Determining x squared plus y squared

Very Hard Data Sufficiency Analyzing Information

Let $x$ and $y$ be two distinct positive integers. We need to determine whether we can find the value of $x^2 + y^2$ based on the following statements:

Statement (1): The sum of $x$ and $y$ is equal to 10.

Statement (2): The product of $x$ and $y$ is equal to 24.

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.

Hint

Submitted9.5K

Correct7.8K

% Correct82%