GATE CS 2019 QGA-9 — General Aptitude

We can solve this problem using a 3-set Venn diagram representing the three clubs: Drama, Dance, and Maths.

Let the sets be defined as follows:

• Only Drama = $60$
• Only Dance = $80$
• Only Maths = $30$
• All three clubs (Drama $\cap$ Dance $\cap$ Maths) = $2$

We are given the intersections of the clubs:

• Students in both Drama and Dance = $40$
  $\implies$ Students in Drama and Dance only = $40 - 2 = 38$
• Students in both Dance and Maths = $12$
  $\implies$ Students in Dance and Maths only = $12 - 2 = 10$
• Students in both Drama and Maths = $7$
  $\implies$ Students in Drama and Maths only = $7 - 2 = 5$

Now, we calculate the total number of students who are in at least one club ($N_{\text{club}}$) by summing up all the mutually exclusive regions:

We are given that $75\%$ of the students in the college are not in any of these clubs. This means that the remaining $25\%$ of the students are in at least one club.

Let $T$ be the total number of students in the college:

Thus, the total number of students in the college is $900$.