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CAT 1993 — QA Question 35

Venn DiagramEasy
Passage / Data

Answer the following questions based on the information given below:

ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.

Out of 100 families in the neighbourhood, 45 own radios, 75 have TVs, 25 have VCRs. Only 10 families have all three and each VCR owner also has a TV. If 25 families have radio only, how many have only TV?

Answer & solution

  • A

    30

  • B

    35

  • 40

  • D

    45

Solution

Since each VCR owner also has a TV, therefore, 15 families own both TV and VCR but not Radio.

Since 25 families have radio only, therefore, 10 families own both TV and Radio but not VCR.

Hence, number of families having only TV = 75 – 10 – 10 – 15 = 40.

Hence, option (c).

CAT 1993 QA Q35: Out of 100 families in the neighbourhood, 45 own radios, 75 have TVs, 25 have VCRs. Only 10 families have all — Solution | TheCATExam