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Five pieces of wood have an average length of 124cm and a [#permalink]
08 Apr 2006, 08:04

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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

OA is B - but I am missing why the set cant be {90,110,140,140,140}? Thanks!

this question is best done with backsolving... it took me less than a minute to figure out. when you have values in the answer and a semi obscure question start with the middle value and that will let you know if you should go up or down.

so you know the avg is 124 thus the sum is (124)*5 you know the middle value is 140 and you know your range. start pluging in the answer choices for the smallest value ... i started with C it didnt work out the next largest was B and it worked

Last edited by NTLancer on 08 Apr 2006, 12:22, edited 1 time in total.

- - 140 - - we have four spaces to fill with 480 and two of them are > 2*140 so the remaining are less or equal to 200. So the maximu shortes possible value of the shortest word has to be 100.

ok.. so you know you have a median of 140 and 5 values thus you know you need 2 values above 140 and 2 below 140 and you need the sum to be 620.

So start with C) 110

first value is 110 the next one need to be larger than 110 but less than 140 and the smallest value for the last 2 you can have are 140 ( since you need the largest possible value to start of the sequence you can set the last 3 values to be all 140) so now 110 + x + 3*140=620 ... X = 90 .. since x is less that 110 it must go first and you sequence flips to become 90+110+3*140= 620

Actually my way is slower than realizing that the first two value must be the same and less than 140 and the last two values are 140. but whatever gets the answer right haha Im not the Professor the best solution comes to me after solving it the wrong way a few times.

Quick question...
Why wouldn't it be 90 though
If the two pieces are of equal length, there is no "shortest" piece of wood
There are shortest pieces of wood, each 100 in length?

[quote="novase101"]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

Avg = 124 thus, total = 124*5 = 620

Median is 140
So. in order to get maximum possible length, 3 greater piece should be the same length as median length.

I think it should be 90 based on the wording of the question
It asks for the shortest piece which is singular
Logically you can't have a shortest "piece" if two pieces are equal in length

I think it should be 90 based on the wording of the question It asks for the shortest piece which is singular Logically you can't have a shortest "piece" if two pieces are equal in length

let say.. there are 3 ppl.

A is 20 years old, B is 10 years old, C is 10 years old.

Who is the youngest among 3? Well, B and C..

This is the same as above example...

100, 100, 140, 140, 140

What is the shortest length? => 100

The q is asking about what is the maximum possible shortest piece
thus 100 is the maximun shortest possible piece. _________________