If x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?
I. x + y is odd
II. (x+z)/y is an integer
III. xz is even Answers:
A) I only  B) II only  C) III only  D) I and II only  E) I, II, and III
consecutive odds are:   2x+1, 2x+3, 2x+5   I. 2x+1+2x+3=4x+4=2(2x+2), so divisible by 2 and even - NOT TRUE   II. 2x+1+2x+5=4x+6/2x+3=2(2x+3)/2x+3=2, so integer - TRUE   III. (2x+1)*(2x+5)=4x^2+10x+2x+5=4x^2+12x+5=(2x(x+6)+5)/2 is not integer, so NOT TRUE   ANSWER: II only
<result>B</result>
If x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?
I. x + y is odd
II. (x+z)/y is an integer
III. xz is even