What was the total number of schools having exactly three of the four facilities?
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.
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
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).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.