If a, b, c are consecutive positive integers and a<b<c, which of the following must be true?
I. b-c is positive integer
II. abc is an even integer
III. (a+b+c)/3 is an integer  Select the correct option:  A) I  B) II  C) I and II  D) II and III  E) I, II and III
1. b-c is negative because c is greater than b   2. abc   a can be either even or odd   if a=even; abc=even;   if a=odd,b=even; abc=even   Rule:   multiple of any number of integers if atleast once multiplied by an even number will result in even.   even*even=even   even*odd=even   Correct   3. (a+b+c) /3 is an integer   Again;   a=a   b=a+1   c=a+2   a+b+c=(a+a+1+a+2)=3a+3   3a is always divisible by 3   3 is divisible by 3.   Thus3a+3is also divisible by 3.   Rule:   if integer x is divisible by n   and   integer y is divisible by n   then; x+y must be divisible by n   Correct.   Ans :II and III( + +1+ +2)= 
<gadget id="calculator">( + +1+ +2)</gadget>
<output>3</output>
3a+3   3a is always divisible by 3   3 is divisible by 3.   Thus3a+3is also divisible by 3.   Rule:   if integer x is divisible by n   and   integer y is divisible by n   then; x+y must be divisible by n   Correct.   Ans :II and III
<result>D</result>
If a, b, c are consecutive positive integers and a<b<c, which of the following must be true?
I. b-c is positive integer
II. abc is an even integer
III. (a+b+c)/3 is an integer