In order for (x+7)/2 to be an integer, x+7 must be even because
only even/even=integer.
Case I: If x is odd, then x+7 will be even because odd+odd
= even. So this one works.
Case II: If x is a multiple of 7, it won’t always work because
multiples of 7 such as 14 can be even, which would make x+7 odd because
even+odd = odd. This case does not hold true.
Case III: Since x is odd (Case I), x+5 is even, which
means (x+5)/2 is an integer. This holds true as well.
Cases I and III must be true, so the answer is E.