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Problem Of The Week 40

with 5 comments


When the mean, median and mode of the list 10,2,4,2,5,2,and x are arranged in increasing order, they form a non-constant arithmetic progression. FInd the sum of all such real x?

A)   3    B)  6  C) 9  D) 17   E) 20


Source : AMC 12

Written by Implex

October 2, 2008 at 1:05 pm

5 Responses

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  1. Nice one.
    Now the mode is 2 is quite evident.
    Median depends on the value of x that is if 2<x4 then 4 is the median.
    Mean = (25+x)/7
    So now consider 2<x4, then 4 is the median so the mean should be 6. So x=17
    So the sum of values is 17+3=20

    Celebrating Life

    October 2, 2008 at 4:20 pm

  2. Typo
    Median is x if 2<x4

    Celebrating Life

    October 2, 2008 at 4:21 pm

  3. hmm I thought its a typo but it’s not getting typed at all..regarding median,
    If x lies b/w 2 and 4, then median is x and if x is greater than 4 the median is 4.

    Celebrating Life

    October 2, 2008 at 4:22 pm

  4. Option E
    17 +3 = 20
    mode=2
    If x is the median
    2,2,2,x,4,5,10
    value of x comes to be three
    When x considered to be greater than 4 , its value 17. As mode , median ,mean are in A.p. x cannot be placed in first 4 places as that would make mode and median equal.

    tyro

    October 2, 2008 at 5:03 pm

  5. x cannot be placed before 2 in the first 4 places when arranged in an increasing order and cannot be equal to 2.

    tyro

    October 2, 2008 at 5:05 pm


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