massi2884 wrote:4 6 8 10 12 14 16 18 20 22
List M (not shown) consists of 8 different integers, each of which is in the list shown. What is the standard deviation of the numbers in list M?
1) The avergae of the numbers in list M is equal to the average of the numbers in the list shown
2) List M does NOT contain 22
OA is C please explain
On the GMAT, one is NEVER asked to calculate the SD of a set. However, one might be asked, as in this question, whether it's POSSIBLE to calculate the SD of a set.
In order to determine the SD of a set, you need 2 pieces of information about the set:
1) the number of terms; and
2) the exact spacing of the set.
Of course, if you know all of the numbers in the set, that covers both requirements.
In this question, we're asked to find the SD of an eight number subset of the given set. For sufficiency, we likely need to know which 8 numbers we're keeping for the subset (although if we knew the exact spacing, that would be enough without actually knowing which 8 remain).
(1) tells us the average of the subset. However, we can keep the same average as the main set by dropping off any symmetric pairs of numbers (e.g. we could drop 4/22, 6/20, 8/18, ...). Since dropping 4/22 and dropping 6/20 give us 2 different spacing patterns (2,2,2,2,2,2,2 vs 4,2,2,2,2,2,4), we get different possible SDs: insufficient.
(2) tells us that 22 is off the list. However, we could drop any other number to get down to our subset of 8 and end up with different spacing patterns: insufficient.
Together, we know that we have to drop a symmetric pair and that we have to drop 22. The only way to satisfy both conditions is to drop 4 and 22. We now know the final subset, which means we can answer ANY question about that new set. Sufficient, choose C!
