How many prime factors does the number X have?

Statement 1

If X is divisible by 53, then X could just be '53' (in which case only 1 prime factor, 53) or X could be '53*2 = 106' (in which case 2 prime factors, 2 and 53).
So we cannot be sure about the number of prime factors of X. Not Sufficient.


Statement 2

X is divisible by 4 distinct integers, this means X has total 4 factors. Now any number having 4 factors in total, could have two kinds of prime factorisation:

a) X = p^3. So X could be cube of a prime number. In this case X will have total 4 factors, but only 1 prime factor (p).
b) X = p1 * p2. So X could be a product of two distinct prime numbers. In this case also X will have total 4 factors, but there are 2 prime factors (p1 and p2).

So we cannot be sure about number of prime factors of X. Not Sufficient.


Combining the statements, we know X is divisible by 53 and X has 4 total factors.

So if X looks like p^3, then X = 53^3. In this case X has only 1 prime factor 53.
But if X looks like p1 * p2, then X = 53*p2 (product of 53 with any other prime number). In this case X has 2 prime factors 53 and p2.

So we still cannot be sure, as there are two possibilities. Not Sufficient.


Hence E answer