We can see that statements (1) and (2) alone do not provide sufficient information since each statement provides no information about one of the variables.
However, if you add statements (1) and (2) we get (x+z)+(y+z) = x+y+2z
Since (x+z) is even and (y+z) is even, their sum (x+y+2z) must also be even.
Hence C
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