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Set R contains five numbers that have an average value of 55

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Joined: 15 Aug 2013
Posts: 247
Re: Largest possible range in Set R  [#permalink]

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New post 27 May 2014, 15:24
Bunuel wrote:
russ9 wrote:

Hi Bunuel,

Since the statement says that the median = mean, aren't we supposed to assume that it's an evenly spaced set? If so, wouldn't a2 and a4 be different from a1 and a3?


For evenly spaced set mean = median, but the reverse is not necessarily true. Consider {1, 1, 2, 2, 4} --> mean = median = 2, but the set is not evenly spaced.


thanks for clarifying.
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Re: Set R contains five numbers that have an average value of 55  [#permalink]

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New post 24 Aug 2018, 02:50
Orange08 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
E. 52


To maximize the range, we want to make the smallest number as small as possible and the largest number as large as possible. So the five numbers would be:

x, x, 55, 55, y

The set above will minimize the smallest number (x) because the two smallest values are the same. It will maximize the largest number (y) because the next largest number (55) is the same as the median.

Since the largest number is 20 more than 3 times the smallest number, y = 20+3x. So our list of numbers can be rewritten as:

x, x, 55, 55, 20+3x

Since the average is 55, the sum of the five numbers = 5*55 = 275.
Thus, x + x + 55 + 55 + 20+3x = 275.
5x = 145
x= 29.

Thus, y = 20+3x = 20 + 3*29 = 107.

Thus, the largest possible range is y-x = 107-29 = 78.


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Re: Set R contains five numbers that have an average value of 55 &nbs [#permalink] 24 Aug 2018, 02:50

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Set R contains five numbers that have an average value of 55

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