Bunuel wrote

**Quote:**

If positive integers x and y are not both odd, which of the following must be even?

(A) xy

(B) x + y

(C) x - y

(D) x + y -1

(E) 2(x + y) - 1

I took a mostly similar approach, but also tested values, which often help me to track on even and odd rules.

If x and y are not both odd:

O O is NOT a possibility - list the possibilities that ARE allowed

E E okay.

E O, or O E, okay.

So 1) x and y are both even; or 2) one is odd and the other is even.

And: What if x and y ARE both odd?

Property often tested:

only odd * odd = odd. Just one even factor means product is even.

Here we have at least one even factor and possibly two. E x O = E, E x E = E. Answer A jumped out.

Decided to test values to be sure. Eliminated three choices with x=4, y=3

(A) xy: 4 x 3 =12. Even. Because I think this is the answer, I try the other possibility: both x and y are even. If x=4 and y=2, xy=8. Both answers, even. KEEP

(B) (x+y): 4 + 3 = 7. Odd. Eliminate.

(C) (x-y): 4-3=1. Odd. Eliminate.

(D) (x+ y-1): 4+3-1=6, even.

Keep for the moment. I want to see whether or not I can eliminate E before I pick new numbers.

(E) 2(x+y)-1: 3+4=7, 2(7) - 1 = 13. Odd. Eliminate.

Left with A and D, but haven't tried different variables for D. Use different numbers, both even. If x=4 and y=2, 4+2-1=5. Odd. Eliminate. Answer A