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There are 8 integers such that the range of them is 14 and the smalles

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There are 8 integers such that the range of them is 14 and the smalles  [#permalink]

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New post Updated on: 01 Dec 2019, 23:09
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Question Stats:

58% (02:35) correct 42% (03:01) wrong based on 12 sessions

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There are 8 integers such that the range of them is 14 and the smallest number of them is 5. The difference between the greatest possible average (arithmetic mean) of them and the smallest possible average (arithmetic mean) of them is what fraction of the range of them?

A. 1/2
B. 2/3
C. 3/4
D. 4/5
E. 5/6

Originally posted by indu1954 on 01 Dec 2019, 06:58.
Last edited by Bunuel on 01 Dec 2019, 23:09, edited 2 times in total.
Renamed the topic and edited the question.
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Re: There are 8 integers such that the range of them is 14 and the smalles  [#permalink]

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New post 01 Dec 2019, 10:15
The smallest term = 5
Range = Largest term - smallest term = 14
Hence, Largest term = 5+14= 19

Now for min Average, terms are 5,5,5,5,5,5,5,19
Min Average = total/8 = 6.75

For Max Average, terms are 5,19,19,19.19.19.19.19
Max Average = 17.25

The difference between the greatest possible average (arithmetic mean) of them and the smallest possible average (arithmetic mean) = 17.25-6.75= 10.5

Required Fraction = 10.5/14 = 0.75 = 3/4

Answer = C

indu1954 wrote:
There are 8 integers such that the range of them is 14 and the smallest number of them is 5. The difference between the greatest possible average (arithmetic mean) of them and the smallest possible average (arithmetic mean) of them is what fraction of the range of them?

A. 1/2
B. 2/3
C. 3/4
D. 4/5
E. 5/6

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Re: There are 8 integers such that the range of them is 14 and the smalles  [#permalink]

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New post 01 Dec 2019, 16:26
We get the greatest avg when all 6 integers between 5 and 19 are 19. Avg(g) = (5+19*7)/8 = 138/8
We get the smallest avg when all 6 integers between 5 and 19 are 5. Avg(s) = (5*7+19)/8 = 54/8
Difference = 21/2
Ratio = difference/range = 3/4.

I am getting C as the answer, but the OA shows something else.
Can someone pls help ?
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Re: There are 8 integers such that the range of them is 14 and the smalles  [#permalink]

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New post 01 Dec 2019, 22:49
I also got answer as 3/4.
Can someone please help with the solution as OA says 1/2

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Re: There are 8 integers such that the range of them is 14 and the smalles  [#permalink]

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New post 01 Dec 2019, 23:35
OA has been revised.

SantoshSukumaran wrote:
I also got answer as 3/4.
Can someone please help with the solution as OA says 1/2

Posted from my mobile device

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Re: There are 8 integers such that the range of them is 14 and the smalles   [#permalink] 01 Dec 2019, 23:35
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