Sufficiency of Two Statements Relating to Sum of Integers

Hard Data Sufficiency Determining Sufficiency

Let $x$ and $y$ be two integers. We want to determine whether $x + y$ equals 10.

Statement (1): $x - 2y = 4$.

Statement (2): $x + 3y = 15$.

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.

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