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If x+y+z is even, & xyz are integers then in any case xyz will also be even. But the question has given us two options, hence assuming that x,y & z are not integers or not all integers. e.g x=3.5 y=4.5 z=2 or vice versa.

Given condition -> x+y+z = even, so only two possibles either 2 of them are odd and one is even, or all three are even

Stmt 1 - considering both the possibilities, if x*y is even means withe x can be odd or y can be even or vice versa, or both can be even. Now if z is odd or even, the result will be an even integer. SUFFICIENT

Stmt 2 - y*z is odd, means both should be odd. That means x is even (to satisfy given condition). the result will be an even integer. SUFFICIENT

x+y+z is even, is x*y*z even? 1) x*y even 2) y*z odd

How does one answer if the variables are not specified as integers? Does gmat try to sneak in this kind of question? thanks! P/S : I don't know the OA

Note that we are not told that x, y, and z are integrs.

Given: x+y+z=even. Question: xyz=even?

(1) xy=even --> if x=\frac{4}{5}, y=5 and z=\frac{1}{5} (xy=even=4, x+y+z=6=even), then the answer would be NO as xyz=\frac{4}{5}\neq{integer} but if x=0 and y+z=any \ odd+any \ odd=some \ even, then the answer would be YES. Not sufficient.

(2) yz=odd --> again if x=\frac{4}{5}, y=5 and z=\frac{1}{5} (yz=odd=1, x+y+z=6=even), then the answer would be NO as xyz=\frac{4}{5}\neq{integer} but if x=0 and y+z=any \ odd+any \ odd=some \ even, then the answer would be YES. Not sufficient.

(1)+(2) the same here: if x=\frac{4}{5}, y=5 and z=\frac{1}{5}, then the answer would be NO as xyz=\frac{4}{5}\neq{integer} but if x=0 and y+z=any \ odd+any \ odd=some \ even, then the answer would be YES. Not sufficient.

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