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OTLP

CAT 2020 Slot 3 · Data Interpretation & Logical Reasoning · Medium · Venn Diagrams

This is a medium Data Interpretation & Logical Reasoning question set from the CAT 2020 Slot 3 paper. It tests Venn Diagrams. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Passage / data set

A survey of 600 schools in India was conducted to gather information about their online teaching learning processes (OTLP).

The following four facilities were studied:

  • F1: Own software for OTLP
  • F2: Trained teachers for OTLP
  • F3: Training materials for OTLP
  • F4: All students having laptops

The following observations were summarized from the survey:

  1. 80 schools did not have any of the facilities – F1, F2, F3, F4.
  2. 40 schools had all four facilities.
  3. The number of schools with only F1, only F2, only F3, and only F4 was 25, 30, 26 and 20 respectively.
  4. The number of schools with exactly three of the facilities was the same irrespective of which three were considered.
  5. 313 schools had F2.
  6. 26 schools had only F2 and F3 (but neither F1 nor F4).
  7. Among the schools having F4, 24 had only F3, and 45 had only F2.
  8. 162 schools had both F1 and F2.
  9. The number of schools having F1 was the same as the number of schools having F4.

Question 1 of 4

What was the total number of schools having exactly three of the four facilities?

  1. A.

    80

  2. B.

    64

  3. C.

    200

  4. D.

    50

Answer

C

Explanation

Each group with 3 facilities has 50 schools, making a total of 4×50=2004 \times 50 = 200 schools.

Question 2 of 4

What was the number of schools having facilities F2 and F4?

  1. A.

    185

  2. B.

    95

  3. C.

    45

  4. D.

    85

Answer

A

Explanation

Summing the relevant regions in the 4-set Venn diagram gives 185 schools.

Question 3 of 4

What was the number of schools having only facilities F1 and F3?

Answer

42

Explanation

The number of schools having only facilities F1 and F3 is 42.

Question 4 of 4

What was the number of schools having only facilities F1 and F4?

Answer

20

Explanation

The number of schools having only facilities F1 and F4 is 20.

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