If \(p\) and \(n\) are positive integers and \(p > n,\) what is the remainder when \(p^2 - n^2\) is divided by \(15?\)

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If \(p\) and \(n\) are positive integers and \(p > n,\) what is the remainder when \(p^2 - n^2\) is divided by \(15?\)

(1) The remainder when \(p + n\) is divided by \(5\) is \(1.\)
(2) The remainder when \(p - n\) is divided by \(3\) is \(1.\)

Answer: E

Source: GMAT Prep