Problem Solving

IMO: All five answers are cannot be true. Pls help me.

Set S = 9 numbers
Set T = 8 numbers all of which are in S except one

Let S be 1,2,3,4,5,6,7,8,9
Let T be 1,2,3,4,6,7,8,9

Both have mean of 5
Both have med of 5
Ranges are both 8

For the mean of S to be bigger than T, instead of taking 5 out of the set for T take the 9 out instead. You now should have T = 1,2,3,4,5,6,7,8 and S is still 1,2,3,4,5,6,7,8,9

That would give you a mean of 5 for S still, and a Mean of 4.5

That leaves us with E . Since every number in T will always be in S, there's noway the range can ever be bigger than S