CAT 2020 Slot 1 QA Q13 Inequalities & Modulus

Question 13 of the Quantitative Ability (QA) section, CAT 2020 Slot 1, with CAT's official answer and a worked solution.

Among 100 students, x1 have birthdays in January, x2 have birthdays in February, and so on. If x0 = max(x1, x2, ..., x12), then the smallest possible value of x0 is
  1. A
    8
  2. B
    10
  3. C
    12
  4. D
    9

Answer: (D) 9 Inequalities & Modulus MCQ

Solution

  1. 100 birthdays over 12 months: if every month had at most 8, the total would be at most 96 < 100.
  2. So the maximum is at least \(\lceil 100/12\rceil = 9\), achievable (e.g. four months with 9 and eight with 8). Answer 9.

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