请教两道prep数学题，请高人指教！

ashleyker

1、for every  positive even number 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
(1) between 2 and 10   (2) between 10 and 20   (3) between 20 and 30     (4) between 30 and 40    (5) greater than 40    

the answer is (5)

2、if n is a multiple of 5 and n=(p^2) *q, where p and q are prime number, which of the following must be a multiple of 25?
(1) p^2   (2) q^2   (3) p*q   (4) (p^2)*(q^2)   (5)  (p^3)*q

the answer is (4)

ashleyker

自己顶一下，请教高人！

faintfroggie

1. h(100) is multiple of all the prime number <100. So if a prime number is a factor of h(100)+1, then this prime number has to be greater than 100.
2. n is a multiple of 5, so either P or Q has to be 5. Thus, P^2 and q^2 guarantee that it's a multiple of 25.