The ways a - b can be even is that either both a, b are even or both of them are odd.
The ways a / b can be even is that a, b are even (also considering above that both numbers are either even or odd, as odd/odd cannot result in even so both numbers should be even)
Now we know both numbers are even, so question is which of following must be odd.
a/2 No as a can be multiple of 4 as well.
b/2 No as b can be multiple of 4 as well.
(a+b)/2 No as both a and b can be multiple of 4 as well.
(a+2)/2 = a/2 + 1 As a is even number a/2 may or may not be even.
(b+2)/2 = b/2 + 1 As b is even number b/2 may or may not be even.
So there is no clear cut answer. If at all I will choose between D, & E. By picking some numbers.
I agree this problem isnt clear.
Essentially simplifying for D and E we have D: A/2+1 E: b/2+1