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Official PYQ · 2024Set 2 · Q3MCQ1 mark

GATE CS 2024 Set 2 Q3 — General Aptitude

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​​​​In an engineering college of 10,00010,000 students, 1,5001,500 like neither their core branches nor other branches. The number of students who like their core branches is 1/4th 1 / 4^{\text{th }} of the number of students who like other branches. The number of students who like both their core and other branches is 500500.

The number of students who like their core branches is

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Answer: A

Let CC represent the set of students who like their core branches, and OO represent the set of students who like other branches.

We are given the following information:

  • Total number of students, U=10,000U = 10,000
  • Students who like neither branch, ∣C∪O‾∣=1,500|\overline{C \cup O}| = 1,500
  • Students who like both branches, ∣C∩O∣=500|C \cap O| = 500
  • The relationship between the two groups: ∣C∣=14∣O∣  ⟹  ∣O∣=4∣C∣|C| = \frac{1}{4}|O| \implies |O| = 4|C|

First, we find the number of students who like at least one of the branches:

∣C∪O∣=U−∣C∪O‾∣=10,000−1,500=8,500|C \cup O| = U - |\overline{C \cup O}| = 10,000 - 1,500 = 8,500

Using the principle of inclusion-exclusion:

∣C∪O∣=∣C∣+∣O∣−∣C∩O∣|C \cup O| = |C| + |O| - |C \cap O|

Substitute the known values into the equation:

8,500=∣C∣+4∣C∣−5008,500 = |C| + 4|C| - 5008,500=5∣C∣−5008,500 = 5|C| - 5005∣C∣=9,0005|C| = 9,000∣C∣=1,800|C| = 1,800

Thus, the number of students who like their core branches is 1,800.

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