请教MATH PREP

lynn_lin · 发表于 2012-4-27 15:37:06

PREP1 --7
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
不知道怎么做？

43 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

我是用最笨的办法列出所有组合，很费时间，请高人指教算法。

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

我是用最笨的办法列出所有组合，很费时间，请高人指教算法。

a8455462 · 发表于 2012-4-27 15:59:49

第一个

H(100)=2*4*....*100+1 = 2*(1*2*3*..*50) +1=2*(50!)+1

2*(50!)+1 这个数显然是不能被1-50的数字整除的，所以p肯定大于50 也就是大于40，选E

第二个

(8*6*4)/A33

lynn_lin · 发表于 2012-4-27 23:38:05

谢谢 a8455462，虽然觉得第一题也不能被50以上的数整除，但看起来答案中就E最靠谱。

请教MATH PREP

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