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Two-set inclusion-exclusion with a total: find only one set, neither, or the unknown count

This type of question, asked 3 times: CDS 2 2018, CDS 1 2020, CDS 2 2024. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2018

    38
    In a class of 60 boys, there are 45 boys who play chess and 30 boys who play carrom. If every boy of the class plays at least one of the two games, then how many boys play carrom only ?

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  2. Question 2

    CDS 1 2020

    5
    In a competitive examination, 250 students have registered. Out of these, 50 students have registered for Physics, 75 students for Mathematics and 35 students for both Mathematics and Physics. What is the number of students who have registered neither for Physics nor for Mathematics ?

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  3. Question 3

    CDS 2 2024

    34
    In a class containing 200 students, nn students prefer both tea and coffee; 2n2n students prefer coffee, 3n3n students prefer tea; 4n4n students prefer neither tea nor coffee. What is the value of nn ?

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