Discussion

Explanation:

Given, the number of schools with exactly three of the facilities was the same irrespective of which three were considered.

Let us assume this number to be ‘a’ for every possible combination of three OTLPs.

The following diagram can be drawn from the given information.

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It is also given that 162 schools had F1 and F2

∴ Number of students having only F1 and F2 = 162 – (a + 40 + a) = 122 – 2a.

Total schools having F2 = 313 = 162 + 30 + 26 + a + 45

⇒ a = 50

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Total number of schools having F1 is equal to total number of schools having F2.

∴ (162 + 25 + y + 50 + x) = (50 + 40 + 50 + 24 + x + 50 + 45 + 20)

⇒ y = 42

Now there are a total of 600 schools

∴ 600 = 25 + 42 + 50 + x + 313 + 26 + 24 + 20 + 80

⇒ x = 20

Therefore, the complete Venn diagram is

​​​​​​​

Number of schools having exactly 3 of the 4 facilities = 50 + 50 + 50 + 50 = 200

Hence, option (d).

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