Official Solution: For the sum of \(x\) and \(y\) to be even, the two variables must both be even or both be odd.

Statement (1): INSUFFICIENT. We know that at least one of the variables is even, but we do not know whether they are both even.

Statement (2): INSUFFICIENT. We know that \(x = y \times \text{(some even integer)}\). Since an even integer multiplied by any other integer is also even, we know that \(x\) is even. However, we do not know whether \(y\) is even.

Statements (1) & (2): INSUFFICIENT. Using both statements, we only know that \(x\) is even. Meanwhile, y could be even, but it does not have to be. As a result, we cannot determine whether the sum of \(x\) and \(y\) is even or odd. All of these results can be confirmed by picking numbers.

Answer: E

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