Given a-b is even=> both even or both odd
Given a/b is even=> both even or a is even and b is odd. Condition satisfied by both the statements is that both a and b are even. Now, if both a & b are even and a/b is an integer, then a must be greater than b and a multiple of 4.
Now option D reads: (a+2)/2= a/2+1 and any multiple of 4 when halfed will be an even number and 1+even is odd. Hence D is the correct answer



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