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by [email protected] » Fri Dec 19, 2008 10:24 am
Five pieces of wood have and average length of 124 centimeters and a median length of 140 centimeters. What is the maximum possible length, in centimeters of the shortest piece of wood?

A. 90
B. 100
C. 110
D. 130
E. 140

B
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by Brent@GMATPrepNow » Fri Dec 19, 2008 10:54 am
Five pieces of wood have and average length of 124 centimeters and a median length of 140 centimeters. What is the maximum possible length, in centimeters of the shortest piece of wood?

A. 90
B. 100
C. 110
D. 130
E. 140
If the mean length is 124, then we know that the sum of all 5 lengths must be 620 (5 x 124).
A median of 140, tells us that our lengths (in ascending order) are ?, ?, 140, ?, ?
To maximize the length of the shortest piece, we want the 2 longest pieces to be a short as possible (and keep a median of 140)
So, we get ?, ?, 140, 140, 140
The two remaining numbers must add to 200 (to get a sum of 620)
The way to maximize the shortest piece is to make both numbers 100.
We get 100, 100, 140, 140, 140
The answer is B
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by dmateer25 » Fri Dec 19, 2008 10:55 am
We have 5 pieces and we know the median is 140 and the total length of the 5 is 124 x 5 = 620

__ __ 140 __ __

We need to maximize the smallest piece. So the biggest pieces need to be minimized.

Since 1 has to be at least 140 (since it is the median) the smallest we can make the biggest piece is also 140. We will make the 3 biggest pieces 140.

__ __ 140 140 140


That takes up 420 centimeters. Now there are 200 centimeters left over. Make both pieces of wood below the median 100. And no the smallest piece is 100 centimeters.

100 100 140 140 140

100 + 100 + 140 + 140 + 140=620

The median = 140
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