Multiple Choice Questions on In a competition a school awarded medals in different categories 36 medals in dance 12 medals ........... for Mathematics - All Exams Preparation

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Multiple Choice Questions

In a competition a school awarded medals in different categories 36 medals in dance 12 medals ...........

Quantitative Aptitude ( CCS) Set theory
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     In a competition, a school awarded medals in different categories. 36 medals in dance, 12 medals in dramatics and 18 medals in music. If these medals went to a total of 45 persons and only 4 persons got medals in all the three categories, how many received medals in exactly two of these categories?

    1

    Incorrect Answer

    3

    Correct Answer

    5

    Incorrect Answer

    7

    Incorrect Answer
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    Explanation:

    Let A = set of persons who got medals in dance.
    B = set of persons who got medals in dramatics.
    C = set of persons who got medals in music.

    Given,
    n(A) = 36
    n(B) = 12
    n(C) = 18
    n(A ∪ B ∪C) = 45
    n(A ∩ B ∩ C) = 4
    We know that number of elements belonging to exactly two of the three sets A, B, C
    = n(A ∩ B) + n(B ∩ C) + n(A ∩ C) - 3n(A ∩ B ∩ C)
    = n(A ∩ B) + n(B ∩ C) + n(A ∩ C) - 3 × 4 ……..(i)
    n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(A ∩ C) + n(A ∩ B ∩C)
    Therefore, n(A ∩ B) + n(B ∩ C) + n(A ∩ C) = n(A) + n(B) + n(C) + n(A ∩ B ∩ C) - n(A ∪ B ∪ C)
    From (i) required number
    = n(A) + n(B) + n(C) + n(A ∩ B ∩ C) - n(A ∪ B ∪ C) - 12
    = 36 + 12 + 18 + 4 - 45 - 12
    = 70 - 67
    = 3

    By: Amit Kumar
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