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Mean problem

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by Anurag@Gurome » Wed Mar 14, 2012 8:10 pm
jkelk wrote:Hi

Please help solve the attached.

Thanks,
J
Let the length of the pieces of wood in increasing order be L1, L2, L3, L4, L5.
So, L3 = 140
Also, L1 + L2 + L3 + L4 + L5 = 124 * 5 = 620
L1 + L2 + L4 + L5 = 620 - 140 = 480
If L1 has to be maximum, L2, L4 and L5 have to be minimum.
Now L4 and L5 have to be more than or equal to median.
So, their minimum value is 140 each.
Also, L2 has to be more than or equal to L1.
So the minimum value of L2 is L1.
L2 ≥ L1
L4 ≥ 140
L5 ≥ 140
So, L1 + L2 + L4 + L5 ≥ 2L1 + 280
480 ≥ 2L1 + 280
200 ≥ 2L1
L1 ≤ 100
So, the maximum value of L1 is 100.

The correct answer is B.
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by sam2304 » Wed Mar 14, 2012 11:26 pm
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Mean = 124
Median = 140

Sum = 124 * 5 = 620.

We are asked to find the maximum value of first wooden piece.

__ __ 140 __ __ = 620

For the lowest value in the set to be maximum the highest value must be equal to the median, so that we can maximize the values less than the median. Anything greater than the median we cannot get the maximum value in the left side.

__ __ 140 140 140 = 620.

Sum of the three nos is 420.

Sum of remaining 2 values = 620-420 = 200

100 each for the lowest one to be maximum. If you choose any values to be less than or greater than 100 then the order changes and the lowest won't be of maximum value.

IMO B.
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