Which of the following pairs of numbers, when added to the set above,

I am responding to a pm from mydreammba.

First of all, your reasoning as regards these three pairs of numbers is perfectly correct. Option #2 increases the SD, option #3 flamboyantly increases the SD, and option #1 decreases the SD.

Now, as far as generalizing --- what you are suggesting there is not correct.

Think about mean first. Suppose Set Q has a mean of 7. If I add a new number that's more than the mean, more than 7, adding it to the set will increase the mean of the set. If I add a number that's less than the mean, less than 7, adding it to the set will decrease the mean of the set.

Well, the Standard Deviation is a kind of mean, a kind of average. If you add a pair of numbers, equal and opposite distances from the mean, whose deviations from the mean is (in absolute values terms) more than the standard deviation of the set, then adding these numbers will increase the average among the deviations from the mean, that is to say, it will increase the SD of the set. If you add a pair of numbers, equal and opposite deviations from the mean, whose distance from the mean is less than the standard deviation of the set, then adding these numbers will decrease the average among the deviations from the mean, that is to say, it will decrease the SD of the set. If you add numbers that are not symmetrically distributed with respect to the mean, then that changes the mean itself, which means every single value has a new deviation from the mean, so all bets are off (the test will not ask you about this case, unless it's really obvious, as in Option #3).

In problems like this, no one actually expects you to calculate the SD. The GMAT will not expect you to do that. You are just be asked to estimate.

Now, when I look at the set {9,12,15,18,21}, it's symmetrically distributed. I know the mean is 15. The deviations from the mean are {-6, -3, 0, 3, 6} ----- none of them in this particular set has an absolute value greater than six, so the SD absolutely can't be greater than 6 --- in fact it has to be less than 6. (Any average over several values has to be lower than the largest value.) That's why six is a crucial number in this particular case.

In the set {30, 40, 50, 60, 70}, the mean is 50, and the largest deviations from the mean are +/-20, so the SD must be less than 20. Adding {47, 53} would definitely decrease the SC. Adding {30, 70) would definitely increase the SD. Adding {30, 500) would also increase the SD.

Does all this make sense?

Mike