请教俩道PREPMATH题～希望好心人帮助解答～跪谢～～

lingdangyour

1.   

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 3

(D) between 30 and 40

(E) greater than 40

2.  

38, 69, 22, 73, 31, 47, 13, 82

Which of the following numbers is greater than three-fourths of the numbers but less than one-fourth of the numbers in the list above?

 

 

(A) 56

(B) 68

(C) 69

(D) 71

(E) 73

 

 

第一题不会做，第二题竟然看不懂题目的意思。。。。

弱弱地向NN们请教。。。

弱弱地向NN们请教。。。

tulipmontrealer

第二题的意思是:答案中有哪个数字大于上列数字的3/4, 但是小于他们的1/4.

第一题是: h(100)+1与h(100)是连续的两个整数，那么的最大公约数为1，也就是说h(100)中有的因子，在h(100)+1中是没有的。那么我们只要分析h(100)就可以了。

h(100)=1*2*3***100把偶数都提取出来后，等于2^N（2*3*5*7***47）这里不管N的值是多少，括号里面的都是质因子，说明h(100)里包括了小于等于47的所有的质因子，那么h(100)+1就不可以包括这些了，也就是它的质因子一定大于47，所以选E。-----摘自FF

kenisjacque

First arrange the numbers in increasing order....
13 22 31 38 47 69 73 83
in all total 8 nos.
now the number which is greater than 3/4 of the total numbers mean and less than 1/4 of the total numbers.
that means the number has to be greater than 3/4= 6/8 meaning that 6 out of 8 numbers.

ANd the numnbers are 13 22 31 38 47 and 69

And less than 1/4= 2/8 meaning that  2 out of eight numbers.

The numbers are 73 and 83. only number that satisfies the condition is 71.

And hence D is the answer.

huangxiaoxiao

h(100)=1*2*3***100把偶数都提取出来后，等于2^N（2*3*5*7***47）这里不管N的值是多少，括号里面的都是质因子，说明h(100)里包括了小于等于47的所有的质因子，那么h(100)+1就不可以包括这些了，也就是它的质因子一定大于47，所以选E。-----摘自FF

好像解释错了吧， 不过思路是可以理解的。

lingdangyour

谢谢解答，发现自己的理解力很有问题，还没有找到ETS的出题方式。。。

还需要好好加油。。。。

现在正在做PREPMATH，很多很多问题啊，继续努力，不懂就问————

向NN们致谢，致敬！！

lingdangyour

小小的总结这2题，NN看看这样说对不？

第一题：

做不来的原因：没有弄懂质因子的概念，没有搞清相邻2个数的最大公约数是1，所以n有的n+1肯定没有，要算n+1,从n下手。

第二题：

greater than three-fourths of the numbers but less than one-fourth of the numbers:

这句理解为找出一个数大于这些数当中的四分之三，但是小于这些数当中的四分之一。

kenisjacque

Yes,

Actually, it is a tricky question. Some may make the following mistakes:

1. Greater than the sum of the three-fourth of the numbers.

2. Less than the sum of the one-fourth of the numbers.

Actually, in GMAT land to understand the trick is important.

Thanks.