The only way the Sum/difference can be odd is if E + O = O or E - O = O

sincs E^2 = E and O^2 = O

Choice 1: E + O = O; So this rules out the first possibility

Choice 2: E + E (2 times any number is E) + O = O; So this rules out the second possibility

Choice 3: E + O = O; Same as the first choice so this rules out the third possibility as well.

So the answer left is (A)

Plug in k=3 and t=2

both k and t are integers and both satisfy the condition

k^2 -t^2 = 9 - 4 = 5(odd integer)

So we find that none of the conditions are full-filled.

So answer none.