If positive integers x and y are NOT both odd, which of the following must be even?

A. xy

B. x + y

C. x - y

D. x + y - 1

E. 2(x + y) - 1

My Effort:

I decided to experiment by letting x be 3 and y be 2.

Doing this quickly revealed the fact that choice A and D both

yield an even number. The book's answer is A.

Question:

Why is choice D not the answer?