Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

math assignment?

Consider a set consists of seven distinct positive integers having a mean and median equal to 50. A certain element of the set was removed such that the median of the remaining set is still 50. What is the largest possible element of the set?

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    The sum of the elements of your set was 350

    a , b , c , 50 , d , e , f

    We removed one of the elements and the median was still 50.  The only way that's possible (since all of the elements are distinct) is if we remove 50 and the average of c and d is 50

    (c + d) / 2 = 50

    c + d = 100

    a , b , c , 50 , d , e , f

    c + d + 50 = 150

    a + b + c + 50 + d + e + f = 350

    a + b + e + f + 150 = 350

    a + b + e + f = 200

    If a and b are 1 and 2

    1 + 2 + e + f = 200

    e + f = 197

    The minimum value for e is 52 (since the minimum value of d is 51)

    52 + f = 197

    f = 145

    The greatest value possible in the set is 145

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