School Amenities Venn Diagram

CAT 1991 Slot 1 · QA · Medium · Set Theory

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Passage / data set

There were a hundred schools in a town. Of these, the number of schools having a play-ground was 30, and these schools had neither a library nor a laboratory. The number of schools having a laboratory alone was twice the number of those having a library only. The number of schools having a laboratory as well as a library was one fourth the number of those having a laboratory alone. The number of schools having either a laboratory or a library or both was 35.

Question 1 of 2

How many schools had none of the three viz., laboratory, library or play-ground?

  1. A.

    20

  2. B.

    5

  3. C.

    30

  4. D.

    35

Answer

D

Explanation

Total schools = 100.

  • Playground only = 30.
  • Laboratory or Library or both = 35.
  • Total schools with at least one facility = 30+35=6530 + 35 = 65.
  • Schools with none of the three = 100−65=35100 - 65 = 35.

Question 2 of 2

What was the ratio of schools having laboratory to those having library?

  1. A.

    1 : 2

  2. B.

    5 : 3

  3. C.

    2 : 1

  4. D.

    2 : 3

Answer

B

Explanation

Let Library only =x= x.

  • Laboratory alone =2x= 2x.
  • Both Laboratory & Library =2x4=x2= \frac{2x}{4} = \frac{x}{2}. Given total having Lab or Library or both =2x+x+x2=3.5x=35  ⟹  x=10= 2x + x + \frac{x}{2} = 3.5x = 35 \implies x = 10.
  • Total having Laboratory =2x+x2=20+5=25= 2x + \frac{x}{2} = 20 + 5 = 25.
  • Total having Library =x+x2=10+5=15= x + \frac{x}{2} = 10 + 5 = 15.
  • Ratio = 25:15=5:325 : 15 = 5 : 3.

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