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In the figure ,small circel with radius r intersects larger [#permalink]
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11 May 2011, 23:45
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In the figure, small circel with radius r intersects larger circle with radius R (R>r). If k>0, what is the difference in the areas of the non overlapping parts of two circles? (1) R=r+3k (2) kR/(kr6)=1
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Re: circles! [#permalink]
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12 May 2011, 04:59
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Area 1 = OVerlap + ( pi*r^2  Overlap) Area 2 = OVerlap + ( pi*R^2  Overlap) So ( pi*R^2  Overlap)  ( pi*r^2  Overlap) = ? = pi(Rr)(r+R) (1) Rr = 3k Insufficient (2) kR = kr +6 => r+R = 6/k Insufficient (1) + (2) So difference = pi* 3k * 6/k = 18pi Answer  C What is the OA ?
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Re: circles! [#permalink]
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12 May 2011, 09:14
C1C2 = pi* (R^2r^2) a. R=r+3k does not give R+r value. b really not sure what this option says is it (kR/kr) = 5 then R/r = 5. not sufficient. a+b 5r = r+3k gives 4r = 3k. substituting in original equation gives area in terms of k. Hence not sufficient. E. PS: option B has to be mentioned clearly.
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Re: circles! [#permalink]
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12 May 2011, 16:49
@amit2k9, I think (2) should say : (kR) / (kr – 6) = 1 @AnkitK, please confirm if what I've suggested is correct.
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Re: circles! [#permalink]
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12 May 2011, 18:04
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Let x be the overlapping area.
we were asked find difference in non overlapping areas = \((pi*R^2x)(pi*r^2x)\)
= pi*(R^2r^2) = pi*(R+r)*(Rr)
1. Not sufficient.
we only know Rr ,not R+r.
2. Not sufficient
\(kR/(kr6) = 1\) => R+r = 6/k. but we dont know Rr
Together, its sufficient.
= pi*(R+r)(Rr) = pi*(6/k)(3k) = 18pi.
Answer is C.



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Re: circles! [#permalink]
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13 May 2011, 21:37
@subhashghosh:I regret the delay caused .OA is C only.Yes your approach is correct.
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Re: circles! [#permalink]
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14 May 2011, 10:05
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yes , the explanation is a decent one. we have (Rr) from 1 and (R+r) from 2. if we can eliminate the overlapped area from the equation , the question is solved. So C is the answer.
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Re: circles! [#permalink]
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14 May 2011, 10:19
Good Question .. I assumed that solving both equation will give answer in terms of K so chose E. Rather careless way of thinking...
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Re: circles! [#permalink]
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14 May 2011, 10:20
Good Question .. I assumed that solving both equation will give answer in terms of K so chose E. Rather careless way of thinking...
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Re: circles! [#permalink]
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03 Mar 2012, 04:14
Spidy001 wrote: Let x be the overlapping area.
we were asked find difference in non overlapping areas = \((pi*R^2x)(pi*r^2x)\)
= pi*(R^2r^2) = pi*(R+r)*(Rr)
1. Not sufficient.
we only know Rr ,not R+r.
2. Not sufficient
\(kR/(kr6) = 1\) => R+r = 6/k. but we dont know Rr
Together, its sufficient.
= pi*(R+r)(Rr) = pi*(6/k)(3k) = 18pi.
Answer is C. I have one question in the above explanation. Shouldnt x be deducted only once in the equation ?? .. (pi*R^2x)(pi*r^2x) > (pi*R^2)(pi*r^2)  x



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Re: circles! [#permalink]
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03 Mar 2012, 08:24
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rohitgoel15 wrote: Spidy001 wrote: In the figure, small circel with radius r intersects larger circle with radius R (R>r). If k>0, what is the difference in the areas of the non overlapping parts of two circles?
(1) R=r+3k (2) kR/(kr6)=1
Let x be the overlapping area.
we were asked find difference in non overlapping areas = \((pi*R^2x)(pi*r^2x)\)
= pi*(R^2r^2) = pi*(R+r)*(Rr)
1. Not sufficient.
we only know Rr ,not R+r.
2. Not sufficient
\(kR/(kr6) = 1\) => R+r = 6/k. but we dont know Rr
Together, its sufficient.
= pi*(R+r)(Rr) = pi*(6/k)(3k) = 18pi.
Answer is C. I have one question in the above explanation. Shouldnt x be deducted only once in the equation ?? .. (pi*R^2x)(pi*r^2x) > (pi*R^2)(pi*r^2)  x Look at the diagram: Attachment:
Circles.JPG [ 13.02 KiB  Viewed 6990 times ]
We are asked about the difference between the areas of green and yellow regions. {Green}={Big circle}  {Red} and {Yellow}={Small circle}  {Red}, so, as you can see we should subtract red region (x) from the areas of both circles. Difference between the areas will be: {Green}{Yellow} = ({Big circle}  {Red})  ({Small circle}  {Red}) = {Big circle}  {Small circle}. Hope it's clear.
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Re: In the figure ,small circel with radius r intersects larger [#permalink]
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13 Dec 2013, 05:38
AnkitK wrote: Attachment: circles.png In the figure, small circel with radius r intersects larger circle with radius R (R>r). If k>0, what is the difference in the areas of the non overlapping parts of two circles? (1) R=r+3k (2) kR/(kr6)=1 What does 'k' stand for in the question stem?



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Re: In the figure ,small circel with radius r intersects larger [#permalink]
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13 Dec 2013, 05:47



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Re: In the figure ,small circel with radius r intersects larger [#permalink]
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