CAT 2024 Slot 3 QA Q5 Set Theory

Question 5 of the Quantitative Ability (QA) section, CAT 2024 Slot 3, with CAT's official answer and a worked solution.

In a group of 250 students, the percentage of girls was at least 44% and at most 60%. The rest of the students were boys. Each student opted for either swimming or running or both. If 50% of the boys and 80% of the girls opted for swimming while 70% of the boys and 60% of the girls opted for running, then the minimum and maximum possible number of students who opted for both swimming and running, are
  1. A
    72 and 80, respectively
  2. B
    75 and 90, respectively
  3. C
    72 and 88, respectively
  4. D
    75 and 96, respectively

Answer: (A) 72 and 80, respectively Set Theory MCQ

Solution

  1. Let girls \(= G\) (\(110 \le G \le 150\)), boys \(= 250 - G\).
  2. Swimming \(= 0.5(250-G) + 0.8G\), running \(= 0.7(250-G) + 0.6G\). Everyone chose at least one, so both \(=\) swimming \(+\) running \(- 250 = 300 + 0.2G - 250 = 50 + 0.2G\).
  3. \(G = 110\): 72; \(G = 150\): 80. So 72 and 80.

Same concept in other years

See every question on Three-set Venn diagrams: maximise or minimise a region.

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