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anand.quantum
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Standard Deviation Question

by anand.quantum Sat Jul 27, 2013 8:14 pm

Hi I came across this question online on GMAT Club.
11. During an experiment, some water was removed from each of the 6 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment?
(1) For each tank, 30% of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.
(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.
Answer: A.

The forum had answered this question with choice A - But I thought the answer was E.

Here's my rationale: The answer choice #1 seems to be saying that each tank had 30% of it's water removed by the end of the experiment. While it is tempting to say, the same amount of water was removed from each tank and therefore - the "spread does not change" and hence standard deviation remains unchanged - But I dont think we can say that conclusively here.

This is because, we don the exact amount of water in each tank therefore the per tank math becomes ( x being the initial water in each tank) --> x -0.3x=0.7x , since we dont know what "x" is in each tank - we are not necessarily subtracting the "same number" from each tank. Is my reasoning right? Please let me know.
tim
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Re: Standard Deviation Question

by tim Sat Jul 27, 2013 8:27 pm

As per the forum rules, we need a verifiable original source for the problem before we can deal with this question. GMAT Club is not an original source. If the question is not one of ours or one that is copyright-free, we will have to delete the question.
Tim Sanders
Manhattan GMAT Instructor

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