Divisibility of n by Prime p

Very Hard Data Sufficiency Determining Sufficiency

Let $p$ be a prime number and $n$ be a positive integer. We want to determine if $n$ is divisible by $p$.

Statement (1): The product $np$ is even.

Statement (2): The sum $n + p$ is greater than $p$.

Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Both statements (1) and (2) together are sufficient, but neither statement alone is sufficient.

Each statement alone is sufficient.

Statements (1) and (2) together are not sufficient.

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