SAT Math Multiple Choice Practice Question 104: Answer and Explanation
16. Given that x and y are positive integers, and that (xy) - (x + y) is even, which of the following must be true?
A. Both x and y must be even.
B. Both x and y must be odd.
C. Either x or y must be even.
D. Either x or y must be odd.
E. One of the two numbers must be even, and the other one must be odd.
Correct Answer: A
A. You can do this one by picking numbers, but you can also reason it out: If both numbers are odd, then xy is odd, but x + y is even, so (xy) - (x + y) is odd. But if one is even and one is odd, then the opposite happens, so the result is still odd. Only if both numbers are even will the result be even.