The average (arithmetic mean)Q of the four distinct positive integers p, q, s and t is x. If p and q are odd, and s and t are even, which of the following must be true?
I. x is an integer
II. (x−0.5) is an integer.
III. 2x is an odd integer.	Pick: A) I only B) II only C) III only D) II and III only E) None of the above
Given :   p + q = EVEN (odd + odd =even)   p + q + s + t = EVEN (even + even = even) nothing more....   (p + q + s + t) / 4 = x   I.   x may or may not be integer, we only know sum of 4 variables is even not necessarily multiple of 4. I is out.   II.   Similarly, x an integer if sum of 4 variables is multiple of 4 but not an integer if it is not multiple of 4, we only know it is even. II is out.   III.   As in II, if X is integer 2x is Even, if X has decimal part (a.5), 2x is odd. III is out.   Answer None of the above, None.
<result>E</result>
The average (arithmetic mean)Q of the four distinct positive integers p, q, s and t is x. If p and q are odd, and s and t are even, which of the following must be true?
I. x is an integer
II. (x−0.5) is an integer.
III. 2x is an odd integer.