Sufficiency of Two Statements Involving Integer Equations

Medium Data Sufficiency Determining Sufficiency

Let $x$ and $y$ be integers. We want to determine if $x + y = 10$.

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

Statement (2): $2x + y = 22$.

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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