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    Question

    In a survey of 200 people: 112 like coffee (C), 125 like

    tea (T), 90 like juice (J). 60 like both C and T, 55 like T and J, 52 like C and J. If 30 like all three, how many like exactly one drink?
    A 83 Correct Answer Incorrect Answer
    B 66 Correct Answer Incorrect Answer
    C 49 Correct Answer Incorrect Answer
    D 99 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Use inclusion: |CтИкTтИкJ| = 112 + 125 + 90 тИТ 60 тИТ 55 тИТ 52 + 30 = 190. Let only C = 112 тИТ 60 тИТ 52 + 30 = 30. Only T = 125 тИТ 60 тИТ 55 + 30 = 40. Only J = 90 тИТ 55 тИТ 52 + 30 = 13. Exactly one = 30 + 40 + 13 = 83.

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