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GATE 2022 CE (CE2) – Question 4

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 1 mark · Multiple choice

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. Based on the above information, the number of students interested in Humanities is

  1. 10
  2. 30
  3. 40
  4. 45

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Correct answer: (D) 45

Explanation

Use inclusion–exclusion, subtracting pairwise intersections and adding the triple intersection once. The number interested in at least one science subject is $150+200+175-50-60-40+30=405$.

The remaining $450-405=\mathbf{45}$ students prefer Humanities. **Answer: D**.