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GMATPrep - Median, Mean [#permalink]
 04 May 2007, 13:44
Can anyone explain this ?
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The answer is B and this is how I got it:
We know that the median length is 140. This means that there are at least 2 pieces that are less than or equal to 140 and 2 pieces that are greater than or equal to 140.
using the avg equation of x+x/n=avg we know that the sum of all the pieces is 620.
Now, to make things easy on us, let's assume that the two shorter pieces are both 110 (I'm starting at C because it's in the middle). If we put those into the equation we get: 110+110+140+x+x=620, which simplifies to 2x=260
We know that these last two lengths (x) have to be greater than or equal to 140. So if we assume that they are equal to each other they have to be 130 each. This is less than the median, so answer C is not correct and you know you have to go lower.
If you try 100 you get 100+100+140+x+x=620 which simplifies to 340+2x=620 --> 2x=280 --> x=140. This satisifies the median requirement so the answer is B.
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that's how is did it
we know that mean of 5 numbers is 124 therefore sum of all number is 620
median is the middle number of sequence N1, N2, 140, N4, N5
we have to take the minimum possible number that is >=140 N4 and N5 and it is 140
so we have N1,N2, 140,140,140
We are interested in finding N1.
620-3*140=200
because all numbers are sorted the maximum number we can take is 200/2 =100
answer is 100
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