Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2

Hey, here's how I would answer this question. I'm going to try and write it out as clearly as I can. Minus the explanation this can be solved well within 2 minutes.

1. Highest number in the set is 6

Since they're all integers and distinct, the mean will be highest when a and b equal 3 & 5 (or vice versa, doesn't matter).

=> {2,3,4,5,6}
Mean = 4
Median = 4

Mean will be at its lowest when a & b equal 1 & 3.

=> {1,2,3,4,6}
Mean = 3.2
Median = 3

This is all we need to know to conclude that the first statement is INSUFFICIENT. In the first case the mean is not greater than the median, but in the second case it is.

2. The lowest number in the set is 2

Since the numbers are positive and there is now no upper limit on the integers, it is important to first find the lowest possible value of the mean since adding 300 or any huge number will ensure that the mean is greater than the median.

a & b equal 3 & 5

=> {2,3,4,5,6}
Mean = 4, Median = 4.

Again we have a case where the mean is not greater and one where it is (i.e. adding a huge number to the set). INSUFFICIENT.

Combining the two we know that 2 is the lowest number and 6 is the highest, and from our calculations it is clear that while the mean can equal the median, it CAN NOT be greater.

Answer: C

Hope this was helpful.