GATE 2017 EC (EC2) – Question 5

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

Five hundred students take one or more of Chemistry, Physics and Mathematics. Enrolments are Chemistry 329, Physics 186 and Mathematics 295. Chemistry and Physics have 83, Chemistry and Mathematics 217, and Physics and Mathematics 63 students in common. How many take all three?

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Correct answer: (D) 53

Explanation

Apply inclusion–exclusion, where pairwise overlaps include students in all three courses:
$$500=810-363+x.$$
The single-course totals sum to 810 and the pairwise overlaps sum to 363, giving $500=447+x$.

Therefore **x=53, D**. The triple overlap must be added back after subtracting the three pairwise overlaps.

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