Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
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•(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.
The correct answer is E: Even taken together, the statements are not sufficient to answer the question.