IMO A.

Stmt1: I can't think of a number n that has (n+1) factors. There can be only 2 factors for a prime number, 1 & itself. Since we can answer this question by saying NO, this statement is sufficient.

Stmt2: (n+1) is not a prime number can be true with n is either a prime or a composite number, i.e. when n=3, (n+1)=4, but when n=8, (n+1)=9. So, this statement is not sufficient.

n is prime can be (1, 2, 3, 5, 7, 11, 13, ... etc)

1) number of factors of n is n+1
if they are asking about distinct prime factors then none of the above choices can fit the n+1 criteria --> suff
if they are asking about ALL factors then 1 can have 1 and itselft (so 1) hence 2 factors = n+1 --> insuff

2) n+1 is not prime
there are several n+1 is not prime options, ie 3, 5, 7, 11, 13 -->insuff

so answer (assuming they are asking for distinct factors) is A otherwise it's C

a friend of mine asked me this question to me.....
and the OA he told me is A

I believe that it is A for what Ian said.

In order for a number to be prime, it can only have two factors, n and 1.

If the number of factors of n is n+1, then n can NOT be prime. This is because the only number that satisfies N having 2 factors is 1, which is not prime.

2.) is obviously insufficient.

But, this is a bad question because the question is technically saying that "1" has two factors.

As usual, Ian is all-knowing.