simple integer ques......But still not getting.need Help????

[pardeep_10sharma]

If a and b are positive integers such that (a - b) and (a/b) are both even integers, which of the following must be an odd integer?
A. a/2
B. b/2
C. (a+b)/2
D. (a+2)/2
E. (b+2)/2

I am getting answer None of these but answer given at end is C.Plz confirm

[sanju09]

If a and b are positive integers such that (a - b) and (a/b) are both even integers, which of the following must be an odd integer?
A. a/2
B. b/2
C. (a+b)/2
D. (a+2)/2
E. (b+2)/2

I am getting answer None of these but answer given at end is C.Plz confirm

It's definite that both a and b are even positive integers such that a > b and a = k b, where k again is an even positive integer.

(A) a/2 must be an even positive integer for 2 being the smallest possibility for b.

(B) b/2 may or may not be an odd integer, take a = 48, b = 8 & a = 48, b = 6 for better understanding the contradiction.

(C) The same examples for a and b as taken in explanation (B) above disapprove this option as well.

(D) Remember, whenever a/2 is an even positive integer, (a + 2)/2 is always an odd integer.

(E) [spoiler]Are we on some picnic or something?

(C) cannot be the OA from my point of view, check it again or take away (D)[/spoiler]