In a class of 100 students,
i. there are 30 students who neither like romantic movies nor comedy movies,
ii. the number of students who like romantic movies is twice the number of students who like comedy movies, and
iii. the number of students who like both romantic movies and comedy movies is 20.
How many students in the class like romantic movies?
A. 40 B. 20 C. 60 D. 30
GATE 2023 · General Aptitude · Venn Diagram · medium
Answer: 60 students like romantic movies.
Find the union of R and C: |R union C| = 100 - 30 = 70
Set up the sum equation using inclusion-exclusion: 70 = |R| + |C| - 20 => |R| + |C| = 90
Apply the ratio condition and solve: 2|C| + |C| = 90 => 3|C| = 90 => |C| = 30; |R| = 2 x 30 = 60