GMATprep question

[Carlo75]

For every even integer n, the function h(n) is defined to be the product of all the even integer from 2 to n, inclusive.

If p is the smallest prime factor of h(100) +1, the p is:

A) between 2 and 10
B) between 10 and 20
C) between 20 and 30
D) between 30 and 40
E) greter than 40

OA is E

please explanation

[aatech]

f(2) = 2

f(4) = 2*4

f(100) = 2*4*6..... *98*100 = 2(1*2*3*...50)
means all numbers from 1 to 50 is a factor of f(100).
in turn, means NO numbers from 1 to 50 will be factor of f(100)+1.

so, the smallest prime no that will be factor of f(100)+1 will be >50

Ans E suits that. So E

[egybs]

This is not correct:
f(100) = 2*4*6..... *98*100 = 2(1*2*3*...50)

It would be f(100) = 2*4*6..... *98*100 = 2^(100/2)(1*2*3*...50)

[aatech]

This is not correct:
f(100) = 2*4*6..... *98*100 = 2(1*2*3*...50)

It would be f(100) = 2*4*6..... *98*100 = 2^(100/2)(1*2*3*...50)

Totally Agree