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