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CMAT 2018 · Quantitative Techniques & Data Interpretation · Medium · Set Theory

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In a survey conducted among 120 houses, it was found that 50 read Times of India, 60 read Indian Express and 48 read Hindustan Times; 20 read Times of India and Indian Express, 18 read Times of India and Hindustan Times and 24 read Indian Express and Hindustan Times. If 10 read all three, how many read only one newspaper?

  1. A.

    50

  2. B.

    32

  3. C.

    64

  4. D.

    84

Answer

C

Explanation

Let T,I,HT, I, H be the sets of readers. Given:

  • n(T∩I∩H)=10n(T\cap I\cap H) = 10
  • n(T∩I)=20  ⟹  n(T\cap I) = 20 \implies only (T∩I)=20−10=10(T\cap I) = 20 - 10 = 10
  • n(T∩H)=18  ⟹  n(T\cap H) = 18 \implies only (T∩H)=18−10=8(T\cap H) = 18 - 10 = 8
  • n(I∩H)=24  ⟹  n(I\cap H) = 24 \implies only (I∩H)=24−10=14(I\cap H) = 24 - 10 = 14

Only T=50−(10+10+8)=22T = 50 - (10 + 10 + 8) = 22. Only I=60−(10+10+14)=26I = 60 - (10 + 10 + 14) = 26. Only H=48−(8+10+14)=16H = 48 - (8 + 10 + 14) = 16.

Total reading only one newspaper = 22+26+16=6422 + 26 + 16 = 64.

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