Bunuel wrote:

If x > 1, is positive integer b a factor of positive integer a?

(1) \(x^{(a + b)} = x^{(ab)}\)

(2) \(x^{(\frac{a}{b})} = x^{(\frac{a}{2})}\)

The question stem implies that whether \(a=b*Integer\)

Statement 1: this implies \(ab=a+b\) or \(ab-b=a\)

Hence \(a=b*(a-1)= b*Integer\) as \(a\) & \(b\) are integers, hence \(a\) is a multiple of \(b\) or \(b\) is a factor of \(a\).

SufficientStatement 2: implies \(\frac{a}{b}=\frac{a}{2}\) or \(b =2\). But we cannot find the value of \(a\). Hence

InsufficientOption

A