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CAT 1991 — QA Question 16

Venn DiagramEasy

Fifty college teachers are surveyed as to their possession of colour TV, VCR and tape recorder. Of them, 22 own colour TV, 15 own VCR and 14 own tape recorders. Nine of these college teachers own exactly two items out of colour TV, VCR and tape recorder; and, one college teacher owns all three. How many of the 50 teachers own none of the three, colour TV, VCR or tape recorder?

Answer & solution

Correct answer: 10

  • A

    4

  • B

    9

  • 10

  • D

    11

Solution

Let us find out how many teachers own at least one of the three items.

We konw, A∪B∪C = A + B + C – (exactly two of A, B and C) - 2(all three)

∴ TV∪VCR∪TR = 22 + 15 + 14 - (9) - 2(1) = 40

∴ 40 people own at least one of TV, VCR and Tape Recorder.

Hence the number of teachers owing none = 50 – 40 = 10.

Hence, option (c).

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CAT 1991 QA Q16: Fifty college teachers are surveyed as to their possession of colour TV, VCR and tape recorder. Of them, 22 ow — Solution | TheCATExam