Determining if a Number is Prime

Very Hard Data Sufficiency Determining Sufficiency

Let $x$ be a positive integer. We want to determine whether $x$ is a prime number.

Statement (1): $x^2 - x - 6 = 0$

Statement (2): $x$ is an even number greater than 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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