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

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Math Expert
Joined: 02 Sep 2009
Posts: 46251
The average (arithmetic mean) of a set of numbers is 12. How many numb [#permalink]

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22 Jan 2018, 01:22
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Difficulty:

65% (hard)

Question Stats:

53% (01:21) correct 47% (01:06) wrong based on 48 sessions

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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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22 Jan 2018, 07:59
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   [#permalink] 22 Jan 2018, 07:59
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