What should be the best answer and the explanation?

[Chelseaer]

If x and y are both integers, and x/y is not an integer, then which of the following statements must be true?

A. x is odd and y is even
B. x is odd and y is odd
C. x is even and y is odd
D. x < y
E. None of the above

[Ian Stewart]

That is not a real GMAT question, because you don't see answers like "none of the above" on the GMAT to questions like this. But that is the right answer here -- there is no way to decide which of the two unknowns is even or odd (x/y might be 8/5 or 9/5 or 8/6 or 9/6), and as all of those examples illustrate, x can be greater than y, leaving only answer E.