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# The average (arithmetic mean) of 7 numbers in a certain list

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The average (arithmetic mean) of 7 numbers in a certain list [#permalink]  29 Aug 2018, 16:14
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76% (02:07) correct 23% (00:31) wrong based on 17 sessions
The average (arithmetic mean) of 7 numbers in a certain list is 12. The average of the 4 smallest numbers in this list is 8, while the average of the 4 greatest numbers in this list is 20. How much greater is the sum of the 3 greatest numbers in the list than the sum of the 3 smallest numbers in the list?

(A) 4
(B) 14
(C) 28
(D) 48
(E) 52
[Reveal] Spoiler: OA

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Re: The average (arithmetic mean) of 7 numbers in a certain list [#permalink]  30 Aug 2018, 00:00
Let the seven numbers be a,b,c,d,e,f,g
By question the sum of these seven numbers is $$84$$
Also by question, $$a+b+c+d = 32$$ and
$$d+e+f+g = 80$$

If we sum the summation of 4 smallest numbers and 4 greatest numbers we get = 112
In other words $$a+b+c+2d+e+f+g = 112$$. If we reduce the sum of all numbers i.e. 84 from this we get 28 which is the value for d

If we reduce d from the list of 4 greatest as well as 4 smallest number we get sum for 3 greatest numbers and 3 smallest numbers.
Therefore, new sums will be 52 and 4 their difference 48.
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Re: The average (arithmetic mean) of 7 numbers in a certain list [#permalink]  15 Oct 2018, 09:29
Total sum 7*12= 84
Sum of greatest 4 numbers = 4*20= 80 therefore, sum of smallest 3 numbers = 84-80= 4
Sum of smallest 4 numbers = 4*8= 32 therefore, sum of gratest 3 numbers = 84-32= 52
The difference is 52-4= 48 . D is Answer
Re: The average (arithmetic mean) of 7 numbers in a certain list   [#permalink] 15 Oct 2018, 09:29
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