Bunuel wrote:

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

Given, the sum of 7 numbers=12*7=84

Sum of the 4 smallest numbers=4*8=32----(a)

Sum of the 4 greatest numbers=4*20=80 (here 3 numbers are different from the smallest numbers, one number is common to both smallest and greatest numbers)--(b)

To find:- sum of 3 greatest numbers-sum of 3 smallest numbers

3S+common number+3G+common number=80+32=112

=84+common number=112-84=28

So, common number=28

Now, from(a), 3S+common number=32

Or, 3S=32-28=4

from(b), 3G+common number=80

Or, 3G=80-28=52

So, 3G-3S=52-4=48

Where 3S and 3G denote the sum of 3 greatest numbers and sum of 3 smallest numbers respectively.

Ans. (D)

_________________

Regards,

PKN

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