CAT 2023 Slot 2 QA Question 12: The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct inte

Question

The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct inte

Accepted Answer

Let the price of a stone of weight $w$ be $kw^2$.

To minimize the total price after breaking, the four distinct integer weights should be as close as possible.
$3 + 4 + 5 + 6 = 18$
$	ext{Minimum split price} = k(3^{2} + 4^{2} + 5^{2} + 6^{2}) = 86k$

To maximize the total price, three pieces shoul