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# The average (arithmetic mean) of eight numbers is 44.1. If the sum of

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Math Expert
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The average (arithmetic mean) of eight numbers is 44.1. If the sum of  [#permalink]

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29 Jun 2016, 06:48
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25% (medium)

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90% (01:25) correct 10% (01:38) wrong based on 50 sessions

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The average (arithmetic mean) of eight numbers is 44.1. If the sum of half of these numbers is 158.4, what is the average of the other half?

A. 12.8
B. 24.2
C. 48.6
D. 72.1
E. 96.8

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Re: The average (arithmetic mean) of eight numbers is 44.1. If the sum of  [#permalink]

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29 Jun 2016, 07:41

Let the sum of one half be x and other half be y,
$$so (x + y) / 8 = 44.1$$
$$(158.4 + y)/8 = 44.1$$
$$Solve for y/4 (average of the other half)$$
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Re: The average (arithmetic mean) of eight numbers is 44.1. If the sum of  [#permalink]

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29 Jun 2016, 07:52
arithmetic mean = sum / total numbers
sum = 44.1 * 8 = 352.8

sum of half of these numbers is 158.4. So, 4 numbers sum is 158.4. Rest 4 numbers sum = 352.8-158.4 = 194.4

Arithmetic mean of the 4 nos = 194.4/4 = 48.6

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Re: The average (arithmetic mean) of eight numbers is 44.1. If the sum of  [#permalink]

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29 Jun 2016, 09:29
Bunuel wrote:
The average (arithmetic mean) of eight numbers is 44.1. If the sum of half of these numbers is 158.4, what is the average of the other half?

A. 12.8
B. 24.2
C. 48.6
D. 72.1
E. 96.8

Total of 8 numbers= 44.1*8= 352.8

Total of remaining 4 = 352.8-158.4= 194.4

Avg= total/4= 194.4/4= 48.6

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Re: The average (arithmetic mean) of eight numbers is 44.1. If the sum of  [#permalink]

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29 Jun 2016, 19:15
Bunuel wrote:
The average (arithmetic mean) of eight numbers is 44.1. If the sum of half of these numbers is 158.4, what is the average of the other half?

A. 12.8
B. 24.2
C. 48.6
D. 72.1
E. 96.8

44.1*8=352.8

352.8-158.4=194.4

194.4/4=48.6

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Re: The average (arithmetic mean) of eight numbers is 44.1. If the sum of  [#permalink]

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29 Jun 2016, 22:21
Arithmetic Mean =sum of terms / No. of terms

44.1 = Sum / 8 so sum = 352.8

sum of half of these numbers is 158.4
so remaining half sum = 352.8 - 158.4 = 194.4

Average is 194.4 / 4 = 48.6

So C is the correct Answer
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The average (arithmetic mean) of eight numbers is 44.1. If the sum of  [#permalink]

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29 Jun 2016, 23:19
Bunuel wrote:
The average (arithmetic mean) of eight numbers is 44.1. If the sum of half of these numbers is 158.4, what is the average of the other half?

A. 12.8
B. 24.2
C. 48.6
D. 72.1
E. 96.8

There are nice gap in answer choices. So I can safely make round numbers.

The average = 44.1 close to 45
Sum=158.4 close to 160

Sum of 8 numbers = 8 * 45=360
Sum of other 4 numbers =360 -160= 200

Average of other 4 numbers= 200/4=50

clearly the closest number is 48.6

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Joined: 02 Jul 2016
Posts: 18
Re: The average (arithmetic mean) of eight numbers is 44.1. If the sum of  [#permalink]

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02 Jul 2016, 08:24
Sum of 8 nos = 44.1x8
Sum of 4 = 158.4
Difference= 194.4

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Re: The average (arithmetic mean) of eight numbers is 44.1. If the sum of   [#permalink] 02 Jul 2016, 08:24