Hi All,
This is an interesting statistics-based question. To solve it in an efficient way (notice that I did not say "fast"), you'll likely need a mix of TESTing VALUES, Number Property knowledge and pattern-matching skills.
We're told a number of facts about a set of numbers:
1) The average of the set = 20
2) The range of the set = 20
3) We are NOT told how many terms there are in this set
4) We are NOT told if the terms are integers
Next, we're told that we're going to add one additional number to this set. We're asked if the range of this NEW set is > 20. This is a YES/NO question.
Fact 1: The number added is 32
Let's TEST VALUES...
IF....
The starting set is {10, 30}
The average is 20 and the range is 20
Adding a 32 makes the range 32 - 10 = 22 and the answer to the question is YES.
IF....
The starting set is {12, 16, 32}
The average is 20 and the range is 20
Adding a 32 makes the range 32 - 12 = 20 and the answer to the question is NO.
Fact 1 is SUFFICIENT
Fact 2: The average of the new set is 24.
This is an interesting piece of information - it means that the one new value that is added is enough to "pull up" each of the existing values by 4 (from an average of 20 to 24). As such, this new number has to be big enough to offset ALL of the existing values in the set. Here's where 'pattern-matching' comes in handy.
IF....
The starting set is {10, 30}, the missing number has to "pull up" each of those 2 numbers by 4. The new number = 24+4+4 = 32.
32 - 10 = 22 and the answer to the question is YES.
IF....
We have MORE terms, then the missing number has to "pull up" MORE numbers by 4....
The starting set is {12, 16, 32}, then the new number = 24+4+4+4 = 36.
36 - 12 = 24 and the answer to the question is YES.
If you choose a set with a "lowest number" that gets closer to 20, the largest number gets closer to 40 (because the range = 20). However, since the AVERAGE = 20, you end up needing MORE numbers to pull the average down....
Consider if you had {nineteen 19s and one 39}, here we have 20 terms, each of which would need to be "pulled up" by 4. The new number would be 24 + 20(4) = 104
This range is considerably bigger....104 - 19 = 85 and the answer to the question is still YES.
This pattern proves that Fact 2 is SUFFICIENT. It's not something you can likely deduce by staring at the screen, so you have to be ready do enough work to pattern-match this deduction.
Final Answer:
GMAT assassins aren't born, they're made,
Rich