Data Sufficiency

crackgmat007 wrote:A

If same amount of water is removed from 6 tanks, SD will remain the same.

That's not quite what's happening here. We're removing 30% of the water from each tank - the amounts we remove from each tank will be different. If a tank contains 20 gallons, we'd remove 6 gallons; if a tank contains 40 gallons, we'd remove 12 gallons. That said, if we remove exactly 30% from each tank, then all of the distances within the set will fall by 30%, and the new standard deviation will be 30% lower than the old standard deviation.

crackgmat007 wrote: Thanks for pointing out Ian. If the question were to state that 5 gallons were removed from each tank that has more than 5 gallons, would the SD be the same then?

Yes, exactly - if every tank had more than 5 gallons of water, and you remove 5 gallons from each tank, then the standard deviation of the amounts of water in the tanks would not change. In general, if you subtract a constant from every value in a set, none of the distances within the set change, so the range and standard deviation stay the same.

Nee wrote:Hi Ian, Can you please explain how the answer to this question is A ??

hi -

in general, you won't actually need to calculate standard deviations on this exam, so, if you understand the properties of the standard deviation, then you should be fine. if that understanding includes a fair amount of memorization, then so be it.

in general:

you can CONCEPTUALIZE standard deviation as the average distance from the mean. this is not quite the way the SD is defined, but, as a conceptual approximation, it will justify all important properties of the standard deviation.

for instance:

* if you add or subtract the same number to/from all points in a data set, this is like "sliding" the entire set a constant distance up or down the number line. if you do that, then none of the distances within the set (including the mean) will change; therefore, the standard deviation will not change.
(this is not what is happening in this problem)

* if you multiply all points in a data set by the same constant, this is like "shrinking" or "expanding" the data set by that factor, as you would with a pantograph.
if you "shrink" or "expand" the data set in this manner, then ALL of the distances - including those involving the mean - will shrink or expand by the same factor. therefore, the standard deviation will be multiplied by the same factor.

the latter of these is what is happening in statement (1).
so, the standard deviation will just be 30% less than 10, or 7.
therefore (a)