GATE | GATE CS 2019 | Question 9

In a college, there are three student clubs, Sixty students are only in the Drama club, 80 students are only in the Dance club, 30 students are only in Maths club, 40 students are in both Drama and Dance clubs, 12 students are in both Dance and Maths clubs, 7 students are in both Drama and Maths clubs, and 2 students are in all clubs. If 75% of the students in the college are not in any of these clubs, then the total number of students in the college is _____________.
(A) 1000
(B) 975
(C) 900
(D) 225


Answer: (C)

Explanation: Note that given 2 students are in all clubs so these are common in given each two group. After deducting 2, the Venn diagram is,

Therefore, total number of students participating in any of these clubs,

= 60 + 80 + 30 + 38 + 2 + 10 + 5
= 225 

Given only these are only 25% of the total number of students in the college (75% of the students in the college are not in any of these clubs.). Therefore, total total number of students in the college,

x*0.25 = 225
= 225/0.25
= 900 

So, option (C) is correct.

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