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PS - Statistics

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Manager
Joined: 12 Apr 2006
Posts: 213
Location: India

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24 May 2009, 04:15
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Set R contains five numbers that have an average value of 55. If the median of the set is equal to the mean, and the largest number in the set is equal to 20 more than three times the smallest number, what is the largest possible range for the numbers in the set?

a) 78
b) 77 1/5
c) 66 1/7
d) 55 1/7
5) 52
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Joined: 29 Aug 2007
Posts: 2467

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27 May 2009, 07:30
humans wrote:
Set R contains five numbers that have an average value of 55. If the median of the set is equal to the mean, and the largest number in the set is equal to 20 more than three times the smallest number, what is the largest possible range for the numbers in the set?

a) 78
b) 77 1/5
c) 66 1/7
d) 55 1/7
5) 52

Mean = 55
Total = 55 x 5 = 275
The five numbers are: a, b, m, x, y
y = 3a + 20

How the gap between a and y can be widened?
We can re-phrase 5 numbers: a, a, m, m, y
They are again: a, a, 55, 55, 3a+20

Why? because we can widen the gap between a and y only when we assign minimum possible values for b and x. The minimum possible value for b is a and of x is m. Some may say that why not a+1 for b? Its snot because the question does not say that 5 numbers are different. This is what I am supposing..

Their sum = 275 = a+a+55+55+3a+20
a = 29
y = 107
range = 107 - 29 = 78
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Re: PS - Statistics   [#permalink] 27 May 2009, 07:30
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