GMATPrep Qn.

[pavithra]

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?

[briantime]

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

[pavithra]

Thanks for the explanation.

Pavithra

[gmatplayer]

This question has been answered several times.
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.