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GATE CSE 2024 Session 2 Q3: Students who like their core branch (Venn diagram)

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 1/4th 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

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Answer: A (official GATE 2024 final answer key)

Concept used: Inclusion–exclusion for two sets: ∣C∪O∣=∣C∣+∣O∣−∣C∩O∣|C \cup O| = |C| + |O| - |C \cap O|.

First step: ∣C∪O∣=10000−1500=8500|C \cup O| = 10000 - 1500 = 8500, so ∣C∣+∣O∣=9000|C| + |O| = 9000 with ∣O∣=4∣C∣|O| = 4|C|.

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Source: official GATE 2024 Session 2 CS question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key

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