x, y, and z are positive integers. The average (arithmetic mean) of x, y, and z is 11. If z is two greater than x, which of the following must be true?
I. x is even
II. y is odd
III. z is odd
Choose the correct answer
A) I only B) II only C) III only D) I and II only E) I and III only
Given that:   x+y+z = 33 and z=x+2   using both equations   2x(Even) + y = 31 (Odd)   Since the sum is Odd 'y' has to be odd. Hence , only options (B) and (D) to be verified.   To check for 'x'.   x+y+z=33   x+z= 33- Odd   x+z= Even   Even + Even = Even   Odd+Odd = Even   ANSWER:II only
<result>B</result>
x, y, and z are positive integers. The average (arithmetic mean) of x, y, and z is 11. If z is two greater than x, which of the following must be true?
I. x is even
II. y is odd
III. z is odd