Data Sufficiency

Set X is composed of the total daily rainfall for a 5 day period.Is the mode of set X greater than the median?
1. mean and median od set X is equal to 5
2. If the median was removed from set X,the mean and mode would remain unchanged,but the median would decrease.

I miserably failed to do this in under 3 minutes. So I would in a test env taken a guess and moved on.

That said,

I could prove that statement 1 is not sufficient.

For a set S = {5,5,5,5,5}, removal of the median does nothing to the value of the mode. It remains equal to the median.

However for a set S = {0,0,5,10,10}, the value of the mode can be more or less than the median when 5 is removed (It is even less and more at the same time before the 5 is removed).

How would one prove statement 2?

I would have guessed E for this btw

GMAT gurus..?Stmt 2 is the real gem here...

The main problem I had with this ques was the difficulty in coming up with examples of sets..

*BUMP*

my answer is E...not sure if it's right