Statement 1 can't be sufficient, because it gives no information about q.
Addition and subtraction obey identical even/odd rules (because subtracting
is addition, you're just adding a negative) so any time a-b is even, so is a+b, and vice versa, and Statement 2 is instantly sufficient to give a 'no' answer to the question, so the answer is B.
I should add that the above is true only if a and b are integers, but that's always going to be the case in a GMAT even/odd problem.
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