CAT 2023 Slot 2 QA Q16 Inequalities & Modulus

Question 16 of the Quantitative Ability (QA) section, CAT 2023 Slot 2, with CAT's official answer and a worked solution.

If a certain amount of money is divided equally among \(n\) persons, each one receives Rs 352 . However, if two persons receive Rs 506 each and the remaining amount is divided equally among the other persons, each of them receive less than or equal to Rs 330 . Then, the maximum possible value of \(n\) is

TITA: type in the answer. There are no options and no negative marking.

Answer: 16 Inequalities & Modulus TITA

Solution

Total money \(= 352n\).
After two people take 506 each, the rest is shared by \(n-2\) people: \(\frac{352n - 1012}{n-2} \le 330\).
\(352n - 1012 \le 330n - 660 \Rightarrow 22n \le 352 \Rightarrow n \le 16\).
Maximum \(n = 16\).