Hi ziyuenlau,
While this question requires some specific knowledge about Standard Deviation, you don't actually have to do much math to solve it.
To start, it's worth noting that the GMAT will NEVER ask you to calculate the Standard Deviation of a group using the S.D. formula, so that is NOT what this question is actually about.
We're told that there are four ODD integers and the greatest difference between ANY TWO of them is 4. This significantly limits the range of values.
For example, the group: 1, 1, 1, 5 fits everything that we were told. If you take ANY TWO of those values, then the greatest difference is 4. That group would have a certain S.D., but if we change any of those individual numbers, then the S.D. will also change. Thus, we really just have to think in terms of how many changes we could make while still keeping the greatest difference as 4. We also have to be careful about not creating groups that have the SAME S.D.
For example, the group: 1, 1, 1, 5 has the same S.D. as the group: 1, 5, 5, 5.... The prompt asks us for the number of different S.D.s that are possible here, so we would count this option just once (and not twice).
The other possibilities would be....
1, 1, 5, 5
1, 1, 3, 5 which has the same S.D. as 1, 3, 5, 5
1, 3, 3, 5
That gives us a total of four possibilities.
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
