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shortest piece of wood

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by sanju09 » Wed Apr 08, 2009 5:13 am
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


OA B
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by moutar » Wed Apr 08, 2009 6:08 am
Let the 5 lengths be: a, b, c, d, e (a≤b≤c≤d≤e)

c = median = 140

We need to minimise d & e to maximise a.

Minimum value of d&e = 140

Total length = 124*5 = 620

a+b=720-(3*140)=620-420= 200

Minimum value of a when a=b

Therefore, a=200/2=100. Answer D.
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by sacx » Wed Apr 08, 2009 6:14 am
Average length of 5 pieces = 124

total length = 124 * 5 = 620

now we are given median = 140

a,b,140,c,d

to maximise the length of the shortest piece of wood c and d must equal 140

a,b,140,140,140

a+b+140+140+140 = 620
a+b = 200

to maximise the length a =b

2a = 200
a = 100
SACX
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by sanju09 » Wed Apr 08, 2009 6:24 am
moutar wrote:Let the 5 lengths be: a, b, c, d, e (a≤b≤c≤d≤e)

c = median = 140

We need to minimise d & e to maximise a.

Minimum value of d&e = 140

Total length = 124*5 = 620

a+b=720-(3*140)=620-420= 200

Minimum value of a when a=b

Therefore, a=200/2=100. Answer D.
[spoiler]Howdy! How D? :lol: [/spoiler]
The mind is everything. What you think you become. -Lord Buddha



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by moutar » Wed Apr 08, 2009 9:59 am
I meant B. I had the write answer though.
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by margogan » Wed Apr 08, 2009 12:08 pm
sacx wrote:Average length of 5 pieces = 124

total length = 124 * 5 = 620

now we are given median = 140

a,b,140,c,d

to maximise the length of the shortest piece of wood c and d must equal 140

a,b,140,140,140

a+b+140+140+140 = 620
a+b = 200

to maximise the length a =b

2a = 200
a = 100
This is the best reply! Easy to understand, thanks!
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