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Ratio of Positive Integers a, b, c

CAT 2017 Slot 2 · Quantitative Ability · Medium · Ratios

This is a medium Quantitative Ability question from the CAT 2017 Slot 2 paper. It tests Ratios. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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If a,b,ca, b, c are three positive integers such that aa and bb are in the ratio 3:43 : 4 while bb and cc are in the ratio 2:12 : 1, then which one of the following is a possible value of (a+b+c)(a + b + c)?

  1. A.

    201

  2. B.

    205

  3. C.

    207

  4. D.

    210

Answer

C

Explanation

Given: a:b=3:4a : b = 3 : 4 b:c=2:1=4:2b : c = 2 : 1 = 4 : 2

So a:b:c=3:4:2a : b : c = 3 : 4 : 2.

Sum a+b+c=3k+4k+2k=9ka + b + c = 3k + 4k + 2k = 9k.

Therefore, (a+b+c)(a + b + c) must be a multiple of 9.

Checking options for divisibility by 9:

  • 201: sum of digits = 3 (not divisible)
  • 205: sum of digits = 7 (not divisible)
  • 207: sum of digits = 9 (divisible by 9)
  • 210: sum of digits = 3 (not divisible)

Hence, 207 is a possible value.

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