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
Explanation:
The average of lowest two number is 14, hence their sum = 28 The average of highest two number is 28, hence their sum = 56
To maximize the average of these six numbers, we need to maximize the middle two numbers. But it is also given that all the numbers are distinct.
Since all numbers are distinct out of the two highest numbers, one must be greater than 28 (a) and the other less than 28 (b).
To maximize the middle two numbers we need to maximize ‘b’. The maximum value ‘b’ can take is 27.
∴ Maximum value of the two middle numbers can be 25 and 26.
⇒ Maximum sum of the six numbers = 28 + 25 + 26 + 56 = 135 ⇒ Maximum average of the six numbers = 135/6 = 22.5
Hence, option (b).
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