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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?
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- Sum or difference of an even and odd entity is always ODD. So,
(X-Y-Z)-(Y-Z-W)=X-2Y+W is odd.
(X-Y-Z)+(Y-Z-W)=X-2Z-W is odd.
Now x is even means its of the form x=2k. Thus,
2(k-Y)+W is odd means W IS ODD.
2(k-Z)-W is odd means W IS ODD.
Ans: W is always ODD.
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