CAT 2020 Slot 1 QA Q8 Equations

Question 8 of the Quantitative Ability (QA) section, CAT 2020 Slot 1, with CAT's official answer and a worked solution.

Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is
  1. A
    6
  2. B
    4
  3. C
    7
  4. D
    5

Answer: (A) 6 Equations MCQ

Solution

  1. \(2A+B+C=10\) and \(A+2B+C=14\). Subtracting gives \(B-A=4\).
  2. With positive integers: \(A=1, B=5\) gives \(C = 10-2-5 = 3\) (and the check \(1+10+3 = 14\) holds). \(A=2\) would force \(C=0\).
  3. \(A+B=6\).

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