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Of an entire rectangular farmland 8m by 10m, Rogers wants to

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Of an entire rectangular farmland 8m by 10m, Rogers wants to [#permalink] New post 01 Nov 2012, 13:51
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Of an entire rectangular farmland 8m by 10m, Rogers wants to clear a circular space of radius 1m. If he randomly chooses the center of the circular space, what are the chances that he does not extend beyond the edges of the farmland?

A. 0.2
B. 0.5
C. 0.6
D. 0.8
E. 1.0
[Reveal] Spoiler: OA

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Last edited by Bunuel on 01 Nov 2012, 13:57, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Of an entire rectangular farmland 8m by 10m, Rogers wants to [#permalink] New post 01 Nov 2012, 14:06
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gmatbull wrote:
Of an entire rectangular farmland 8m by 10m, Rogers wants to clear a circular space of radius 1m. If he randomly chooses the center of the circular space, what are the chances that he does not extend beyond the edges of the farmland?

A. 0.2
B. 0.5
C. 0.6
D. 0.8
E. 1.0


The center of the circle must be at least one meter from any edge of the farmland. Look at the diagram blow:
Attachment:
Farm.png
Farm.png [ 2.14 KiB | Viewed 880 times ]
If the center is anywhere in the green area, then the circle won't extend beyond the edges.

Therefore, P=favorable/total=(8*6)/(10*8)=0.6.

Answer: C.

Hope it's clear.
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Re: Of an entire rectangular farmland 8m by 10m, Rogers wants to [#permalink] New post 01 Nov 2012, 14:28
got confused by the word "circular space", but now am clear.
Thanks Bunuel.
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Re: Of an entire rectangular farmland 8m by 10m, Rogers wants to [#permalink] New post 19 Nov 2012, 03:35
Bunuel wrote:
gmatbull wrote:
Of an entire rectangular farmland 8m by 10m, Rogers wants to clear a circular space of radius 1m. If he randomly chooses the center of the circular space, what are the chances that he does not extend beyond the edges of the farmland?

A. 0.2
B. 0.5
C. 0.6
D. 0.8
E. 1.0


The center of the circle must be at least one meter from any edge of the farmland. Look at the diagram blow:
Attachment:
Farm.png
If the center is anywhere in the green area, then the circle won't extend beyond the edges.

Therefore, P=favorable/total=(8*6)/(10*8)=0.6.

Answer: C.


Hope it's clear.





if I take the favorable area to be 9*7 then how it is wrong ?
The circle that needs to be drawn can certainly touch the edge, as long as it does not exceed the edge .

So if I leave a distance of 1 meter from each edge , and draw a circle having radius of 1 meter , then the circumference of the circle will certainly coincide with the edges , but not exceed it .
.

According to me 9*7/ 10*8= 63/80=0.78 ->approx - 0.8, Please tell me why this is wrong , what am I missing?
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Re: Of an entire rectangular farmland 8m by 10m, Rogers wants to [#permalink] New post 20 Nov 2012, 04:42
I was just about to ask the same question.

stne wrote:
Bunuel wrote:
gmatbull wrote:
Of an entire rectangular farmland 8m by 10m, Rogers wants to clear a circular space of radius 1m. If he randomly chooses the center of the circular space, what are the chances that he does not extend beyond the edges of the farmland?

A. 0.2
B. 0.5
C. 0.6
D. 0.8
E. 1.0


The center of the circle must be at least one meter from any edge of the farmland. Look at the diagram blow:
Attachment:
Farm.png
If the center is anywhere in the green area, then the circle won't extend beyond the edges.

Therefore, P=favorable/total=(8*6)/(10*8)=0.6.

Answer: C.


Hope it's clear.





if I take the favorable area to be 9*7 then how it is wrong ?
The circle that needs to be drawn can certainly touch the edge, as long as it does not exceed the edge .

So if I leave a distance of 1 meter from each edge , and draw a circle having radius of 1 meter , then the circumference of the circle will certainly coincide with the edges , but not exceed it .
.

According to me 9*7/ 10*8= 63/80=0.78 ->approx - 0.8, Please tell me why this is wrong , what am I missing?
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Joined: 27 May 2012
Posts: 213
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Re: Of an entire rectangular farmland 8m by 10m, Rogers wants to [#permalink] New post 21 Nov 2012, 07:12
fastcompany wrote:
I was just about to ask the same question.

@fast company
sometimes we miss simple things.
in the farm land we have to take 1 meter from each edge so 1 meter from top, 1 meter from bottom, 1 meter from left, and 1 meter from right .
so our favorable space will become (8-2) and (10-2) = 6*8 hence probability will be 48/80=6/10=.6

P.S. initially we were taking the distance from one edge only and wrongly assuming 9*7 as favorable area.
it should be clear now, please do ask if anything is still unclear.
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Re: Of an entire rectangular farmland 8m by 10m, Rogers wants to   [#permalink] 21 Nov 2012, 07:12
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