Data Sufficiency

With questions such as these, it is best to start by asking ourselves this important question: What do I need? We need to know whether x is even, so if we knew that x is an even number times some other number that would be enough information. Similarly, if we knew that x was a multiple of two odd numbers, then we would know for sure that x was not even. Either case would do.

Statement 1: We can rearrange this statement to read: x = y^5 - y, which can be phrased as x = y(y^4 - 1). Accordingly, if y is even, then x is definitely even. What if y is odd? Then y^4 will be odd, and y^4-1 will be even. So either way, we know that x must be even. Sufficient. Our answer choices are either A or D.
Statement 2: We can rearrange this statement to read: x = 3y-y. We can rephrase that as x = y(3-1). Since 3-1 is 2, we know that y is a multiple of 2 and thus is even.

Accordingly, the best answer is (D)