a < b < c

[sanju09]

If a, b, and c are consecutive integers and a < b < c, which of the following must be true?

I. b - c = 1.
II. (a b c)/3 is an integer.
III. a + b + c is even.

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only

[kyabe]

Since a<b<c and all the three are consecutive
We can write it as a<a+1<a+2

Therefore,

I - False as b-c = -1
II - True as (3a+3)/3 = a+1 ie an integer
III - False as a + b + c is even because it can be either odd+Even+Odd = Even or Even+Odd+Even = Odd.

Hence B is the answer.