The set is going to have to have the 3 smallest numbers (to get the smallest possible median) and the two highest numbers (to get the highest possible mean).

So the set is {1,2,3,9,10}

Median is 3.
Mean is (1+2+3+9+10)/5 = 25/5 = 5


5-3 = 2


Ans. C

vaivish wrote:...what is the greatest possible value that the average of five numbers is greater than the median of five numbers?

How am I supposed to interpret this sentence, first of all???

Is it:
A) What is the greatest possible average of five numbers that is greater than the median of five numbers?

B) What is the greatest possible value when the average of five numbers is greater than the median of five numbers?

I'm not trying to single-out the original author of this post, especially since I see a LOT of people who violate basic grammar on these forums. Seriously, is it not worth polishing your Sentence Correction skills by posting questions that make sense?

I agree with beeparoo,

I don't think that this question would appear on the actual GMAT in the existing form. Instead, it would ask, what is the greatest possible difference between the mean and median of a set of 5 numbers chosen from a set of 1 through 10.

After choosing three sets of numbers, you notice that as the numbers get larger the difference gets smaller. Therefore, the best choice is to minimize the median - as is evident from the above example by egybs - and to maximize the mean, which requires choosing the two largest numbers to serve as the last two at the upper limit.