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Math Help - Proof

  1. #1
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    Proof

    Prove the following:

    Assume that the average of four integers (all integers are different) is 20. Prove that at least 1 of those 4 integers has to be greater than 21.
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  2. #2
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    Quote Originally Posted by DiscreteW View Post
    Prove the following:

    Assume that the average of four integers (all integers are different) is 20. Prove that at least 1 of those 4 integers has to be greater than 21.
    Assume that they are all <= 21.

    The biggest total possible would then be 21+20+19+18 so the biggest mean possible would be 19.5 but the mean is 20 so they are not all <=21 so at least one is greater than 21.
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  3. #3
    Senior Member topher0805's Avatar
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    Proof:

    We know that for average of 4 integers to be 20, the sum of those integers must be 80. With this in mind, we attempt to find the maximum sum of 4 different integers less than or equal to 21.

    <br />
21 + 20 + 19 + 18 = 78

    and,

    78 < 80

    Therefore, there is no combination of 4 different integers less than or equal to 21 that have an average of 20.
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