Consider two statements
If X is an integer and $X=2p+1$ where p is not an integer.
If Y is an integer and $Y=2q$ where q is not an integer

Which of the following correctly specifies the Even/Odd nature of X and Y respectively

I think the trick is that for Y, if q is not an integer, Y=2q could be even? Wait, no. If Y is even, then Y=2k for integer k, so q=k, which is integer. Contradiction. So Y cannot be even. So Y must be odd. Similarly for X, if p is not integer, 2p is even, so X is odd. So both odd. But the answer is C? That's weird. Maybe I'm missing something. Can someone clarify?

This is a good one. The key is to realize that if Y=2q and Y is integer, then q must be either integer or half-integer. But q is not integer, so q is half-integer, making Y odd. For X, if p is not integer, 2p is even, so X is odd. So both odd. But the answer is C? That's odd. Maybe the question meant 'p is an integer'? If p is integer, then 2p is even, X odd. If q is not integer, Y odd. Still both odd. Hmm. I think the answer should be B, but the site says C. I'll go with the site's answer for practice, but I'm skeptical.