x, y and z are consecutive positive integers such that x < y < z; which of the following must be true?
1. xz is even
2. (z-x)(y-x+1) = 4
3. xy is odd
Choose the correct choice:
A) I only B) II only C) II 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 1can not be ascertain as is not related to y directly ---not true   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 not true.   So, II are always true and hence answer is   II only
<result>C</result>
x, y and z are consecutive positive integers such that x < y < z; which of the following must be true?
1. xz is even
2. (z-x)(y-x+1) = 4
3. xy is odd