\(a-b\) even --> either both even
or both odd
\(\frac{a}{b}\) even --> either both even
or \(a\) is even and \(b\) is odd.
As both statements are true --> \(a\) and \(b\) must be even.
As \(\frac{a}{b}\) is an
even integer --> \(a\) must be multiple of 4.
Options A is always even.
Options B can be even or odd.
Options C can be even or odd.
Options D: \(\frac{a+2}{2}=\frac{a}{2}+1\), as \(a\) is multiple of \(4\), \(\frac{a}{2}\) is even integer --> even+1=odd. Hence option D is always odd.
Options E can be even, odd.
Answer: D.
Hope this helps. The answer is one and only.
Regards
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