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# PS shortest wood

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Current Student
Joined: 31 Aug 2007
Posts: 368

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02 Aug 2008, 17:25
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This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Now I'm getting worried, this question also seems suspect to me:

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

I get that the 2 woods below the median sum to 200...I don't understand how BOTH being 100 in length allows the question to say that there is a SHORTEST piece of wood. If both are 100 then there is not shortest piece...so I picked A, but obviously this is wrong. WTF?

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Director
Joined: 23 Sep 2007
Posts: 782

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02 Aug 2008, 17:50
I agree with your interpretation, but the people who wrote the question get to invent their own rules. Just move on.

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Manager
Joined: 15 Jul 2008
Posts: 205

Kudos [?]: 68 [0], given: 0

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02 Aug 2008, 17:57
young_gun wrote:
Now I'm getting worried, this question also seems suspect to me:

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

I get that the 2 woods below the median sum to 200...I don't understand how BOTH being 100 in length allows the question to say that there is a SHORTEST piece of wood. If both are 100 then there is not shortest piece...so I picked A, but obviously this is wrong. WTF?

just like you could say 140 as the longest, even when you have 3 140s. its fair.

Kudos [?]: 68 [0], given: 0

VP
Joined: 17 Jun 2008
Posts: 1374

Kudos [?]: 406 [0], given: 0

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02 Aug 2008, 21:08
bhushangiri wrote:
young_gun wrote:
Now I'm getting worried, this question also seems suspect to me:

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

I get that the 2 woods below the median sum to 200...I don't understand how BOTH being 100 in length allows the question to say that there is a SHORTEST piece of wood. If both are 100 then there is not shortest piece...so I picked A, but obviously this is wrong. WTF?

just like you could say 140 as the longest, even when you have 3 140s. its fair.

We cannot get shortest plank at 100 cm answer should be 99
according to my calculations but noi option present here
_________________

cheers
Its Now Or Never

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Manager
Joined: 09 Jul 2008
Posts: 111

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Location: Dallas, TX
Schools: McCombs 2011

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02 Aug 2008, 22:27
Let the pieces be a, b, c, d, e arranged from shortest to longest.

Then c must be equal to 140, the median; And a <= 140 and b <= 140

Because average = 124, (a+b) < 248 and (d+e) > 248

A 90 --> if a=90, b<=158. Does not satisfy b<140
B 100 --> if a=100, b<=148. Does not satisfy b<140
C 110 --> if a=110, b<=138. Satisfies b<140
D 130 --> if a=120, b<=118. Then 130 is not the shortest length anymore
E 140 --> if a=140, b<=108. Then 140 is not the shortest length anymore

Is it C then?

Kudos [?]: 42 [0], given: 1

Re: PS shortest wood   [#permalink] 02 Aug 2008, 22:27
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