Multiple Choice Questions on 95 of the students in a class have taken Marketing 80 have chosen Finance 84 have chosen operations ........... for Mathematics - All Exams Preparation

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    95% of the students in a class have taken Marketing, 80% have chosen Finance, 84% have chosen operations (ops), and 90% have chosen Human Resources (HR). What is the maximum and minimum percentage of people who have chosen all of the four?

    80% and 56%

    Incorrect Answer

    95% and 53%

    Incorrect Answer

    80% and 49%

    Correct Answer

    80% and 51%

    Incorrect Answer
    Explanation:

    Finding the maximum percentage is easy.
    If F ⊂ O ⊂ H ⊂ M , then the percentage of people who have taken all 4 should be 80% and this is the maximum value it can take.
    For the value to be minimum, the numbers should be as far ‘apart´ as possible. Let us do this iteratively.
    First, let us take Marketing and Finance, and see if we can find the minimum percentage of students who should have taken both.

    When M and F, are as far ‘apart´ as possible, M ∩ F would be minimum. And the minimum value would be 80% + 95% – 100% = 75%.
    Now, let us start with this M ∪ F and add Ops to the mix.

    Now, the minimum value of M ∩ F ∩ O would be when these are as far ‘apart’ as possible.
    And the minimum value would be 75% + 84% – 100% = 59%.
    Adding HR also to the mix, we get -

    The minimum possible value of M ∩ F ∩ O ∩ H = 59% + 90% – 100% = 49%.
    As a formula, the minimum value is 100% – (100% – 95%) – (100% – 80%) – (100% – 84%) – (100% – 90%).
    = 100% – 5% – 20% – 16% – 10% = 100% – 51% = 49%.
    Again, do not go with just the formula. See the trial and error iteration.
    The trial and error iteration is far more useful than knowing the formula for a template.
    Hence, the answer is "80% and 49%".


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