The answers are D and E.

Since a-b = even and a/b = even, then both a and b are positive even integers.

We can rewrite D as a/2 + 2/2. a/2 will always be even, 2/2 = 1. Even+1 = Odd.

The same for E

\(a-b\) 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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How is E wrong?
if a = 4, b = 2

then b--> 2+2/2 = 2 which is even?
Please explain what is wrong here?

what if a=12 and b=4?
then a/b will not be even. plz explain. thanks in advance