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 most appropriate option
A) a/2  B) b/2  C) (a+b)/2  D) (a+2)/2  E) (b+2)/2
Initially substitute a and b with 8 and 2 respectively.   a = 8   b = 2   8 - 2 = even number   8/2 = even number   so these numbers satisfy requirements   a) a/2: 8/2 = 4 EVEN   b) b/2: 4/2 = 2 EVEN   c) (a+b)/2: (8+4)/2 = 6 EVEN   d) (a+2)/2: (8+2)/2 = 5 O(a+2)/2(a+2)/2   substitute another set (a=4 &amp; b=2) for check    (4+2)/2= 
<gadget id="calculator"> (4+2)/2</gadget>
<output>3</output>
3 Again, O(a+2)/2(a+2)/2   e) (b+2)/2: (4+2)/2= 3 O(a+2)/2(a+2)/2   substitute another set (a=4 &amp; b=2) for check    (2+2)/2= 
<gadget id="calculator"> (2+2)/2</gadget>
<output>2</output>
2 EVEN   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?