The average (arithmetic mean)W of the four distinct positive integers p, q, s and t is x.
The average (arithmetic mean)W 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.
Answer/Solution
None of the above
Steps/Work
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 E, None.
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 E, None.