T is a set of y integers, where 0<y<7. If the average of Set T is the positive integer x, which of the following could not be the median of Set T.
a) 0
b) x
c) -x
d) y/3
e) 2y/7
If we have a set of y INTEGERS, there are two possible cases when it comes to the MEDIAN.
Case a: y is an ODD number, in which case the MEDIAN equals the
one middle integer (when all of the integers are arranged in ascending order). In this case,
the median must be an integer.
Case b: y is an EVEN number, in which case the MEDIAN equals the average of the
two middle-most integers (when all of the integers are arranged in ascending order). To find the average of the two middle-most integers, we'll add them together and divide the SUM by 2. So, if their SUM is even, then
we'll get an integer value for the median. If their SUM is odd, then
the median will be something.5. For example, if the two middle-most integers are 3 and 6, the median will be 4.5.
CONCLUSION: In this scenario, the median of Set T will be EITHER
an integer OR
something.5.
When we check the answer choices, answer choice [spoiler]2y/7[/spoiler] can equal NEITHER
an integer NOR
something.5. We know this because y must be an integer AND 0 < y < 7. So, there's no way for [spoiler]2y/7[/spoiler] to ever evaluate to be an integer or something.5.
Answer:
E
Cheers,
Brent
