x, y and z are consecutive positive integers such that x < y < z; which of the following must be true?
1. xyz is divisible by 6
2. (z-x)(y-x+1) = 4
3. xy is even
Options:
A) I only
B) II only
C) III only
D) I and II only
E) I, II, and III
Since x, y and z are consecutive integers such that x &lt; y &lt; z, we can say x = y-1 and Z = y+1   Statement 1 would be true as at least one of the three numbers is divisible by 2 and one by 3 so xyz would be divisible by 6.   Statement 2 can be simplified if we write everything in terms of y as ((y+1)-(y-1))*(y-(y-1)+1) = 2*2= 
<gadget id="calculator">2*2</gadget>
<output>4</output>
4 So, always true   Statement 3 talks about xy Since x and y are consecutive integers one of them is odd and other is even so product would always be even and hence true.   So, I II and III are always true and hence answer is   I, II, and III.
<result>E</result>
x, y and z are consecutive positive integers such that x < y < z; which of the following must be true?
1. xyz is divisible by 6
2. (z-x)(y-x+1) = 4
3. xy is even