P Value

[Ashetty]

For every positive 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, 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

Ans: E

[cans]

h(n)=2*4*6...*n
h(100)+ 1=2*4*6*8*...100 = 2^50(1*2*3*..*50) +1
p is prime factor and thus p divides h(100)+1.
thus p>50..
IMO E