y, and z is 770, and if 1zyz, what is the value of
7、 +z?(A) 10(B) 13(C) 16(D) 18(E) 21（分数：5.00）A.B.C.D.E.13.In an office, 40 percent of the workers have at least 5 years of service, and a total of 16 workers have at least 10 years of service. If 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but
8、 fewer than 1 0 years of service?(A) 48(B) 64(C) 80(D) 144(E) 160（分数：5.00）A.B.C.D.E.14.Of 30 applicants for a job, 14 had at least 4 years experience, 18 had degrees, and 3 had less than 4 years experience and did not have a degree. How many of the applicants had at least 4 years experience and a de
9、gree?(A) 14(B) 13(C) 9(D) 7(E) 5（分数：5.00）A.B.C.D.E.15.How many three-digit numerals begin with a digit that represents a prime number and end with a digit that represents a prime number?(A) 16 (B) 80(C) 160 (D) 180(E) 240（分数：5.00）A.B.C.D.E.16.In how many different ways can 3 people be assigned to fi
10、ll 3 different positions so that each person is assigned to exactly one position?(A) Twelve (B) Nine(C) Six (D) Three(E) One（分数：5.00）A.B.C.D.E.17.On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. The actu
11、al number of miles per gallon that Cindys car got on this trip must have been between（分数：5.00）A.B.C.D.E.18.Three stacks containing equal numbers of chips are to be made from 9 red chips, 7 blue chips，and 5 green chipsIf all of these chips are used and each stack contains at least 1 chip of each colo
12、r, what is the maximum number of red chips in any one stack?(A) 7 (B) 6 (C) 5(D) 4 (E) 3（分数：5.00）A.B.C.D.E.19.If 75 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questi
13、ons correctly, what percent answered both correctly?(A) 10% (B) 20% (C) 30%(D) 50% (E) 65%（分数：5.00）A.B.C.D.E.20.If x and y are prime numbers, which of the following CANNOT be the sum of x and y?(A) 5 (B) 9 (C) 13(D) 16 (E) 23（分数：5.00）A.B.C.D.E.21.If n is a prime number greater than 3, what is the re
14、mainder when n2 is divided by 12?(A) 0(B) 1(C) 2(D) 3(E) 5（分数：5.00）A.B.C.D.E.22.S is a set of integers such that i) if a is in S. then -a is in S, andii) if each of n and b is in S, then ab is in S. Is -4 in S?(1)1 is in S.(2)2 is in S.(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
15、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.23.LEAGUE RESULTS Team Number of Games Won A 4B 7C 9D 2E 2XAccording to the incomplete table above, if each of the 6 teams in the league played each of the other teams exactly twice and there were no ties
16、, how many games did team X win? (Only 2 teams play in a game.)(A) 4 (B) 5 (C) 6 (D) 8 (E) 10（分数：5.00）A.B.C.D.E.24.If X and Y are sets of integers, XY denotes the set of integers that belong to set X or set Y, but not both. If X consists of 10 integers, Y consists of 18 integers，and 6 of the integer
17、s are in both X and Y, then XY consists of how many integers?(A) 6 (B) 16 (C) 22(D) 30 (E) 174（分数：5.00）A.B.C.D.E.25.When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n?(A) 3 (B) 4(C) 7 (D) 8(E) 12（分数：5.00）A.B.C.D.E.26.If an integer n is
18、divisible by both 6 and 8, then it must also be divisible by which of the following?(A) 10(B) 12(C) 14(D) 16(E) 18（分数：5.00）A.B.C.D.E.27.If 10 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?(A) 10987654321(B) 1010(C)
19、 109(D) 45(E) 36（分数：5.00）A.B.C.D.E.28.If 1d2, is the tenths digit of the decimal representation of d equal to 9?(1)d+0.012(2)d+0.052(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.29.A cer
20、tain packing crate contains between 50 and 60 books. How many books are there in the packing crate?(1)If the books are counted out by three, there will be one book left over.(2)If the books are counted out by sixes, there will be one book left over.(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)
21、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.30.For the positive numbers, n, n+1, n+2, n+4 and n+8, the mean is how much greater than the median?(A) 0(B) 1(C) n+1(D) n+2(E) n+3（分数：5.00）A.B.C.D.E.31.If M and N are positive integers that
22、have remainders of 1 and 3, respectively, when divided by 6, which of the following could NOT be a possible value of M+N?(A) 86 (B) 52 (C) 34(D) 28 (E) 10（分数：5.00）A.B.C.D.E.32.If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of
23、 the digits 1, 2, 3, and 6，what is the greatest number of fourdigit extensions that the company can have?(A) 4(B) 6(C) 12(D) 16(E) 24（分数：5.00）A.B.C.D.E.33.If 77,777=70, 707+(7.07n), then n(A) 1,000(B) 100(C) 10(D) (E) （分数：5.00）A.B.C.D.E.34.What fractional part of the total surface area of cube C is
24、red?(1)Each of 3 faces of c is exactly （分数：5.00）A.B.C.D.E.工商管理硕士入学考试-算术(三)答案解析(总分：170.00，做题时间：90 分钟)一、单项选择题(总题数：34，分数：170.00)1.The positive integer n is divisible by 25. If is greater than 25, which of the following could be the value of （分数：5.00）A.B.C.D.E. 解析：解析 因为 n 是正整数，所以由 大于 25 可推知 n25 2，因此2.If
25、 a is a positive integer, and if the units digit of a2 is 9 and the units digit of (a+1)2 is 4, what is the units digit of (a+2)2?(A) 1(B) 3(C) 5(D) 7(E) 9（分数：5.00）A. B.C.D.E.解析：解析 根据 a2的个位数是 9 可推知 a 的个位数可能为 3 或 7，又根据(a+1) 2的个位数是 4，可推知 a 的个位数只能是 7。由以上分析可知(a+2) 2的个位数应为 1。3.The average (arithmetic mea
26、n) of 3 different positive integers is 100 and the largest of these 3 integers is 120, what is the least possible value of the smallest of these 3 integers?(A) 1(B) 10(C) 61(D) 71(E) 80（分数：5.00）A.B.C. D.E.解析：解析 其余两个数的和为 3100-120=180，要使最小数尽可能地小，就应使另一个数尽可能地大，但因为三个数中的最大数是 120，所以第二大的数最大只能取 119，因此最小数的最小可
27、能值为 180-119=61。4.How many integers 72 greater than 10 and less than 100 are there such that, if the digits of n are reversed, the resulting integer is n+9?(A) 5(B) 6(C) 7(D) 8(E) 9（分数：5.00）A.B.C.D. E.解析：解析 设 n 的个位数字为 a，十位数字为 b，则n=10b+a根据题意得：10b+a+9=10a+ba-b=1即个位数字比十位数字大 1。满足此特征的数字有 12，23，34，45，56，67
28、，78，89 共 8 个数字。5. （分数：5.00）A.B.C. D.E.解析：解析 由图可知，第一个分支有两条路，第二个分支也有两条路，第三个分支有 3 条路，则根据乘法原则可知不同小路的数目为：223=126.If n is an integer, is an integer?(1) is an integer.(2) （分数：5.00）A.B. C.D.E.解析：解析 (1)不充分，因为很明显由 是一个整数无法推出 是一个整数；因为 15 和 8 互质，所以若 n 不能被 15 整除，则 8n 也不能被 15 整除，反过来由 8n 能被 15 整除，则 n 中一定含有 15 这个因子，
29、也即 n 能被 15 整除，7.A jar contains only x black balls and y white balls. One ball is drawn randomly from the jar and is not replaced. A second ball is then drawn randomly from the jar. What is the probability that the first ball drawn is black and the second ball drawn is white?（分数：5.00）A.B.C.D.E. 解析：解析
30、 第一次为黑球的概率是 ，第二次为白球的概率是 ，因此第一次为黑球而第二次为白球的概率为：8.What is the least positive integer that is divisible by each of the integers 1 through 7, inclusive?(A) 420 (B) 840(C) 1,260 (D) 2,520(E) 5,040（分数：5.00）A. B.C.D.E.解析：解析 该题也即让考生求 1，2，3，4，5，6 和 7 这 7 个数的最小公倍数。根据最小公倍的求解公式可得其最小公倍数=2 2357=2120=420。9.If a and
31、 b are positive integers, what is the value of a+b?（分数：5.00）A.B.C. D.E.解析：解析 本题正确答案为(C)。(1)不充分，根据10.How many factors of 60 are greater than （分数：5.00）A.B.C.D.E. 解析：解析 60=2 235，所以 60 共有(2+1)(1+1)(1+1)=12 个因子。根据本书中所讲的因子数的性质(当某一个正整数 n 有偶数个因子时，n 必不是完全平方数，且大于 的因子数与小于 的因子数相同)可知 60 有 6 个比11.Set S consists o
32、f n distinct positive integers, none of which is greater than 12. What is the greatest possible value of n if no two integers in S have a common factor greater than 1?(A) 4(B) 5(C) 6(D) 7(E) 11（分数：5.00）A.B.C. D.E.解析：解析 集合 S 中任两个整数的公约数都不大于 1 说明该集合中的数字都为互质数，小于 12 的质数共有 2，3，5，7，11；同时 1 虽然不是质数，但它也满足题设条件
33、，所以 n 的最大可能值为 5+1=6。12.If the product of the integers , x, y, and z is 770, and if 1zyz, what is the value of +z?(A) 10(B) 13(C) 16(D) 18(E) 21（分数：5.00）A.B. C.D.E.解析：解析 由题可知，770 可分解成四个不同的因子相乘的形式：770=25711再根据 1xyz 可推知 =2，x=5，y=7，z=11，所以 +z 的值为 2+11=13。13.In an office, 40 percent of the workers have a
34、t least 5 years of service, and a total of 16 workers have at least 10 years of service. If 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but fewer than 1 0 years of service?(A) 48(B) 64(C) 80(D) 144(E) 160（分数：5.00）A. B.C.D.E.解析：解析 这类题最好借助用文氏图
35、来解，根据题意可画出如下的文氏图：14.Of 30 applicants for a job, 14 had at least 4 years experience, 18 had degrees, and 3 had less than 4 years experience and did not have a degree. How many of the applicants had at least 4 years experience and a degree?(A) 14(B) 13(C) 9(D) 7(E) 5（分数：5.00）A.B.C.D.E. 解析：解析 此题可以通过画文氏
36、图来解，如下图所示：15.How many three-digit numerals begin with a digit that represents a prime number and end with a digit that represents a prime number?(A) 16 (B) 80(C) 160 (D) 180(E) 240（分数：5.00）A.B.C. D.E.解析：解析 只有一位的正质数有 2，3，5，7 四个，而要求的 3 位数的首位和末位都是质数，且中间的十位数可为 0 至 9 中 10 个数中的任一个，因此具有这种特征的 3 位数共有：16.In h
37、ow many different ways can 3 people be assigned to fill 3 different positions so that each person is assigned to exactly one position?(A) Twelve (B) Nine(C) Six (D) Three(E) One（分数：5.00）A.B.C. D.E.解析：解析 把这三个职位固定为 1，2，3，然后求这三个人有多少种不同的排列来占取这三个位置，其排列数为17.On a recent trip, Cindy drove her car 290 miles,
38、 rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Cindys car got on this trip must have been between（分数：5.00）A.B.C.D. E.解析：解析 to the nearest 指四舍五入，根据四舍五入的定义，可知 C 开车的实际英里数应在 285 至295 英里之间，而使用的汽油加仑数应在 11.5 至 12.
39、5 加仑之间，所以 Cindy 每加仑汽油所行驶的英里数的范围应在最小英里数除以最大加仑数与最大英里数除以最小加仑数之间，即：18.Three stacks containing equal numbers of chips are to be made from 9 red chips, 7 blue chips，and 5 green chipsIf all of these chips are used and each stack contains at least 1 chip of each color, what is the maximum number of red chip
40、s in any one stack?(A) 7 (B) 6 (C) 5(D) 4 (E) 3（分数：5.00）A.B.C. D.E.解析：解析 因为筹码的总数为 9+7+5=21，所以每堆中有 7 个筹码；又因为每堆中至少有每种颜色的一个筹码，所以在任一堆中红色筹码最多为 5 个，蓝色筹码最多为 5 个，绿色筹码最多为 3 个。19.If 75 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the te
41、st correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?(A) 10% (B) 20% (C) 30%(D) 50% (E) 65%（分数：5.00）A.B.C.D. E.解析：解析 因为 20%的学生连一道题也没答对，所以至少答对两道题中的任一道题的比率为 80%，所以答对两道题的学生所占的百分比为：55%+75%-80%=50%20.If x and y are prime numbers, which of the foll
42、owing CANNOT be the sum of x and y?(A) 5 (B) 9 (C) 13(D) 16 (E) 23（分数：5.00）A.B.C.D.E. 解析：解析 此题应该采用排除法：5=2+3，9=7+2；13=11+2；16=3+13 最后发现只有 23 不能分解成两个质数的和。21.If n is a prime number greater than 3, what is the remainder when n2 is divided by 12?(A) 0(B) 1(C) 2(D) 3(E) 5（分数：5.00）A.B. C.D.E.解析：解析 考生在做该题时可
43、以用尝试法：任取一个大于 3 的质数去除以 12，发现任一大于 3 的质数平方后被 12 整除时，余数总为 1，例如 72=49，4912 得到商为 4，余数为 1。22.S is a set of integers such that i) if a is in S. then -a is in S, andii) if each of n and b is in S, then ab is in S. Is -4 in S?(1)1 is in S.(2)2 is in S.(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
44、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，因为根据 1 在 S 中，只能推出-1 也在 S 中，而得不到有关-4 的任何信息；(2)充分，根据 2 在 S 中，由 i)可推知-2 也在 S 中，再根据 ii)可知 2 与-2 的乘积-4 也在 S 中。23.LEAGUE RESULTS TeamNumber of Games Won A 4B 7C 9D 2E 2XAccording to the inco
45、mplete table above, if each of the 6 teams in the league played each of the other teams exactly twice and there were no ties, how many games did team X win? (Only 2 teams play in a game.)(A) 4 (B) 5 (C) 6 (D) 8 (E) 10（分数：5.00）A.B.C. D.E.解析：解析 该题也即让考生求该联盟所进行比赛的总次数，6 支队伍中任两支比赛两次，则共进行了24.If X and Y are
46、 sets of integers, XY denotes the set of integers that belong to set X or set Y, but not both. If X consists of 10 integers, Y consists of 18 integers，and 6 of the integers are in both X and Y, then XY consists of how many integers?(A) 6 (B) 16 (C) 22(D) 30 (E) 174（分数：5.00）A.B. C.D.E.解析：解析 根据题意可知 XY
47、 中的整数数目为：(10-6)+(18-6)=16。25.When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n?(A) 3 (B) 4(C) 7 (D) 8(E) 12（分数：5.00）A.B.C. D.E.解析：解析 根据题意可得 mn+(n-4)=10，其中 m 为正整数。把五个选项代入发现，只有当 n=7 时，m 取整数 1，其余几个值得出的 m 值均不为整数。26.If an integer n is divis
48、ible by both 6 and 8, then it must also be divisible by which of the following?(A) 10(B) 12(C) 14(D) 16(E) 18（分数：5.00）A.B. C.D.E.解析：解析 能被 6 整除，则该数一定能被 2 和 3 整除；能被 8 整除，则该数一定能被 2 和 4 整除；去掉相同的因子，则 n 一定能被 3 和 4 整除，而 3 和 4 是互质数，所以 n 一定能被 34=12 整除。27.If 10 persons meet at a reunion and each person shakes
49、 hands exactly once with each of the others, what is the total number of handshakes?(A) 10987654321(B) 1010(C) 109(D) 45(E) 36（分数：5.00）A.B.C.D. E.解析：解析 此题即为求从 10 个人中任取两人的所有不同取法，根据组合方法的知识，可知他们握手的次数为28.If 1d2, is the tenths digit of the decimal representation of d equal to 9?(1)d+0.012(2)d+0.052(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
