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Five pieces of wood have an average length of 124cm and a [#permalink]
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25 Oct 2005, 00:08
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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 OPEN DISCUSSION OF THIS QUESTION IS HERE: fivepeicesofwoodhaveanaveragelengthof124inchesand123513.html
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B. 100
sum of all lengths of all 5 pieces of wood = 124 * 5 = 620
3rd piece (sorted in increasing length) length = 140 (median)
for sum of first 2 wood length to become max, last two should be least.
let 4th, 5th wood also have length 140 each.
total of last 3 = 140 * 3 = 420
sum of first 2 = 620  420 = 200
each of these 2 will have length 200/2 = 100



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how can the shortest piece have maximum length ? when all other pieces have a min value. thats 100 100 140 140 140. B)...
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Averages [#permalink]
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21 Feb 2006, 06:43
Five pieces of wood have an average (arithmetic mean) length of 124cm and a median length of 140 cm. What is the maximum possible length, in centimetres, of the smallest piece of wood?
a) 90
b) 100
c) 110
d) 130
e) 140



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A ) 90
here is my explanation
x140 , y140, 140 , z+140 , m+140
______________________________ = 124
5
x140 + y140 + 140 + z+140 + m+140 = 600
x140 + y140 + z+140 + m +140 = 460
now i assumed z & m == 1 > x140+ y140 = 460  280 = 180
so the loewst value can be 180/2 = 90
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think there is something wrong with this Q. If the median is 140cm and AVRG is 124 then the total lenght of the woods is 620cm.Since median is 140cm the values above the median should be > or = to the median.Their minimum value is 140x3=420cm.The max possible lenght of the shortest piece is 200124=76cm
May be i am wrong



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Answer is 100...
The average of 5 pieces is 124, this means the total length of all pieces=620
We now the median is 140, which gives us that 140 is the middle value of all the fives pieces... which means two pieces are below 140 and two pieces above 140....
To get the maximum length of the smallest piece of wood we must minimize the length of the two largest pieces....
Remember we have the total length of 620... and the middle value 140... all we need is to distribute 380 (i.e. 620140) in such a way that two of the values would be below 140 and two at least 140... so 100+100+140+140+140=620, the maximum value of the smallest piece is 100, since if we chose 110, two other values would only yield 130 which cannot be the case...
Hope i wrote it in understandable way...
Last edited by SimaQ on 21 Feb 2006, 07:49, edited 1 time in total.



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BG wrote: think there is something wrong with this Q. If the median is 140cm and AVRG is 124 then the total lenght of the woods is 620cm.Since median is 140cm the values above the median should be > or = to the median.Their minimum value is 140x3=420cm.The max possible lenght of the shortest piece is 200124=76cm May be i am wrong
Everything is perfect with your reasoning... you got that 3 values must be at least 140*3=420cm so we need to distribute 200 among the rest pieces (i.e 2) which would equal 100...



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Thanx SimaQ for your help, what was i thinking of!!!???



Manager
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I would select 100.
The way I solved the question as follows.
Median is 140
Average is 124
Total length is 620
Now based on the available information 2 Lengths <= 140 <= remaining two lengths.
Sum of these 4 lengths has to be 620  140 = 480
To maximize the shortest length, I considered that two short lengths are equal is size = x and remaining two lengths equal in size = 140 so now the addition of two short lengths is
2X = 480  (140 + 140)
2X = 200
X = 100
I hope this makes sense.
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yeah guys i calculated as 600 , it is 620 , then it will be 100... thnks
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PS Median [#permalink]
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09 Jun 2007, 21:15
Five pieces of wood have an average length of 124 cm and median length 140 cm. What is the maximum length in cm of the shortest peice of wood.
1.90
2.100
3.110
4.130
5.140



Director
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We already know that the middle piece, when ordering the pieces from longest to shortest, is 140 cm long [the median of five pieces is the middle one]
To result in a maximum length for the shortest piece, the two longest pieces must have minimum possible length > both 140 cm
Now we have 3 pieces with 140 and two other pieces <140> the two short pieces must have equal length [ call it X ]
[2X + (3x140)] / 5 = 124
[2X + 420] = 5 x 124 = 620
2X = 620  420 = 200 > X = 100 cm
ANSWER: B



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Mishari wrote: We already know that the middle piece, when ordering the pieces from longest to shortest, is 140 cm long [the median of five pieces is the middle one]
To result in a maximum length for the shortest piece, the two longest pieces must have minimum possible length > both 140 cm
Now we have 3 pieces with 140 and two other pieces <140> the two short pieces must have equal length [ call it X ]
[2X + (3x140)] / 5 = 124 [2X + 420] = 5 x 124 = 620 2X = 620  420 = 200 > X = 100 cm
ANSWER: B
Perfect  Mishari  I second (B) as the answer.



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PSpiece of wood [#permalink]
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10 Jun 2007, 01:12
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. 90
B. 100
C. 110
D. 130
E. 140



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Pieces of wood [#permalink]
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27 Sep 2007, 09:31
5 pieces of wood have an average length of 124 cm and a median lenght 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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Re: Pieces of wood [#permalink]
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27 Sep 2007, 10:58
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Fistail wrote: ywilfred wrote: 5 pieces of wood have an average length of 124 cm and a median lenght 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 b. 100 = (124 x 5  140x3)/2 = 200/2 =100
yup. it's B. I forgot some pieces could be the same length



Intern
Joined: 28 Nov 2005
Posts: 33

Why should the 2 smallest pieces of wood be 100cm each ?
Why couldn't we have the smallest piece at 71cm and the second smallest at 139cm ??
Since the sum of the 2 smallest should be 200cm.



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hidalgo01

We could, there are so many possibilities for the two shortest pieces. Remember always to focus on what the question is asking: THE MAXIMUM possible length of the shortest piece. Since the average is below the median, then the lower two pieces shall be of the same length to obtain maximum possible length.
On the other hand, the length of the larger two pieces should be minimzed to get larger smaller pieces and still maintaining the same average and median > we have now { X , X , 140, 140, 140 }
2X + 3(140) / 5 = 124 > X = 100
ANSWER: B



Intern
Joined: 28 Nov 2005
Posts: 33

Thanks for your axplanation Mishari !
It makes sence now.







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