GATE EC 2023 Set 1 — Question 4
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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?
(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?
Correct answer
(C) 60
Solution
Let be the set of students who like romantic movies and be the set of students who like comedy movies.
Total students .From (i), the number of students who like neither romantic nor comedy movies is 30. Therefore, the number of students who like at least one of the two is:From (ii), the number of students who like romantic movies is twice the number of students who like comedy movies:From (iii), the number of students who like both is 20:Using the principle of inclusion-exclusion:Now, find the number of students who like romantic movies:Thus, 60 students like romantic movies.
Total students .From (i), the number of students who like neither romantic nor comedy movies is 30. Therefore, the number of students who like at least one of the two is:From (ii), the number of students who like romantic movies is twice the number of students who like comedy movies:From (iii), the number of students who like both is 20:Using the principle of inclusion-exclusion:Now, find the number of students who like romantic movies:Thus, 60 students like romantic movies.
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