In a college, there are three student clubs. Sixty students are only in the…
2019
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
Attempted by 31 students.
Show answer & explanation
Correct answer: C
Solution:
First count students who are only in one club: 60 (Drama) + 80 (Dance) + 30 (Maths) = 170.
The given counts for students in both clubs include those in all three, so subtract the 2 who are in all three to get those in exactly two clubs: Drama & Dance only = 40 − 2 = 38; Dance & Maths only = 12 − 2 = 10; Drama & Maths only = 7 − 2 = 5. Sum of exactly-two counts = 38 + 10 + 5 = 53.
Total number of students in at least one club = only-one total + exactly-two total + all-three = 170 + 53 + 2 = 225.
Since 75% of students are not in any club, the students in at least one club make up 25% of the total. Let T be the total number of students: 0.25 × T = 225, so T = 225 ÷ 0.25 = 900.
Answer: 900.
Check: 25% of 900 = 225, which matches the computed number in at least one club.
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