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x, y, z, and w are integers

x, y, z, and w are integers. The expression x-y-z is even and the
Expression y-z-w is odd. If x is even what must be true?

(A) y-z must be odd.
(B) w must be even.
(C) w must be odd.
(D) z must be even.
(E) Z must be odd

The best answer is C.
The first expression is even and the second is odd, the differences between the two expressions is x instead of w. (remember, there is no difference in odd/even numbers if the number is positive or negative so y-z is like z-y). Therefore if x is even w must be odd.

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