Hi NandishSS,

In this prompt, It's important to note that you do NOT know the number of numbers in the set and we don't know whether those numbers are even integers or not. We're told that the AVERAGE of the set is 20 and the RANGE is 20. We're asked if adding another number to this set will increase the RANGE of the set to something greater than 20. This is a YES/NO question. This question can be answered by TESTing VALUES.

1) The added number is 32.

IF...
the set is {10, 30}, then adding a 32 will increase the range and the answer to the question is YES.
the set is {12, 16, 32}, then adding a 32 will NOT increase the range and the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) The average of set S is 24.

You can TEST as many different examples as you like here and the range of the new set will ALWAYS be greater than 20. Conceptually, the reason why is because since the average of the new set is 24, and the average of the original set is 20, you can think about the 'new' number as being big enough to "be 24" and increase each of the prior terms 'by 4' - and that will always make the new term bigger than the largest number in the original set.

For example...
IF...
the set is {10, 30}, then the extra term would have to be 32 and the answer to the question is YES.
the set is {12, 16, 32}, then the extra term would have to be 36 and the answer to the question is YES.
the set is {14, 14, 18, 34}, then the extra term would have to be 40 and the answer to the question is YES.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich