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The average (arithmetic mean) of a set of numbers is 12. How many numb

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The average (arithmetic mean) of a set of numbers is 12. How many numb  [#permalink]

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New post 22 Jan 2018, 01:22
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The average (arithmetic mean) of a set of numbers is 12. How many numbers are there in the set?

(1) Eliminating the number 8 from the set increases the average by 1.
(2) When adding the number 12, the average remains unchanged.

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Re: The average (arithmetic mean) of a set of numbers is 12. How many numb  [#permalink]

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New post 22 Jan 2018, 07:59
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Bunuel wrote:
The average (arithmetic mean) of a set of numbers is 12. How many numbers are there in the set?

(1) Eliminating the number 8 from the set increases the average by 1.
(2) When adding the number 12, the average remains unchanged.


Assume the initial total was x and the number of elements was n. Hence, average = \(\frac{x}{n}\)

(1) Eliminating the number 8 from the set increases the average by 1.
If we eliminate number 8, the overall average increase by 1(becomes 13)
Now, we can frame equation that \(\frac{x}{n}\) = 12 and x = 12n
Now \(\frac{x-8}{n-1} = 13\) -> \(x-8 = 13n-13\) -> \(x = 13n-5\) -> \(12n = 13n-5\)

Therefore the number of elements(n) = 5(Sufficient)

(2) When adding the number 12, the average remains unchanged.

This information can be true for any number of elements(n) (Insufficient) (Option A)
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Re: The average (arithmetic mean) of a set of numbers is 12. How many numb &nbs [#permalink] 22 Jan 2018, 07:59
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