5 pieces of wood have an average length of 124cm and median length of 140cm. What is the maximum possible length in cm, of the shortest piece of wood?
Ans: 100cm
Could anyone explain how to approach this problem?
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- briantime
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We know that 5 pieces are on average 124cm long.
This means all peaces together are 5*124 = 620cm long.
The median is 140cm.
In a sequence:
w, x, 140, y, z
We want w(the shortest piece of wood) to be as long as possible. Therefore, the values of the other variables should be as low as possible.
The lowest possible values for y and z are 140.
This gives us: w, x, 140, 140, 140
620 - 3(140) = w + x = 200
w + x have therefore to be equal to 200.
To get the highest value for w (which cannot be > x), we can assign both of them 100, which gives us the sequence:
100, 100, 140, 140, 140
This means all peaces together are 5*124 = 620cm long.
The median is 140cm.
In a sequence:
w, x, 140, y, z
We want w(the shortest piece of wood) to be as long as possible. Therefore, the values of the other variables should be as low as possible.
The lowest possible values for y and z are 140.
This gives us: w, x, 140, 140, 140
620 - 3(140) = w + x = 200
w + x have therefore to be equal to 200.
To get the highest value for w (which cannot be > x), we can assign both of them 100, which gives us the sequence:
100, 100, 140, 140, 140
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This question has been answered several times.
https://www.beatthegmat.com/5-pieces-of-wood-t45661.html
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https://www.beatthegmat.com/5-pieces-of-wood-t45661.html
Please search exact text of the question you have, most probably it is answered before.