If w and t are integers and w^2 – t^2 is an odd integer, which of the following must be an even integer?
I. w + t + 2
II. w^2 + 2wt + t^2
III. w^2 + t^2	Select the correct option
A) None B) I only C) II only D) III only E) I, II, and III
w^2–t^2 is an odd integer means that either w is even and t is odd or w is odd and t is even.   Check all options:   I. w + t + 2 --&gt; even+odd+even=odd or odd+even+even=odd. Discard;   II. w^2 + 2wt + t^2 --&gt; even+even+odd=odd or odd+even+even=odd. Discard;   III. w^2 + t^2 --&gt; even+odd=odd or odd+even=odd. Discard.   Nonenswer: None.
<result>A</result>
If w and t are integers and w^2 – t^2 is an odd integer, which of the following must be an even integer?
I. w + t + 2
II. w^2 + 2wt + t^2
III. w^2 + t^2