数学题汇总
For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is
(A) between 2 and 10
(B) between 10 and 20
(C) between 20 and 30
(D) between 30 and 40
(E) greater than 40
是这样的：
h(100) = 2*4*6*8*...*100
h(100) = 2^50*(1*2*3*...*50)
而两个连续自然数的质因子是完全不同的（可验证），所以h(n)+1和h(n）的质因子肯定不一样。而h也就是说50以下的数都是h(100)的因子，即h(100)+1的质因子都大于50。
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The integers m and p are such that 2<m<p and m is not a factor of p. If r is the remainder when p is divided by m, is r > 1 ?
1. the greatest common factor of m and p is 2
2. the least common multiple of m and p is 30
A. 注意最小公倍数是30, 则3和10, 或者6和10都可以
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A committee of three people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
(A) 16
(B) 24
(C) 26
(D) 30
(E) 32
首先从4对couples中选三对。再从三对中任选。2^3. C3/4*8=32
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At a dinner party, 5 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?
(A) 5
(B) 10
(C) 24
(D) 32
(E) 120
圆圈排列解法，参考Feifei数学，第一部分第几题记不清了~~
本来5个人，排列为P5/5，现在为N-1=4，所以排列为P4/4=24
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If m is a positive odd integer between 2 and 30, then m is divisible by how many different positive prime numbers?
(1) m is not divisible by 3
(2) m is not divisible by 5
细心细心再细心....
answer:A
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A school administrator will assign each student in a group of n students to on e of m classrooms. If 3<m<13<n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the the smae number of students assinged to it?
(1) It is possible to assign each of 3n students to one of m classroom s so that each classroom has the same number of students assigned to it.
(2) It is possible to assign each of 13n students to one of m classroom s so that each classroom has the same number of students assigned to it.
细心细心再细心....
题目问n/m是否为整数。
条件A，3n/m为整数，3<m<13<n。该条件不能推出n/m为整数，所以条件不充分。
条件B，13n/m为整数，3<m<13<n。该条件可以推出n/m为整数，所以条件充分。
Key:B
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If the probability is 0.54 that Stock A will increase in value during the next month and the probability is 0.68 that Stock B will increase in value during the next month, what is the greatest possible value for the probability that neither of these two events will occur?
这题好难阿。考试题真有这么难吗 5555555555
我找到解释了。题目问的是the greatest possible value。这就得考虑AB俩个事件是否独立？
看图,
Key:0.32 
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Six card numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 8, what is the probability that one of the two cards drawn is number 5?
To get a sum of 8 可能出现的情况为
(5,3),(3,5)(4,4)(2,6)(6,2)
总共5种情况，有2种包含了数字5
Key: 2/5
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If there are more than two numbers in certain list, is each of the numbers in the list equal to 0?
1) The product of any two numbers in the list equal to 0.
2) The sum of any two numbers in the list equal to 0.
细心,,,!
Answer: B
[此贴子已经被作者于2008-10-22 13:22:04编辑过] | 
