If \(a\) and \(b\) are positive integers such that \(a - b\) and \(\dfrac{a}{b}\) are both even integers, which of the following must be an odd integer?

A. \(\dfrac{a}2\)

B. \(\dfrac{b}2\)

C. \(\dfrac{a+b}2\)

D. \(\dfrac{a + 2}2\)

E. \(\dfrac{b+2}2\)

Answer: D

Source: GMAT Prep