Determining Sum Parity of Integers

Very Hard Data Sufficiency Determining Sufficiency

Let $a$ and $b$ be integers. We want to determine if $a + b$ is even.

Statement (1): $a^2 - b^2$ is even.

Statement (2): $2a + 2b$ is an integer.

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.

Each statement alone is sufficient.

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