Five peices of wood have an average length of 124 inches and

enigma123 · **Posted:** Sun Nov 20, 2011 5:49 am


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5 peices 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?
A. 90
B. 100
C. 110
D. 130
E. 140

Even though I got the correct answer (B) by doing maths, but it was a total guess work. This is how I did.

Let say shortest piece be x

x+x+3*140=5*124
2x+420=620
2x=200
x=100

I have no idea how I did it. So can someone be please kind enough to let me know the mathematical approach and the concept ?

[Reveal] Spoiler: OA

B

blink005 · **Posted:** Sun Nov 20, 2011 7:21 am

Sum of lengths is 124*5=620

Median is 140
Sum of the lengths of other four pieces= 620-140=480

The lengths of pieces-

L1, L2, 140, L4, L5

The sum of the four pieces is constant.

L4 and L5 have to be minimum for L1 to be maximum but median length must be 140.

The minimum possible values of L4 and L5 could be 140, hence the L1+L2 = 620 - 420 = 200.
The maximum possible value of L1 = 100= L2

Bunuel · **Posted:** Sun Feb 05, 2012 3:50 pm

enigma123 wrote:

Apologies blink005, if I am getting this wrong. But how did you get this?

The minimum possible values of L4 and L5 could be 140, hence the L1+L2 = 620 - 420 = 200.

Below is step by step analysis of this question. Hope it helps.

5 peices 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?
A. 90
B. 100
C. 110
D. 130
E. 140

Given: 5 peices of wood have an average length of 124 inches --> total length = 124*5=620. Also median = 140.

If a set has odd number of terms the median of a set is the middle number when arranged in ascending or descending order;
If a set has even number of terms the median of a set is the average of the two middle terms when arranged in ascending or descending order.

As we have odd # of pieces then 3rd largest piece x_3=median=140.

So if we consider the pieces in ascending order of their lengths we would have x_1+x_2+140+x_4+x_5=620.

Question: what is the MAX possible length of the shortest piece of wood? Or max(x_1)=?

General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.

So to maximize x_1 we should minimize x_2, x_4 and x_5. Min length of the second largest piece of wood, x_2 could be equal to x_1 and the min lengths of x_4 and x_5 could be equal to 140 --> x_1+x_1+140+140+140=620 --> x_1=100.

Answer: B.

enigma123 · **Posted:** Sun Nov 20, 2011 10:32 pm

Apologies blink005, if I am getting this wrong. But how did you get this?

The minimum possible values of L4 and L5 could be 140, hence the L1+L2 = 620 - 420 = 200.

boomtangboy · **Posted:** Wed Mar 14, 2012 8:29 am

Five pieces of wood have an average length of 124 cm & a median of 140 cm. What is the maximum possible length in cm of the shortest piece of wood?

A : 90
B: 100
C: 110
D : 130
E : 140

Bunuel · **Posted:** Wed Mar 14, 2012 8:35 am

boomtangboy wrote:

Five pieces of wood have an average length of 124 cm & a median of 140 cm. What is the maximum possible length in cm of the shortest piece of wood?

A : 90
B: 100
C: 110
D : 130
E : 140

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