Data Sufficiency: Analyzing Information with Integer Equations

Very Hard Data Sufficiency Analyzing Information

Let $x$ and $y$ be two positive integers. We want to determine whether the value of the expression $x^2 + y^2$ is greater than 50.

Statement (1): $x + y = 10$.

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

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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% Correct77%