x+y+z is even, is x*y*z even?

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.

Answer: E.