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

Question

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

A. 1/8
B. 1/4
C. 3/8
D. 1/2
E. 3/4

GMATBusters · Accepted Answer

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

KarishmaB · Answer

Use deviations from mean to get the answer quickly.
The smallest number is 5 and range is 14 so greatest number is 19.

For minimum sum, rest of the 6 numbers should also be 5.
For maximum sum, rest of the 6 numbers should all be 19.

Hence the maximum sum will be 14*6 more than minimum sum and hence maximum average will be  \frac{14*6}{8} = \frac{21}{2}  more than the minimum average

Desired fraction is  \frac{21/2}{14} = \frac{3}{4}

Answer (E)

Post on deviations from mean:  https://anaprep.com/arithmetic-usefulness-of-deviations/

bnreddy1990 · Answer

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 ?

SantoshSukumaran · Answer

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

Posted from my mobile device

GMATBusters · Answer

OA has been revised.

Mantrix · Answer

I tried as
smallest number is 5.
as range is given then greatest number would be 19

now we need to calculate the largest mean possible and smallest mean possible.
S1: 5, 5, 5, 5. 5, 5, 5, 19; mean = 54/8
S2: 5, 19, 19, 19, 19, 19, 19, 19; mean = 138/8

difference of both mean = 84/8

hence 84/8 = m*14 = 6/8 = 3/4 (Answer)

hemanthPA · Answer

Given: a1, a2, a3,........a8 R= a8 – a1 = 14 a1 = 5
(Max avg – Min avg)/range = ?

14 = a8 – 5 
a8 = 14+5 = 19

Max avg = (5 + (19*7))/8 = 138/8
Min avg = ((5*7) + 19)/8 = 54/8

Max – Min = 138-54/8 = 84/8

(Max avg – Min avg)/range = (84/8)/14 = 84/ (14*8) = 6/8 = 3/4

bumpbot · Answer

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

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