CAT 2023 Slot 3 QA Q15 Number Systems

Question 15 of the Quantitative Ability (QA) section, CAT 2023 Slot 3, with CAT's official answer and a worked solution.

The number of coins collected per week by two coin-collectors A and B are in the ratio 3 : 4. If the total number of coins collected by A in 5 weeks is a multiple of 7, and the total number of coins collected by B in 3 weeks is a multiple of 24, then the minimum possible number of coins collected by A in one week is

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

Answer: 42 Number Systems TITA

Solution

  1. Per week A = 3k, B = 4k.
  2. 5 weeks of A: \(15k\) divisible by 7, so \(7\mid k\). 3 weeks of B: \(12k\) divisible by 24, so k is even.
  3. Smallest k = 14, giving A = 42 coins per week.

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