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

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Manager
Joined: 09 Oct 2008
Posts: 86
A 5 meter long wire is cut into two pieces. If the longer pi  [#permalink]

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Updated on: 21 Jun 2014, 06:28
1
3
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Difficulty:

85% (hard)

Question Stats:

39% (00:49) correct 61% (00:31) wrong based on 96 sessions

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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, 06:30.
Last edited by Bunuel on 21 Jun 2014, 06:28, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Intern
Joined: 05 Oct 2008
Posts: 12
Re: A 5 meter long wire is cut into two pieces. If the longer pi  [#permalink]

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12 Oct 2008, 07:33
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.
Manager
Joined: 09 Oct 2008
Posts: 86
Re: A 5 meter long wire is cut into two pieces. If the longer pi  [#permalink]

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12 Oct 2008, 08:07
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
VP
Joined: 17 Jun 2008
Posts: 1154
Re: A 5 meter long wire is cut into two pieces. If the longer pi  [#permalink]

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13 Oct 2008, 12:47
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.
Math Expert
Joined: 02 Sep 2009
Posts: 58434
Re: A 5 meter long wire is cut into two pieces. If the longer pi  [#permalink]

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21 Jun 2014, 06:28
3
1
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).

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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20 Oct 2018, 14:05
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A 5 meter long wire is cut into two pieces. If the longer pi   [#permalink] 20 Oct 2018, 14:05
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