CAT 2020 Slot 1 QA Q20 Number Systems

Question 20 of the Quantitative Ability (QA) section, CAT 2020 Slot 1, with CAT's official answer and a worked solution.

If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value of a + b + c is
  1. A
    56
  2. B
    49
  3. C
    46
  4. D
    59

Answer: (C) 46 Number Systems MCQ

Solution

  1. \(b = \frac{96}{c}\) and \(a = \frac{432}{b} = \frac{9c}{2}\), so c is even and divides 96, with c < 9: c = 2, 4, 6, 8.
  2. c = 2: (9, 48, 2), sum 59; c = 4: (18, 24, 4), sum 46; c = 6: (27, 16, 6), sum 49; c = 8: (36, 12, 8), sum 56.
  3. Minimum \(= 46\).

Same concept in other years

See every question on Integer equations solved by listing factor pairs.

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