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Set V consists of 2 distinct positive values. What is the

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Set V consists of 2 distinct positive values. What is the [#permalink] New post 05 May 2012, 08:47
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Set V consists of 2 distinct positive values. What is the standard deviation of set V?

(1) The mean of the set is 10.
(2) The range of the set is 10

Find out the answer and explain it so that others can know!

Cheers!! :)
[Reveal] Spoiler: OA

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Re: Set V consists of 2 distinct positive values. What is the [#permalink] New post 06 May 2012, 02:30
The answer seems to be (B) here.

Statement (1) is insufficient: Just knowing the mean is not enough.
Statement (2):
Let the numbers be x and x+10
Then their mean = x+5
S.D. = sqrt (50/2) = 5
Sufficient.

(B) it is.
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Re: Set V consists of 2 distinct positive values. What is the [#permalink] New post 06 May 2012, 09:23
The answer has to be B.
After simplifying the question, we can arrive to below:
Let's assume the 2 distinct +ve numbers as x and y. Assuming y>x.
Mean= x+y/2
S.D = SQRT(((x+y/2) -x)^2 + (y-(x+y/2))^2)/2)
=SQRT(((x+y-2x)/2)^2 + ((2y-y-x)/2)^2/2)
=SQRT((y-x)^2/2)
=y-x/sqrt(2)...so we just need to know the diff between y and x and we get it from the 2nd statement which gives us the range.

Cheers!
Re: Set V consists of 2 distinct positive values. What is the   [#permalink] 06 May 2012, 09:23
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