Maximum number of persons for division of money

CAT 2023 Slot 2 · Quantitative Ability · Medium · Algebra

If a certain amount of money is divided equally among nn 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 nn is

Answer

16

Explanation

Total money =352n= 352n. When two persons receive Rs. 506 each, the amount remaining is 352n−2(506)=352n−1012352n - 2(506) = 352n - 1012.

This remaining amount is divided equally among n−2n - 2 persons, and each receives ≤330\le 330: 352n−1012n−2≤330\frac{352n - 1012}{n - 2} \le 330 352n−1012≤330n−660352n - 1012 \le 330n - 660 22n≤35222n \le 352 n≤16n \le 16

Therefore, the maximum possible value of nn is 1616.

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