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)60
b)80
c)100
d)120
e)140
5 pieces of Wood
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- theCodeToGMAT
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- vinay1983
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Sorry wanted to post somewhere, answered somewhere
I am between A and C
what is the source?
I am between A and C
what is the source?
Last edited by vinay1983 on Mon Sep 23, 2013 1:56 am, edited 1 time in total.
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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OA - C
in order to do the shortest length max we have to do 4th and 5th lenght min, which could be 140
now 620-420 = 200 , so distribution 100,100,140,140,140
in order to do the shortest length max we have to do 4th and 5th lenght min, which could be 140
now 620-420 = 200 , so distribution 100,100,140,140,140
- theCodeToGMAT
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Source: Some random PDFs which I am solvingvinay1983 wrote:Sorry wanted to post somewhere, answered somewhere
I am between A and C
what is the source?
Even though this question is easy, but the last line is confusing.
"What is the maximum possible length, in centimeters, of the shortest piece of wood?" --> you need to find maximum smallest length..
So,
you cannot assume --> x, 140, 140, 140, 140 .. as by doing so you will get the smallest possible length; we don't need that...
Correct Assumption will be : x, x, 140,140,140 --> 100
Answer {C}
R A H U L
- vinay1983
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Actually yes, I found that 100 should be the correct number.Used the same method.theCodeToGMAT wrote:Source: Some random PDFs which I am solvingvinay1983 wrote:Sorry wanted to post somewhere, answered somewhere
I am between A and C
what is the source?
Even though this question is easy, but the last line is confusing.
"What is the maximum possible length, in centimeters, of the shortest piece of wood?" --> you need to find maximum smallest length..
So,
you cannot assume --> x, 140, 140, 140, 140 .. as by doing so you will get the smallest possible length; we don't need that...
Correct Assumption will be : x, x, 140,140,140 --> 100
Answer {C}
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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_ _ 140 _ _theCodeToGMAT wrote: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)60
b)80
c)100
d)120
e)140
_ _ 140 140 140
a a 140 140 140
420 + 2a = 5*124
420 + 2a = 620
2a = 200
a = 100
Choose C
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https://www.beatthegmat.com/first-attemp ... tml#688494
Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494
- Abhishek009
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Let the pieces be arranged in ascending Order of their Length as follows -theCodeToGMAT wrote: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)60
b)80
c)100
d)120
e)140
A , B , C , D , E
Or , A > B > C > D > E
Arithmetic mean length of 124.
Length of all the pieces is 124*5 = 620 cm
So A + B + C + D + E = 620
Now the part " median length of 140 centimeters " means its the value below which 50% of the cases fall.
Here 50% of the 5 pieces will be 3.
So , A > B > 140 > 140 > 140
So we have A + B + 420 = 620
Hence A + B = 200
Now it boils down to A + B is 200 and we simply require to maximize A.
Keep Checking the options -
a. A = 60 , then B = 40 [ Can be maximized further ]
b. A = 80 , then B = 20 [ Can be maximized further ]
c. A = 100 , then B = 100 Can not be maximized further
d . A = 120 , then B = 80 Not possible because here A becomes more than B and violates our condition of arrangement of the pieces as A > B > C > D > E
e. A = 140 , then B = 60 Not possible because here A becomes more than B and violates our condition of arrangement of the pieces as A > B > C > D > E
Hope this helps...
Abhishek
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If the mean length is 124, then we know that the sum of all 5 lengths must be 620 (5 x 124 = 620).theCodeToGMAT wrote: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)60
b)80
c)100
d)120
e)140
A median of 140, tells us that our lengths (in ascending order) are ?, ?, 140, ?, ?
To MAXIMIZE the length of the shortest piece, we need to MINIMIZE the lengths of the 2 longest pieces (and keep a median of 140)
So, we get ?, ?, 140, 140, 140
The two remaining numbers must add to 200 (to get a sum of 620)
The way to MAXIMIZE the shortest piece is to make both remaining lengths 100.
We get 100, 100, 140, 140, 140
Answer: B
Cheers,
Brent
Hi Brent ,A median of 140, tells us that our lengths (in ascending order) are ?, ?, 140, ?, ?
To MAXIMIZE the length of the shortest piece, we need to MINIMIZE the lengths of the 2 longest pieces (and keep a median of 140)
So, we get ?, ?, 140, 140, 140
The two remaining numbers must add to 200 (to get a sum of 620)
The way to MAXIMIZE the shortest piece is to make both remaining lengths 100.
We get 100, 100, 140, 140, 140
Answer: B
Everything is clear. Just a quick question.
Why can not we do like this ? 140 140 140 140
Then we will get the minimum possible length = 60
Please explain.
Many thanks in advance.
SJ
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Hi SJ,jain2016 wrote:Hi Brent ,A median of 140, tells us that our lengths (in ascending order) are ?, ?, 140, ?, ?
To MAXIMIZE the length of the shortest piece, we need to MINIMIZE the lengths of the 2 longest pieces (and keep a median of 140)
So, we get ?, ?, 140, 140, 140
The two remaining numbers must add to 200 (to get a sum of 620)
The way to MAXIMIZE the shortest piece is to make both remaining lengths 100.
We get 100, 100, 140, 140, 140
Answer: B
Everything is clear. Just a quick question.
Why can not we do like this ? 140 140 140 140
Then we will get the minimum possible length = 60
Please explain.
Many thanks in advance.
SJ
The problem with your solution is that it attempts to MINIMIZE the length of the shortest piece, and we are trying to MAXIMIZE it.
Cheers,
Brent