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:

Always apply the inclusion-exclusion principle carefully and include the count of students outside both sets.

Answer 1

The Correct Option is C

Step 1: Define sets.
Let $R$ = number of students who like romantic movies.
Let $C$ = number of students who like comedy movies.
Given: $R = 2C$.
Number who like both = $R \cap C = 20$.
Neither romantic nor comedy = 30.
Step 2: Apply inclusion-exclusion.
Total students $= 100$.
Thus, $R + C - (R \cap C) + 30 = 100$.
\[ R + C - 20 + 30 = 100 \Rightarrow R + C = 90. \] Step 3: Solve equations.
We have $R = 2C$. Substituting: \[ 2C + C = 90 \Rightarrow 3C = 90 \Rightarrow C = 30. \] Then $R = 2C = 60$.
Step 4: Answer.
Number of students who like romantic movies $= R = 60$.
\[ \boxed{60} \]