Consider six distinct natural numbers such that the average of the two smallest numbers is 14, and the average of the two largest numbers is 28. Then, the maximum possible value of the average of these six numbers is &nbsp;

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Question :

Consider six distinct natural numbers such that the average of the two smallest numbers is 14, and the average of the two largest numbers is 28. Then, the maximum possible value of the average of these six numbers is

Started 1 month ago by Shashank in

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A.
22.5
B.
23.5
C.
24
D.
23

Option A is the correct answer.

Explanatory Answer

We know the sum of the first pair of numbers is 14 * 2 = 28
Sum of the last pair of numbers is 28 * 2 = 56
To maximize the average of all the 6 numbers, we must try to maximize the two numbers in between. This is possible when the last pair of numbers are 27 and 29.
The maximum average case is
a, b, 25, 26, 27, 29
Where a + b = 28
The average of these 6 numbers is 22.5