Venn Diagram Magazine Readership

CAT 2006 Slot 1 · QA · Medium · Quantitative Aptitude

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A survey of 100 people was conducted regarding readership of Golmal in 3 months:

  • Only September: 18
  • September but not August: 23
  • September and July: 8
  • September: 28
  • July: 48
  • July and August: 10
  • None of the three months: 24

What is the number of surveyed people who have read exactly two consecutive issues (out of the three)?

  1. A.

    7

  2. B.

    9

  3. C.

    12

  4. D.

    14

  5. E.

    17

Answer

9

Explanation

Let July = J, August = A, September = S. Only S = 18. S but not A = (Only S) + (S and J only) = 23   ⟹  \implies S and J only = 23−18=523 - 18 = 5. S and J = 8   ⟹  \implies All three (J ∩\cap A ∩\cap S) = 8−5=38 - 5 = 3. Total S = 28   ⟹  \implies Only S (18) + S ∩\cap J only (5) + All three (3) + S ∩\cap A only = 28   ⟹  \implies S ∩\cap A only = 28−26=228 - 26 = 2. July and August = 10   ⟹  \implies J ∩\cap A only = 10−3=710 - 3 = 7.

Consecutive months are (July & August) and (August & September). Exactly two consecutive issues means:

  • Read July & August but NOT September = J ∩\cap A only = 7
  • Read August & September but NOT July = S ∩\cap A only = 2 Total = 7+2=97 + 2 = 9.

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