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