Is x^2 - y^2 even?

(1) x+y is odd
(2) x-y is odd

The OA is C

I figured it as D. Could someone pls help?

My reasoning was,

=> x^2 - y^2 = even?
=> (x+y) (x-y) = even?
=> If we can prove either x+y to be even or both (x+y)and (x-y) to be odd, we can get the ans.

(1) X+Y is odd: My assumption here is X and Y are either Integers or decimals because fraction can't be odd or even.
The sum of two decimals or integers will be odd only if one is even and the other one is odd. Hence, either X or Y is odd and the other is even. Similarly, the difference between an odd number and an even number will always be odd.
=> (odd) (odd) = odd
Hence sufficient.


(2) x-y is odd. My assumption here again is X and Y can either be Integers or decimals because fraction can't be odd or even. The difference between two integers or decimals will be odd only if one is odd and the other is even. Hence, either x or y is odd while the other is even. Similarly, the sum of one odd number and one even number will always be odd.
=> (Odd) (Odd) = (odd) - sufficient.

Hence, D.

Am i missing something here? Though i believe GMAT would never test the same logic in both the statements.

Thanks in advance!