You missed smth here:
"If x and y are nonzero integers, is an integer?"
Is who an integer? I'll assume it's x/y. Don't consider my explanation if this is not the case.
1. if x is the product of 2 and some other integer, this makes x even. But since we do not know anything about y, then we can't tell if x/y is an integer.
2. actually leads us to believe that y is prime, since only prime numbers have exactly one pair of positive divisors, 1 and the number itself. Since we don't have any more info about x, then we can't solve this one.

Taking both equations together won't help, so my guess is E.