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If \(n=x^5\cdot y^7,\) 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.
[spoiler]OA=C[/spoiler]
Source: GMAT Club Tests
(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.
[spoiler]OA=C[/spoiler]
Source: GMAT Club Tests
