GATE 2022 XH2 (English) – Question 26

Reasoning and Comprehension · Quantitative reasoning · 2 marks · Numerical answer

A particular school management wants to contact all parents, all businessmen and all engineers. The following statistics are available with the school.

Businessmen = 50

Engineers = 25

Parents = 2500

Businessmen who are engineers = 0

Businessmen who are parents = 25

Engineers who are parents = 15

The number of people needs to be contacted are _______ .

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Correct answer: 2535

Explanation

By inclusion-exclusion, the number of people is $50 + 25 + 2500 - 0 - 25 - 15 + 0 = 2535$, since nobody is in all three groups (no businessman is an engineer).