If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true?
I. b-a = 2
II. abc is an even integer.
III. (a + b + c)/3 is an integer.
Pick:
A) I only
B) II only
C) I and II only
D) II and III only
E) I, II, and III
Since a, b, and c are consecutive positive integers and a &lt; b &lt; c, thenb= a + 1, from which it follows that b - a = 1. So, I is false.   Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is true.   Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well.   Answer: II and III only.
<result>D</result>
If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true?
I. b-a = 2
II. abc is an even integer.
III. (a + b + c)/3 is an integer.