Divisibility of x by 3

Very Hard Problem Solving Arithmetic

Let $x$ and $y$ represent two positive integers. We want to determine whether $x$ is divisible by $3$.

Statement (1): The sum $x + y$ is a multiple of $6$.

Statement (2): The product $xy$ is a multiple of $15$.

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.

Submitted3.2K

Correct2.4K

% Correct73%