GMAT模拟考试数学问题，

EZZG

遇到数学模拟考试， 求大侠解释一下为什么

先感谢

For every positive intger n, the function of h(n) is defined to be the product of all the even integer from 2 to n, inclusive. If p is the smallest factor of h(100), then p is answer: >40

the number 75 can be written as sum of square of 3 different positive integers, what is the sum of these 3 integers. --> 13? why???

if n is a positive ineger and r is the remainder when (n-1)(n+1) is divided by 24, what is the value of r
1) n is not divisible by 2
2) n is not divisible by 3
answer is C? why

For any positive integer, n, the length of n is defined as number of prime factors whose product is n. For example, the length of 75 is 3 = 3 x 5 x 5 How many two digit positive integers have length of 6??
answer two. But why

Dayamadamide

第一题原题是问h(100)+1最小的质因子是多少。可以参考这个链接，解释的很清楚。https://www.manhattanprep.com/gmat/forums/for-every-positive-even-integer-n-the-function-h-n-t1152.html

第二题，75=49+25+1，所以7+5+1=12

第三题，如果n不被2整除，那么n-1和n+1一定一个被2整除，一个被4整除；如果n不被三整除，那么n-1和n+1一定其中一个被三整除。所以两个条件加起来，(n-1)(n+1)至少有三个因子，2，4，8。三个因子相乘就是24，所以r=0

第四题，我的话，就试一试找找规律。
最小的length是6的数是2^6，也就是64；（满足要求）
然后把其中一个2换成3，2^5*3得96；（满足要求）
再换一个3，2^4*3^2大于100；
如果把一个2换成5，2^5*5大于100；
其他的数（7以上的一定更大，不会满足两位数的要求）

pause

你第一个题写错了，如果按照你这个题干，那最小factor就是2了，原题是这样的：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? 这个还用解释么。。。应该就很容易选了吧。。。

EZZG

Dayamadamide 发表于 2016-6-13 11:25
第一题原题是问h(100)+1最小的质因子是多少。可以参考这个链接，解释的很清楚。https://www.manhattanprep. ...

感谢大侠指点，祝大侠杀G成功

Dayamadamide

EZZG 发表于 2016-6-13 11:39
感谢大侠指点，祝大侠杀G成功

大家一起加油