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# M14#17

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Manager
Joined: 12 Sep 2010
Posts: 224
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24 Jun 2012, 13:04
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) $$\frac{1}{6}$$

B) $$\frac{1}{5}$$

C) $$\frac{3}{10}$$

D) $$\frac{1}{3}$$

E) $$\frac{2}{5}$$

Can someone please explain this problem? Also, the official explanation states: "Look at the diagram below" but the diagram is not provided. Thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 34420
Followers: 6248

Kudos [?]: 79390 [1] , given: 10016

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24 Jun 2012, 13:08
1
KUDOS
Expert's post
Below is OE with the diagram. Was not it displayed on the test?

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).

_________________
Manager
Joined: 12 Sep 2010
Posts: 224
Followers: 2

Kudos [?]: 20 [0], given: 20

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24 Jun 2012, 13:57
Oh, that was suppose to be the diagram. I was expecting a bigger diagram. I thought they were some kind of hash marks. It it posted on the test but it is not color coded. Thanks for the explanation.
Manager
Joined: 28 Feb 2012
Posts: 115
GPA: 3.9
WE: Marketing (Other)
Followers: 0

Kudos [?]: 35 [0], given: 17

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25 Jun 2012, 21:51
Bunuel wrote:
Below is OE with the diagram. Was not it displayed on the test?

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).

Thanks Bunuel, thats very good explanation, but could you clarify onemore thing, isn't 2/5 the probability of getting area of the square which equals to 1. Since cutting on any red sides will leave us longer wire with length 4 which is not more than 1 in area but just equal.
Thanks.
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Director
Joined: 28 Jul 2011
Posts: 563
Location: United States
GPA: 3.86
WE: Accounting (Commercial Banking)
Followers: 2

Kudos [?]: 179 [0], given: 16

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26 Jun 2012, 01:27
Bunuel wrote:
Below is OE with the diagram. Was not it displayed on the test?

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).

Hi Bunnel,

One query...

Seeing the figure how can we say that three(Black dashes) sum to length more than 4?
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Math Expert
Joined: 02 Sep 2009
Posts: 34420
Followers: 6248

Kudos [?]: 79390 [0], given: 10016

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26 Jun 2012, 01:52
ziko wrote:
Bunuel wrote:
Below is OE with the diagram. Was not it displayed on the test?

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).

Thanks Bunuel, thats very good explanation, but could you clarify onemore thing, isn't 2/5 the probability of getting area of the square which equals to 1. Since cutting on any red sides will leave us longer wire with length 4 which is not more than 1 in area but just equal.
Thanks.

kotela wrote:
Hi Bunnel,

One query...

Seeing the figure how can we say that three(Black dashes) sum to length more than 4?

I think you both do not understand one thing: each dash is 1 meter long. So, again if we cut anywhere at the red region (from 0 to 1 meter or from 4 to 5 meters) then the rest of the wire (longer piece) will be more than 4 meter long.
_________________
Manager
Joined: 28 Feb 2012
Posts: 115
GPA: 3.9
WE: Marketing (Other)
Followers: 0

Kudos [?]: 35 [0], given: 17

### Show Tags

26 Jun 2012, 03:39
Bunuel wrote:
ziko wrote:
Bunuel wrote:
Below is OE with the diagram. Was not it displayed on the test?

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).

Thanks Bunuel, thats very good explanation, but could you clarify onemore thing, isn't 2/5 the probability of getting area of the square which equals to 1. Since cutting on any red sides will leave us longer wire with length 4 which is not more than 1 in area but just equal.
Thanks.

kotela wrote:
Hi Bunnel,

One query...

Seeing the figure how can we say that three(Black dashes) sum to length more than 4?

I think you both do not understand one thing: each dash is 1 meter long. So, again if we cut anywhere at the red region (from 0 to 1 meter or from 4 to 5 meters) then the rest of the wire (longer piece) will be more than 4 meter long.

Got it! So basically the crucial point for me here is cutting "at" the red region, for some reason i was concentrating on cutting exactly between the dashes.
Many thanks Bunuel!
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Director
Joined: 28 Jul 2011
Posts: 563
Location: United States
GPA: 3.86
WE: Accounting (Commercial Banking)
Followers: 2

Kudos [?]: 179 [0], given: 16

### Show Tags

26 Jun 2012, 04:02
Bunuel wrote:
ziko wrote:
Bunuel wrote:
Below is OE with the diagram. Was not it displayed on the test?

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).

Thanks Bunuel, thats very good explanation, but could you clarify onemore thing, isn't 2/5 the probability of getting area of the square which equals to 1. Since cutting on any red sides will leave us longer wire with length 4 which is not more than 1 in area but just equal.
Thanks.

kotela wrote:
Hi Bunnel,

One query...

Seeing the figure how can we say that three(Black dashes) sum to length more than 4?

I think you both do not understand one thing: each dash is 1 meter long. So, again if we cut anywhere at the red region (from 0 to 1 meter or from 4 to 5 meters) then the rest of the wire (longer piece) will be more than 4 meter long.

Many thanks Bunnel....Got It
_________________

Re: M14#17   [#permalink] 26 Jun 2012, 04:02
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# M14#17

Moderator: Bunuel

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