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5 pieces of wood

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by uptowngirl92 » Sat Sep 26, 2009 5:38 pm
5 pieces of wood have an average length of 124 inches and a median of 140 inches. What is the MAX possible length of the shortest piece of wood?

90
100
110
130
140

Struggling big time..need DETAILED EXPLANATIONS
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by uptowngirl92 » Mon Sep 28, 2009 2:21 am
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by kaulnikhil » Mon Sep 28, 2009 7:27 am
should be b

x1+x2+x3+x4+x5 = 5*124
x1+x2+x3+x4+x5 = 600
to make the smallest piece largest make x4 , x5 = x3 = 140
so we have x1+x2 = 600 - 3*140 = 200
now largest value that x1 can take is 100
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by GID09 » Thu Oct 01, 2009 10:32 am
5 x 124 = 620.

now median is 140, that leaves us with 480.

Now the shortest possible length of the two largest piece of woods is 140. i.e. x,y, 140,140,140 would give you largest possible length of smallest wood.

That leaves us with 620-420(=140+140+140) = 200. So x could be 60 and y could be 140. 140 is your answer.
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by hypermeganet » Thu Oct 01, 2009 1:46 pm
B is correct.

124*5 = 620.

Since we're looking for the MAX of the smallest piece, we want the numbers greater than the median to be the smallest they can be: 140.

x + y + 140*3 = 620

x + y = 200

X and Y = 100 if we're trying to find the maximum since any adjustment makes one number smaller.
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by Stuart@KaplanGMAT » Thu Oct 01, 2009 1:59 pm
GID09 wrote:5 x 124 = 620.

now median is 140, that leaves us with 480.

Now the shortest possible length of the two largest piece of woods is 140. i.e. x,y, 140,140,140 would give you largest possible length of smallest wood.

That leaves us with 620-420(=140+140+140) = 200. So x could be 60 and y could be 140. 140 is your answer.
Based on choosing 60/140, the correct answer to the question would be 60 (remember, we want the largest possible length of the shortest piece of wood).

You did everything right until this very last step. With our set of:

{x, y, 140, 140, 140}

we see that we have a total of 200 left over for x and y. As Hypermeganet notes, to maximize both of them we simply let x=y and end up with 100/100 as our split.

Accordingly, B is the correct answer.

In general, here are the two rules to remember for these types of questions:

To maximize one number in a set, minimize everything else.

To minimize one number in a set, maximize everything else.
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