Concept: The question tests on advanced applications of Inequalities

If integer k has a factor p such that 1<p<k, then the integer is composite. If it doesn’t, then k is prime.
We can therefore rephrase the question as “Is k prime?”

From statement I alone, k > 4! i.e. k > 24.

This is not sufficient to find out if k is prime, because k could be any integer value greater than 24.
Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II alone, 13! + 2 ≤ k ≤ 13! + 13.

It’s important to note that 13! will be divisible by all integers from 1 to 13. Therefore, regardless of the value of k, k will be divisible by at least one more integer other than 1 and itself.

k is NOT prime.
Statement II alone is sufficient to answer the question with a YES. Answer options C and E can be eliminated,

 The correct answer option is B.