Chufus,
I got tricked by this question too. Here's how I have understood this solution:
-- First realize that the answer choices are all different median, and the question is asking us which median is NOT POSSIBLE. My gut always tends to lean towards quickly solving a problem, but I have reminded myself that whenever I see a CANNOT type question, I will have to go through each answer choices and do "Something" with them. So, I will write down on the top right corner of the scratch pad
MEDIAN CANNOT = __ ?
-- Next realize that all the answer choices are median. So our job is to make a set with the value as Median. If we can't then, well that's our potential answer choice.
1) Start with answer choice a)0
Can we make a set of upto 6 integers with median 0? Lets just make a set and put 0 as the middle value T = { , 0 , } and then fill the remaining. Remember, the set could have 1,2,3,4,5,6,digits( for all odd numbers 1 3 5 median = integer). Since 0 is whole integer, I picked 3 integers in our set T
T={_, 0 , _}
_ could be any value as long as median does not change. IE - once you sort the set after filling in the values, 0 still remains the "middle/median" value.
T = {-1,0,1} -- Works.
2) b) x
Now x is the avg of the set. Lets ask ourselves, can we make a set where mean=median?
Lets see.
T={4,4,4} Mean= X = 4 and Median= 4 as well - Works.
3) c) -x
Can median = -(Mean).
Lets see.
T={-1,-2,9}
PS:- How I made this set was by simply thinking.. I need a -2 in the center and avg as 2. For AVG to be 2 for 3 digits set, the sum needs to be 3*2 =6 and then I just fill in other values.
4) d) 1/3y
Median = 1/3y
==> If there are 3 elements in the set ==> y=3 then
1/3*3 =1=Median. So this is certainly possible. Again, this is not possible if the number of elements in set =2 or any other even number, but our goal is to just come up with 1 value which is possible since this is a "CANNOT Problem"
5) e) 2/7y
No matter what the value of y, the median will never be an integer since y<7.
So this is it. Median can't be 2/7(y).
