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CAT 1991 — QA Question 16

Venn DiagramEasy
Passage / Data

Use the following information:

Prakash has to decide whether or not to test a batch of 1000 widgets before sending them to the buyer. In case he decides to test, he has two options: (a) Use test I ; (b) Use test II. Test I cost Rs. 2 per widget. However, the test is not perfect. It sends 20% of the bad ones to the buyer as good. Test II costs Rs. 3 per widget. It brings out all the bad ones. A defective widget identified before sending can be corrected at a cost of Rs. 25 per widget. All defective widgets are identified at the buyer’s end and penalty of Rs. 50 per defective widget has to be paid by Prakash.

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

  • 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).

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