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Karishma I don't know if the key word "shortest" means the second. It means the least. So the answer should be 99 practically because of the need to differentiate the first from the second- and be compatible with keyword. Your thoughts on this?

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Hey gmat1220,

Smallest just means the smallest element. It doesn't necessarily mean that there should be a unique 'smallest number'.

Say {1, 2, 5, 9, 1, 3, 9} Which is the smallest number here? 1 right? It doesn't matter even if it appears twice. If I arrange them in ascending order {1, 1, 2, 3 ....} .. the first and the second both are smallest (or shortest length). So two pieces of wood could have the shortest length. It would be maximized only if their lengths are equal and both have a length of 100.
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Five pieces of wood have an average (arithmetic mean) 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:

Five pieces of wood have an average (arithmetic mean) 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

Say we list the lengths of our pieces of wood in increasing order:

S, a, 140, b, L

We know that the sum of these lengths is 5*124 = 620. Now, we want to make S, the smallest length, as big as possible. To do that, we want the other unknown lengths to 'use up' as little of the sum of 620 as possible. That is, the smaller we make a, b and L, the larger we can make S. Since b and L must be at least as large as the median, the smallest possible values for b and L are 140. That gives us this set:

S, a, 140, 140, 140

The three largest values now add to 420, so the two smallest values must add to 620-420 = 200. Since making them equal will make a as small as possible (a cannot be less than S), the largest possible value of S is 200/2 = 100.
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Five pieces of wood have an average length of 124cm and a median length of 140cm. What is the maximum possible length, in cm, of the shortest piece of wood?

a) 90 b) 100 c) 110 d) 130 e) 140

to maximize the shortest piece we need to minimize the longest ones. thats why the 4th and 5 th pieces will be the same as the 3d (that is 140). yet we know that our sequence is the following-

x +y +140 +140+ 140=620(5*124) so x must be equal to 100. other answ choices made x more than y. that s why x could be equal only to 100 answ is B
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