For every even integer 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) above 40



the number p is (2)(4)(6)(8)(10)...(98)(100) + 1.
take a look at the left-hand term of that expression (the one that contains everything except the 'plus one' part). note that ALL numbers from 1 through 50 are factors of this term:
1 is a factor, because 2 appears
2 is a factor, because 4 appears
3 is a factor, because 6 appears
4 is a factor, because 8 appears
etc.

...but, if all those numbers are factors of the left-hand term, then NONE of them (except 1) can be factors of the whole expression, because none of them goes into 1.

this means that no number between 2 and 50 (whether prime or not) can be a factor of p.

so the answer is E.