If \(n=x^5y^7,\) where \(x\) and \(y\) are positive integers greater than \(1,\) then how many positive divisors

[VJesus12]

If \(n=x^5y^7,\) where \(x\) and \(y\) are positive integers greater than \(1,\) then how many positive divisors does \(n\) have?

(1) \(x\) does not have a factor \(p\) such that \(1<p<x\) and \(y\) does not have a factor \(q\) such that \(1<q<y.\)

(2) \(n\) has only two prime factors.

Answer: C

Source: GMAT Club Tests