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# Five pieces of wood have an average length of 124cm and a

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12 Oct 2007, 12:28
Mishari wrote:
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

I don't quite understand how the average being below the median allows us to determine that the lower two pieces have to be of the same length? Can you provide some clarity around this?
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12 Oct 2007, 12:40
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,

5 x 124= 620

piece.1 -- piece.2 -- 140 -- piece.4 -- piece.5

since we are looking for a max possible length of the smallest piece we need to take least possible values for the larger pieces and since 140 is the median, the smallest possible value of each of the larger pieces is 140.

140 x 3 =420, so we have 200 left for the 2 smaller pieces.

thus following combinations are possible:

50 150 140 140 140
90 110 140 140 140
100 100 140 140 140.........

the one that yeilds the highest possible value of smallest piece is

100 100 140 140 140
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12 Oct 2007, 12:44
slsu wrote:
Mishari wrote:
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

I don't quite understand how the average being below the median allows us to determine that the lower two pieces have to be of the same length? Can you provide some clarity around this?

Because increasing length of one piece means decreasing legnth of the second piece, thus automaticly the length of the shortest piece decreases.

100 + 100 = 200---------> smallest is 100

50 + 150= 200----------> smallest is 50

99 + 101= 200----------> smallest is 99

we need biggest length of the shortest piece, it is 100.
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25 Jan 2008, 09:46
5 pieces of wood have an average (arithmetic mean) length os 124 cm and a median lenght of 140 cm. What is the maximum possible lenght, in cm, of the shortest piece of wood?

A) 90
B) 100
C) 110
D) 130
E) 140
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26 Jan 2008, 14:40
Why did you multiplied 140*3 and later divided by 2?
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26 Jan 2008, 14:40
OA is B but I don't understand your reasoning!!!
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26 Jan 2008, 16:06
netcaesar wrote:
5 pieces of wood have an average (arithmetic mean) length os 124 cm and a median lenght of 140 cm. What is the maximum possible lenght, in cm, of the shortest piece of wood?

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

ok. i will take a shot on it/try to explain.

(a+b+c+d+e)/5=124
that's is the average arithmetic mean.
then the sum of their length is 124*5=620

then median let's say C=140
then let's assume a is the shortest of all 5
in order for a to be max short wood c=d=e=140 and a=b
so 140*3=420

what is left for a and be is 620-420=200
so the max it can be is 100 as a=b=100

hope this breakdown is quite simple.
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28 Jul 2008, 07:13
. Five pieces of wood have an average length of 124 cm and a median length of 140cm. what is the maximum possible length of the shortest piece of wood?

Need help. Thanks
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28 Jul 2008, 07:30
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singaks wrote:
. Five pieces of wood have an average length of 124 cm and a median length of 140cm. what is the maximum possible length of the shortest piece of wood?

Need help. Thanks

Five pieces of wood in order of increasing length:
A,B,C,D,E
A+B+C+D+E = 124*5 = 620
C is the median and equals to 140
Because Maximum (A+B) occurs when D and E at their minimum; and D and E cannot be lower than 140, so min. D and E = 140
So max. A+B = 620 - 3*140 = 200
A+B = 200 and B > A
So, max A = 99 when B = 101
if B=A is acceptable, max. A = 100
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28 Jul 2008, 08:08
Five pieces of wood have an average length of 124 cm and a median length of 140cm. what is the maximum possible length of the shortest piece of wood?

in order to have the maximum possible height for the shortest wood is to have tallest 3 woods the same as the median..and the shortest 2 woods to have the same height..

avg=sum/n 124*5 =620

620 is the total sum of the heights..now lets the tallest 3 woods=140 each..sum of 3 tallest =3*140 =420.

620-420=200..200/2 =100

100 is the max possible height
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28 Jul 2008, 08:13
singaks wrote:
. Five pieces of wood have an average length of 124 cm and a median length of 140cm. what is the maximum possible length of the shortest piece of wood?

Need help. Thanks

For length to be maximum, two largest pieces other than median has to be 140 which means

140*3 + a +b = 124*5

a + b = 200

largest value of shortest a = 100
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11 Aug 2008, 13:28
See attachment. OA will be provided later.
Attachments

PS2_081108.doc [55.5 KiB]

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11 Aug 2008, 18:43
balboa wrote:
Five pieces of wood have an average (arithmetic mean) length of 124 centimeters and a median length of 140 centimeters. What is the maxium possible length, in centimeters, of the shortest piece of wood?

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

Because 140 is the mean, we know the 3rd (piece in the middle) is going to be 140. It might be easier to number the pieces to keep them straight. #1, #2, #3, #4, #5.

#3 = 140 or it wouldn't be the median.

The average is 124 so we know that 124 * 5 pieces = 620 for total length of all boards. If the median piece is 140, then 620 - 140 is the total for the 4 other pieces, or 480.

I decided to see if 90 would work.
#1 = 90
#2 = ?
#3 = 140
#4 = ? >= 140
#5 = ? >= 140

We can see if #5 is also 140, then 3 * 140 = 420 + 90 for #1 = 510, so we'd have 110 for #2 also. It would go (90, 110, 140, 140, 140). We have to remember that we're looking for the maxium length for the smallest number. I see that if we have 90 & 110 for the 2 smallest numbers, we could also have 100, 100 and it wouldn't change the median or the mean. If we were to go any larger than 100, 100, we would have to increase both, but if we take any from the #3, #4, or #5, that will change the median, even if the average stays the same. It looks like 100 (Answer B) is the maxium length of the shortest piece of the 5.
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11 Aug 2008, 19:27
balboa wrote:
See attachment. OA will be provided later.
140

middle piece is 140 (median)
x1---x2---140 --x4 ---x5 (ascending order of length)

(x1+x2+140+x4+x5) /5 = 124 (average)

to get the max x1 x4 and x5 must be minimum. So the possible mininum values of x4 and x5 should be 140

x1+x2+140+140+140= 124*5=620

x1+x2= 200

x1 is maximum when x1=x2
So x1= 100
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02 Sep 2008, 04:41
dominion wrote:
how is x1 maximized when x=2?

Actually, you need to maximise only the shortest piece. But, if you maximise, say, x1, then x2 will become the shortest piece and vice versa. The only way to maximise one and it still remains the shortest piece, is when x1=x2.
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03 Sep 2008, 12:53
The shortest one to be maximum , we should have the 1st and 2nd wood of equal length and the rest of the 3 woods of equal length.

So length of the 1st wood = (5*124-3*140)/2= 100
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Five pieces of wood GMAT Prep PS [#permalink]

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18 Mar 2009, 17:28
Five pieces of wood have an average length of 124cm and a median lenght of 140cm. What is maximum possible length in cm of the shortest piece of wood

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

Is plugging in answers the shortest way to solve this?
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Re: Five pieces of wood GMAT Prep PS [#permalink]

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18 Mar 2009, 17:52
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Accountant wrote:
Five pieces of wood have an average length of 124cm and a median lenght of 140cm. What is maximum possible length in cm of the shortest piece of wood

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

Is plugging in answers the shortest way to solve this?

Not really. That is too time consuming.

The logic is: Make the distribution of the lengths close to the median.
Since median > avg, the max. shortest valu cannot be the avg.

So it is: (124x5 - 140x3)/2 = (620 - 420)/2 = 100
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Re: Five pieces of wood GMAT Prep PS [#permalink]

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18 Mar 2009, 17:56
average of 5 pieces = 124 => sum of lengths = 124*5=620
median = 140
so we have a,b,140,c,d
we have to find "maximum possible" length for shortest piece i.e a.
for this c,d should have minimum possible lengths i.e 140
so we have a,b,140,140,140

so a+b=200 (given that all sum up to 620)
plug in the answer choices, the "max possible" length of a can be 100.
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Re: Five pieces of wood GMAT Prep PS [#permalink]

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18 Mar 2009, 17:57
@GMAT tiger can you pls explain more ,

why have you taken three nos to be 143 ?
Re: Five pieces of wood GMAT Prep PS   [#permalink] 18 Mar 2009, 17:57

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