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

Question

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

ENGRTOMBA2018 · Answer

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.

douglasvg · Answer

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

CounterSniper · Answer

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

stonecold · Answer

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

Archit3110 · Answer

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

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