Determining If an Integer is Even

Very Hard Problem Solving Arithmetic

Let $x$ be an integer. We want to know if $x$ is even.

Statement (1): $x^2$ is even.

Statement (2): $x + 3$ is odd.

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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