Question

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

Hint:

For set problems with overlapping groups, always apply the inclusion-exclusion principle: \( |A \cup B| = |A| + |B| - |A \cap B| \).

Answer 1

The Correct Option is C

Step 1: Total students = 100. Those who like at least one type of movie = \(100 - 30 = 70\).
Step 2: Let number of students who like comedy movies = \(x\).
Then students who like romantic movies = \(2x\).
Students who like both = 20.
Step 3: By inclusion-exclusion principle:
\[ (2x) + (x) - 20 = 70 \] \[ 3x - 20 = 70 ⇒ 3x = 90 ⇒ x = 30. \]
Step 4: So, number of students who like romantic movies = \(2x = 60\).
Final Answer: \(\boxed{60}\).