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Thread: Median

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    Post Median

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    The average of 5 positive numbers a b c d and e is 16 and a<b<c<d<e if e is 40. what is the greatest possible value of median of 5 integers
    a) 16 b) 18 c) 19 d) 20 e) 22

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    The answer should be 19 that is option c.
    Median is the middle number, thus the median in this case is C.
    16 X 5 = 80.

    E is 40 thus a+b+c+d= 40. In order for C to have the largest possible value we make C less than d but very close to d, Thus the answer is 19.

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    so we will maximize the median or C, by minimizing the rest of the numbers we'll make a=1 and b=2 (because of the inequality none of them will be the same). We'll make c=x and then d=x+1. We know already that e is 40
    The average of the 5 numbers = 16, which means that the sum of all 5 numbers = 80, thus 1+2+x+x+1+40=80 or 2x+44=80 or x=18
    Last edited by BGPC Eliza; 11-21-2014 at 10:07 AM.
    Eliza Chute, GMAT Tutor
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    Re: Median

    There are 5 numbers it says, not 6, so 1+1+x+x+40=5*16 --> 2x = 38 --> x =19 option C. Personally, I would just plug numbers, it's a lot faster.

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    An Urch Guru Pundit Swami Sage
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    Re: Median

    18. The strict inequalities matter

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