CAT 2022 Slot 3 QA Question 13: 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 thes

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 thes

Accepted Answer

Let the six numbers in increasing order be $a, b, c, d, e$ and $f$.
$a + b = 28$
$e + f = 56$
To maximize the average, we need to maximize $c$ and $d$.
The two largest numbers $e$ and $f$ must be distinct natural numbers with sum 56. The largest possible value of $e$ is 27, with $f = 29$.
Then the l

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