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GATE 2019 CS – Question 9

General Aptitude · Quantitative Aptitude: Probability and Combinatorics · 2 marks · Multiple choice

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 the 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 the 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 ________.

  1. 1000
  2. 975
  3. 900
  4. 225

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Correct answer: (C) 900

Explanation

The "both" counts include the 2 students in all three clubs, so the students in exactly two clubs are $38+10+5=53$. The students in at least one club are $60+80+30+53+2=225$. They form 25% of the college, so the total is $\frac{225}{0.25}=900$.