If $p$ and $n$ are positive integers and $p > n,$ what is the remainder when $p^2 - n^2$ is divided by $15?$ - The Beat The GMAT Forum

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

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