Divisibility and Remainders with Positive Integer

Hard Problem Solving Arithmetic

Let $n$ be a positive integer. We are interested in finding the remainder when $n$ is divided by 5.

Statement (1): $n + 3$ is a multiple of 10.

Statement (2): $3n$ is an even integer.

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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