Even Integer

[karthikpandian19]

For every positive even integer n, the function h(n) is defined as 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

between 2 and 10
between 10 and 20
between 20 and 30
between 30 and 40
greater than 40

[GMATGuruNY]

I posted an explanation here:

https://www.beatthegmat.com/tough-prime- ... 25475.html

[Anurag@Gurome]

For every positive even integer n, the function h(n) is defined as 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

between 2 and 10
between 10 and 20
between 20 and 30
between 30 and 40
greater than 40

h(100) = 2 * 4 * 6 * ... * 100
= (2 * 1) * (2 * 2) * (2 * 3) * ... * (2 * 50)
= 2^(50) * (1 * 2 * 3 ... * 50)
Then h(100) + 1 = 2^(50) * (1 * 2 * 3 ... * 50) + 1
Now, h(100) + 1 cannot have any prime factors 50 or below, because dividing this value by any of these prime numbers will give a remainder of 1.

The correct answer is E.