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? Choose the correct choice from the following choices
A) a/2 B) b/2 C) (a+b)/2 D) (a+2)/2 E) (b+2)/2
a−ba−b even --&gt; either both even or both odd   abab even --&gt; either both even or aa is even and bb is odd.   As both statements are true --&gt; aa and bb must be even.   As abab is an even integer --&gt; aa 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: a+22=a2+1a+22=a2+1, as aa is multiple of 44, a2a2 is even integer --&gt; even+1=odd. Hence option D is always odd.   Options E can be even, odd.   Answer: (a+2)/2.
<result>D</result>
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?