Determine Parity of x + 2y

Very Hard Problem Solving Algebra

Let x and y be two integers. We need to determine if the expression x + 2y is even.

Statement (1): x - y = 5

Statement (2): y = 2k, where k 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 (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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