CAT 2020 Slot 1 QA Q10 Ratio, Mixtures & Averages

Question 10 of the Quantitative Ability (QA) section, CAT 2020 Slot 1, with CAT's official answer and a worked solution.

The mean of all 4 digit even natural numbers of the form 'aabb', where a>0, is
  1. A
    5544
  2. B
    4466
  3. C
    4864
  4. D
    5050

Answer: (A) 5544 Ratio, Mixtures & Averages MCQ

Solution

  1. \(aabb = 1100a + 11b\) with a from 1 to 9 and b in {0, 2, 4, 6, 8} (even).
  2. Every (a, b) combination occurs once, so the mean is \(1100\bar a + 11\bar b = 1100(5) + 11(4) = 5544\).

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