Determine if the Ratio is Greater than Two

Hard Data Sufficiency Determining Sufficiency

Consider two numbers, $x$ and $y$, such that $x > 0$ and $y > 0$. We want to determine whether the ratio $\f\frac{x}{y}$ is greater than 2.

Statement (1): $x + y = 12$.

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

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 together are sufficient, but neither statement alone is sufficient.

Statements (1) and (2) together are not sufficient.

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% Correct93%