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Standard Deviation DS

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by The Jock » Fri Dec 10, 2010 2:50 am
Source:Tough 300 GMAT math question from papgust

Some water was removed from each of 6 tanks. If standard deviation of the volumes of water at the beginning was 10 gallons, what was the standard deviation of the volumes at the end?
a. For each tank, 30% of water at the beginning was removed
b. The average volume of water in the tanks at the end was 63 gallons

I know that statement one is suffiicient because if we change the deviation 30% our deviation will change to 7. But I am little confused about statment 2. Is it that because we can not say that how much water a tank held so we can not say about SD here. Please help/clarify.
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Source: — Data Sufficiency |

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by Rahul@gurome » Fri Dec 10, 2010 4:54 am
The Jock wrote:Some water was removed from each of 6 tanks. If standard deviation of the volumes of water at the beginning was 10 gallons, what was the standard deviation of the volumes at the end?
a. For each tank, 30% of water at the beginning was removed
b. The average volume of water in the tanks at the end was 63 gallons
Statement 1: For each tank, 30% of water at the beginning was removed
Standard deviation directly scales with the scaling of variables. Thus we can easily find the new standard deviation as all the tanks contains same fraction of the initial amount of water.

Sufficient.

Statement 2: The average volume of water in the tanks at the end was 63 gallons
This doesn't help us to determine the new standard deviation as any of the following is possible,
  • 1. Same amount of water is taken from each tank => Mean = 63is possible, but standard deviation will not change.
    2. Same fraction of water taken from each tank=> Mean = 63 is possible, but standard deviation changes according to the fraction.
    3. Different amount of water is taken from each tank => Mean = 63 is possible, but no idea about standard deviation.
Not sufficient.

The correct answer is A.
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