For every positive interger n, the function h(n) is defined to be the product of all 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
GMAT Quantitative Question
2008-09-11 8:01 pm
回答 (2)
2008-09-11 9:14 pm
✔ 最佳答案
The answer is e.
h(100) = 2 4 6 8 ........ 98 100
h(100) = 2 x (1 2 3 4 ........ 49 50)
h(100) is a multiple of 2, 3, 4, 5 ........ , 49, 50.
h(100) + 1 is not a multiple of 2, 3, 4, 5 ........ , 49, 50.
Hence, the smallest factor (no matter whether it is prime or not) of h(100) + 1 must be greater than 50. Thus, e is the best answer.
=
2008-09-11 9:27 pm
h(n)=2x4x6x..xn (total n/2 terms)
h(n)=(2^n/2)(1x2x3..x(n/2))
h(100)+1 = (2^50)(1x2x3x..x50)+1
so if there is a prime factor for this expression, this prime factor has to be greated than 50. It is because if it is less than 50, it is a factor of the first term on the right hand side but not the second term (ie. 1).
So the answer is (e)
h(n)=(2^n/2)(1x2x3..x(n/2))
h(100)+1 = (2^50)(1x2x3x..x50)+1
so if there is a prime factor for this expression, this prime factor has to be greated than 50. It is because if it is less than 50, it is a factor of the first term on the right hand side but not the second term (ie. 1).
So the answer is (e)
收錄日期: 2021-04-23 23:06:45
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080911000051KK00439