Problem Solving

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

Hi prachi18oct,

In this prompt, you can TEST VALUES to prove the 4 options that are possible (and the one that's left will be the answer - the one that's NOT possible).

We're told that were dealing with a set of Y INTEGERS (where 0 < Y < 7). We're also told that the average is X (which is a POSITIVE INTEGER). We're asked which of the following could NOT be the median of the group....

Answer A: 0
If the integers are -1, 0, 4
Average = X = 1
Median = 0
Eliminate A.

Answer B: X
If the integers are 1
Average = X = 1
Median = 1
Eliminate B.

Answer C: -X
If the integers are -1, -1, 5
Average = X = 1
Median = -1
Eliminate C.

Answer D: Y/3
If the integers are 1, 1, 1
Average = X = 1
Median = 1
Eliminate D.

There's only one answer left...

Final Answer: E

GMAT assassins aren't born, they're made,
Rich