\(a-b\) 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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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

Yeah, I too got same doubt,Just posted the question with same answer as in material.

Actually, @Carcass solution is the correct one. I did not consider if b=2. That is a mistake

How is E wrong?
if a = 4, b = 2

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

a must be greater than 2 in a way a/b is even.
b can be 2 also in which case b+2/2 is NOT odd

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

Here in the question it is give a/b is even and a-b is even.
So both a and b should be even and also 'a' can be only multiple of 4.
'b' can be only those numbers where the ratio remains even.
so if you consider a=12, b can be = 2, 6 only.