Collage problem


#1

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 ___________.
A. 1000
B. 975
C. 900
D. 225


#2

60 + 80 + 30 + 38 + 2 + 10 + 5
= 225
Hence d is the correct answer


#3


Given:
P(Drama only) = a = 60
P(Dance only) = b = 80
P(Maths only) = c =30
P(Drama and Dance) = d+g = 40
P(Dance and Maths) = e+g = 12
P(Drama and Maths) = f+g = 7
P(All Clubs) = g = 2

Union or sum is a+b+c+d+e+g =225
Only 25% of students are in clubs.
0.25*(Total num of students) = 225.
So total number of students = 1000
Option A is the right answer