Bunuel wrote:
Official Solution:
If \(x\) and \(y\) are even integers, which of the following must also be an even integer?
A. \(x^y\)
B. \(2\frac{x}{y}\)
C. \(\frac{x - y}{x + y}\)
D. \(\frac{x^2 - y^2}{2}\)
E. \((x + 1)(y - 1)\)
\(\frac{x^2 - y^2}{2} = \frac{(x - y)(x + y)}{2} = \frac{even*even}{2} = even*integer = even\).
\(x^y\) is 1 if \(y = 0\) and \(x\) is positive.
\(2*\frac{x}{y}\) is 1 if \(x = 2\) and \(y = 4\).
\(\frac{x - y}{x + y}\) might not be an integer at all.
\((x + 1)(y - 1)\) is always odd.
Answer: D
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