meanjonathan wrote:Fairly straightforward problem...

If x and y are integers, is xy even?

1) x=y+1
2) x/y is an even integer.

Answer guide says D.

How does statement 1) eliminate the possibility of x or y being 0? For instance, y=0, x=0+1, 0*1=0; non-even... or y=-1, x=0, -1*0=0

What am I missing?

Note that 0 is an even integer.

Question: Is xy an even integer?

(1) x = y + 1
If y = 0, then x = 1 and xy = 0, which is an even integer.
If y = 1, then x = 2 and xy = (2)(1) = 2, which is an even integer.
If y = 2, then x = 3 and xy = (2)(3) = 6, which is an even integer.
In general, if y = even, x = even + 1 = odd, and xy = odd * even = even
If y = odd, x = odd + 1 = even and xy = even * odd = even; SUFFICIENT.

(2) x/y is an even integer implies both x and y are even integers. Hence xy will also be an even integer; SUFFICIENT.

The correct answer is D.

Hope that helps.