The function \(f(n)\) is given by the number of factors of \(n.\) If \(p\) and \(q\) are positive integers and \(f(pq)\)

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The function \(f(n)\) is given by the number of factors of \(n.\) If \(p\) and \(q\) are positive integers and \(f(pq) = 4,\) what is the value of \(p?\)

(1) \(p + q\) is an odd integer.

(2) \(q\) is less than \(p.\)

Answer: E

Source: Manhattan GMAT