GATE CE 2022 Set 2 — Question 4
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General Aptitude → Analytical Aptitude → Numerical Relations & Reasoning
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Question
A survey of 450 students about their subjects of interest resulted in the following outcome.
- 150 students are interested in Mathematics.
- 200 students are interested in Physics.
- 175 students are interested in Chemistry.
- 50 students are interested in Mathematics and Physics.
- 60 students are interested in Physics and Chemistry.
- 40 students are interested in Mathematics and Chemistry.
- 30 students are interested in Mathematics, Physics and Chemistry.
- Remaining students are interested in Humanities.
Correct answer
(D) 45
Solution
To find the number of students interested in Humanities, we first find the total number of students interested in at least one of the three subjects (Mathematics, Physics, Chemistry) using the Principle of Inclusion-Exclusion for three sets:Let , , and be the sets of students interested in Mathematics, Physics, and Chemistry respectively.
Given:
Substituting the values:
The total number of students surveyed is 450. The remaining students are interested in Humanities:
Number of students in Humanities = Total students -
Number of students in Humanities = .Therefore, the correct option is (D).
Given:
Substituting the values:
The total number of students surveyed is 450. The remaining students are interested in Humanities:
Number of students in Humanities = Total students -
Number of students in Humanities = .Therefore, the correct option is (D).
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