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The average (arithmetic mean) of 13 numbers is 70. If the av

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sandy
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The average (arithmetic mean) of 13 numbers is 70. If the av [#permalink] New post   29 Aug 2018, 16:17
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The average (arithmetic mean) of 13 numbers is 70. If the average of 10 of these numbers is 90, what is the average of the other 3 numbers?

(A) \(-130\)
(B) \(\frac{10}{3}\)
(C) \(30\)
(D) \(90\)
(E) \(290\)
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B
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Re: The average (arithmetic mean) of 13 numbers is 70. If the av [#permalink] New post   09 Mar 2019, 05:50
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sandy wrote:
The average (arithmetic mean) of 13 numbers is 70. If the average of 10 of these numbers is 90, what is the average of the other 3 numbers?

(A) \(-130\)
(B) \(\frac{10}{3}\)
(C) \(30\)
(D) \(90\)
(E) \(290\)


The average (arithmetic mean) of 13 numbers is 70.
We can write: (sum of all 13 numbers)/13 = 70
We get: sum of all 13 numbers = (13)(70) = 910

The average of 10 of these numbers is 90
We can write: (sum of the 10 numbers)/10 = 90
We get: sum of the 10 numbers = (10)(90) = 900


What is the average of the other 3 numbers?
The SUM of the 3 remaining numbers = (sum of all 13 numbers) - (sum of the 10 numbers)
= 910 - 900
= 10

So, the AVERAGE of the 3 numbers = (sum of the 3 numbers)/3
= 10/3

Answer: B

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Re: The average (arithmetic mean) of 13 numbers is 70. If the av [#permalink] New post   21 Jun 2021, 12:12
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Sum of 13 numbers = 13*70 = 910

Sum of 10 numbers = 9*10 = 900

910-900 = 10 ( sum of 3 numbers)

The avg of three numbers 10/3

hence, B is the answer
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B
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Re: The average (arithmetic mean) of 13 numbers is 70. If the av [#permalink] New post   10 Sep 2021, 04:53
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average of 13 numbers = 70
=> sum of 13 numbers = 70*13 = 910

average of 10 numbers = 90
=> sum of 10 numbers = 09*10 = 900

So, sum of remaining 3 numbers = 910 - 900 = 10
=> Average of remaining 3 numbers = 10/3 (B)
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Re: The average (arithmetic mean) of 13 numbers is 70. If the av [#permalink] New post   10 Sep 2021, 08:43
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average of 13 numbers*13 = 70*10=910=x(sum of 13 nums )
average of 10 numbers*10 = 90*10=900=y(sum of 10 nums)
required avg=(x-y)/3 =10/3(B)
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Re: The average (arithmetic mean) of 13 numbers is 70. If the av [#permalink] New post   01 Aug 2022, 00:25
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Theory

    ➡ Average = Sum of all the Values / Total Number of Values
    ➡ Sum of All the values = Average * Total Number of Values

The average (arithmetic mean) of 13 numbers is 70

Sum of 13 numbers = Average * 13 = 70 * 13 = 910

The average of 10 of these numbers is 90

Sum of 10 numbers = Average * 10 = 90 * 10 = 900

The average of the other 3 numbers

Average = Sum of 3 numbers / 3 = Sum of 13 numbers - Sum of 10 numbers/4 = \(\frac{910 - 900 }{ 3}\)
= \(\frac{10}{3}\)

So, Answer will be B.
Hope it helps!

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Re: The average (arithmetic mean) of 13 numbers is 70. If the av [#permalink]
01 Aug 2022, 00:25
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