GMAT Prep - Functions Question - Weird

tutonaranjo

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

The answer is E.
I can't even begin to tell you how little I understand this question. Really appreciatte a detailed explanation from someone who gets this.

keepsmilinyaar · Posted: Sat Sep 01, 2007 12:00 pm Post subject:

I couldnt get the answer so searched online for it.

Credit goes to dumbJOE if dats his real name:

Explanation:
h(n) = 2 * 2x2 * 2x3 * 2x4 * 2x5 * 2x6 * 2x7 * ....................................
so if n is an even number, all numbers from 1 to n/2 are factors of h(n). This implies that for n=100. 1 to 50 are factors, the last prime number is 47 here. hence if we add 1 to h(n) we cannot get a factor among 1 to 50 for sure, because since h(n) was a multiple of each one of them individually, you need to add atleast the factor itself to get yet another multiple. Since the smallest prime number is 2, this requisite minimum accretion comes to 2.