NinetynineCAT 2023 Slot 2 QA Q13 Inequalities & Modulus
Question 13 of the Quantitative Ability (QA) section, CAT 2023 Slot 2, with CAT's official answer and a worked solution.
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 integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is
- A1296000
- B1944000
- C972000
- D1620000
Answer: (A) 1296000 Inequalities & Modulus MCQ
Solution
- Price \(= k w^2\). Split 18 into four distinct positive integers.
- Largest sum of squares: spread out as far as possible, \(1,2,3,12\): \(1+4+9+144 = 158\).
- Smallest sum of squares: as equal as possible, \(3,4,5,6\): \(9+16+25+36 = 86\).
- \(k(158 - 86) = 72k = 288000 \Rightarrow k = 4000\). Original price \(= 4000 \times 18^2 = 1296000\).