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A 5 meter long wire is cut into two pieces. If the longer pi

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A 5 meter long wire is cut into two pieces. If the longer pi  [#permalink]

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New post Updated on: 21 Jun 2014, 05:28
1
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A
B
C
D
E

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Question Stats:

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A 5 meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point?

A. 1/6
B. 1/5
C. 3/10
D. 1/3
E. 2/5

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-5-meter-long-wire-is-cut-into-two-pieces-if-the-longer-106448.html

Originally posted by vishalgc on 12 Oct 2008, 05:30.
Last edited by Bunuel on 21 Jun 2014, 05:28, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: A 5 meter long wire is cut into two pieces. If the longer pi  [#permalink]

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New post 12 Oct 2008, 06:33
2
A square with an area of 1 has a perimeter of 4.
So for the area to be >1, the longer piece must be >4.
Suppose the wire is a segment AB, and the cut is at C.
The probability that AC is >4 is 1/5, which is also equal to the probability that BC>4.
So the total probability is equal to 2*1/5=2/5.

I think it's E.
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Re: A 5 meter long wire is cut into two pieces. If the longer pi  [#permalink]

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New post 12 Oct 2008, 07:07
Yes your answer is write..but i think you have consider that part will be in integer lengh only..


as they mention in question the ARBITRERY point.. can't it be like 0.5 and 4.5, 0.4adn 4.6..so we are not sure in how many parts we can divide this string..

got my point?

Thanks
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Re: A 5 meter long wire is cut into two pieces. If the longer pi  [#permalink]

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New post 13 Oct 2008, 11:47
echizen wrote:
A square with an area of 1 has a perimeter of 4.
So for the area to be >1, the longer piece must be >4.
Suppose the wire is a segment AB, and the cut is at C.
The probability that AC is >4 is 1/5, which is also equal to the probability that BC>4.
So the total probability is equal to 2*1/5=2/5.

I think it's E.



Good catch. I considered only one segment and my answer was 1/5.
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Re: A 5 meter long wire is cut into two pieces. If the longer pi  [#permalink]

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New post 21 Jun 2014, 05:28
3
A 5 meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point?

A. 1/6
B. 1/5
C. 3/10
D. 1/3
E. 2/5

In order the area of a square to be more than 1, its side must be more than 1, or the perimeter must be more than 4. Which means that the longer piece must be more than 4. Look at the diagram below:

-----

If the wire will be cut anywhere at the red region then the rest of the wire (longer piece) will be more than 4 meter long. The probability of that is 2/5 (2 red pieces out of 5).

Answer: E.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-5-meter-long-wire-is-cut-into-two-pieces-if-the-longer-106448.html
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Re: A 5 meter long wire is cut into two pieces. If the longer pi  [#permalink]

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New post 20 Oct 2018, 13:05
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