Here it goes

From the statement we know either ( xy - odd, z - even ) or (xy even, z - odd)

a) One says : xy + xz = even.

Doesnt help, coz it could be xy and xz are both even, or are both odd

b) y + xz - odd : Doesnt help because, either y is odd and x is even or x is odd and y is even

combining both of them ( lets add the two of them up )

2(xy) + y(x+1 ) is odd ( odd + even = odd )

2xy is most definetly even, so Y(x+1) is most definetly odd [ since the only way we get an odd sum is o+e or e+o - all other combinations give an even sum)

so Y(x+1) = odd - now, the only way we get an odd product is odd X odd so X+1 = odd therefore X = even

QED

Anyone with a better method? I know mine is wayy to long to sit and do in the Gmat

Also, is there a shortcut for doing such problems ( i constantly find my self writing O+E = O and so on... then find the possible results - consumes a hell lot of time )