japped187 wrote:

Does the integer k have a factor p such that 1 < p < k?

(1) k > 4!

(2) 13! + 2 <=(less than or equal to) k <= 13! + 13

Please explain the steps you take!

I'd say B

The question ask whether K is prime number or not

1) is not sufficient. k>24 says nothing. i.e. if k=31 then answer is "no" but if k=25 then answer is "yes"

2) integers from 13!+2 to 13!+13, inclusive, are all non-prime numbers.

To illustrate

13!+2 = 1*2*3*...*13 +2 ->> this is divisible by 2

13!+3 = 1*2*3*...*13 +3 ->> this is divisible by 3

13!+13 = 1*2*2*...*13 +13 ->> this is divisible by 13

Thus, 2) only is sufficient