Standard deviation of the volume?

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Ahmed MS: Senior | Next Rank: 100 Posts; Posts: 74; Joined: Wed Apr 06, 2011 8:35 pmFollowed by: 1 member

by Ahmed MS » Wed Jun 15, 2011 11:49 pm

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 have been struggling to solve this problem. Please help me to solve this!

Cheers!

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Source: Beat The GMAT — Problem Solving | Wed Jun 15, 2011 11:49 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Thu Jun 16, 2011 1:32 am

Refer to this post : https://www.beatthegmat.com/post322714.html#322714

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Thu Jun 16, 2011 1:37 am

Hi,
From(1):
if x1,x2,..,x6 are the values of quantities of water in the tanks and mean is m, SD is d, then after removing 30% from each of the tanks, the values will be 0.7x1,0.7x2,...0.7x6 and the mean is 0.7m
new SD will be 0.7d = 0.7(10) = 7
Sufficient

From(2):avg. volume of water at the end is 63 gallons.
No info. about the volumes of the tanks
Not sufficient

Hence, A

Cheers!

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Ahmed MS: Senior | Next Rank: 100 Posts; Posts: 74; Joined: Wed Apr 06, 2011 8:35 pmFollowed by: 1 member

by Ahmed MS » Thu Jun 16, 2011 9:40 pm

Thanks Frankenstein! That is really smart and helpful answer!

Cheers!

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amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Fri Jun 17, 2011 3:07 am

a set be (1,2,3) with std dev = 1 (considering the deviation from the median only)
subtracting 30% from each will be 0.7( 1,2,3) meaning std dev * 0.7. Hence sufficient.

b no idea about the initial volume and the changed percentage.

Thus a is clean.

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