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Seven pieces of wood have an average length of 100 cm and a median len

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Seven pieces of wood have an average length of 100 cm and a median len [#permalink] New post   21 Dec 2015, 11:48
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Seven pieces of wood have an average length of 100 cm and a median length of 150 cm. What is the maximum possible length, in cm, of the shortest piece of wood? (Lengths of all pieces are Integers)

a) 32
b) 33
c) 34
d) 35
e) None of the above

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B
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Seven pieces of wood have an average length of 100 cm and a median len [#permalink] New post   21 Dec 2015, 11:59
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GMATinsight wrote:
Seven pieces of wood have an average length of 100 cm and a median length of 150 cm. What is the maximum possible length, in cm, of the shortest piece of wood? (Lengths of all pieces are Integers)

a) 32
b) 33
c) 34
d) 35
e) None of the above

Source: https://www.GMATinsight.com


Let the 7 pieces be

A
B
C
150
150
150
150

Out o 700 (=100*7), we have already assigned 600 cm worth of pieces. Thus the only case possible to divide the remaining 3 smaller pieces is either

32 34 34 or 33 33 34

Thus the maximum length of the smallest piece is 33 cm.

B is the correct answer.
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Seven pieces of wood have an average length of 100 cm and a median len [#permalink] New post   21 Dec 2015, 16:58
If we want the maximum possible length of the shortest piece of wood, then we should minimize everything that its at the right of the median.

In other words, we should have the last 4 pieces of woods measuring 150 (including the median)
x,y,z,150,150,150,150

The sum off all the measures is 700, so its going to leave us only 100 to distribute among the first 3 pieces.
700 - (150*4) = 100

100 is not divided by 3, so lets make z measuring 34, and x and y measuring 33.

That's the answer, letter B
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Re: Seven pieces of wood have an average length of 100 cm and a median len [#permalink] New post   22 Dec 2015, 05:53
The total length is 7*100 =700 cm
since median is 150 , we have 3 more pieces of wood having length >= 150 cm
for the shortest piece to have maximum possible length the remaining pieces should have same length as that of the median
so,
let the length of these pieces be 150 each, total length of these 4 pieces =600 cm
length left 700-600=100 cm
the remaining 3 can have length 34, 33 , 33
The smallest being 33 cm
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Re: Seven pieces of wood have an average length of 100 cm and a median len [#permalink] New post   15 Dec 2016, 14:31
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Here is my solution to this Question.
Let W1,W2,W3,W4,W5,W6,W7 be the seven pieces
Here each piece has an integer length.
Mean = 100 cms.


Mean = Sum/#


Sum(7) = 100*7 = 700 Cms

To maximise W1 we must minimise all others.
Hence W1=a=W2=W3
And W4=W5=W6=Median = 150

Hence => 3a+150*4=700
3a=100

Hence the sum of first three pieces is 100.
All of them must be integers.
33,33,34 is the case.

Hence B


P.S=> Good Question but a notch higher than GMAT level i guess

Regards
Stone Cold
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Re: Seven pieces of wood have an average length of 100 cm and a median len [#permalink] New post   17 Sep 2020, 04:28
GMATinsight wrote:
Seven pieces of wood have an average length of 100 cm and a median length of 150 cm. What is the maximum possible length, in cm, of the shortest piece of wood? (Lengths of all pieces are Integers)

a) 32
b) 33
c) 34
d) 35
e) None of the above

Source: https://www.GMATinsight.com


total length ; 100*7 ; 700
and median 150 which is 4th piece its length also length of 5th , 6th &7th would be same
3x+4*150=700
x= 33
OPTION B
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Re: Seven pieces of wood have an average length of 100 cm and a median len [#permalink] New post   22 Mar 2023, 13:21
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Re: Seven pieces of wood have an average length of 100 cm and a median len [#permalink]
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