GATE CS 2024 Set 2 — Question 3
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Question
In an engineering college of 10,000 students, 1,500 like neither their core branches nor other branches. The number of students who like their core branches is of the number of students who like other branches. The number of students who like both their core and other branches is 500.The number of students who like their core branches is
Correct answer
(A) 1,800
Solution
Let be the set of students who like their core branches, and be the set of students who like other branches.
Total students .
Students who like neither: .Therefore, the number of students who like at least one branch is:Let . The problem states that the number of students who like their core branches is of those who like other branches. Thus, , which implies .We are given the number of students who like both branches:Using the principle of inclusion-exclusion:So, the number of students who like their core branches is .
Total students .
Students who like neither: .Therefore, the number of students who like at least one branch is:Let . The problem states that the number of students who like their core branches is of those who like other branches. Thus, , which implies .We are given the number of students who like both branches:Using the principle of inclusion-exclusion:So, the number of students who like their core branches is .
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