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# In the figure ,small circel with radius r intersects larger

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Manager
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11 May 2011, 22:45
4
1
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Difficulty:

85% (hard)

Question Stats:

56% (01:37) correct 44% (02:03) wrong based on 231 sessions

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circles.png [ 7.66 KiB | Viewed 9015 times ]
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/(kr-6)=-1

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03 Mar 2012, 07:24
1
4
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/(kr-6)=-1

Let x be the overlapping area.

we were asked find difference in non overlapping areas = $$(pi*R^2-x)-(pi*r^2-x)$$

= pi*(R^2-r^2) = pi*(R+r)*(R-r)

1. Not sufficient.

we only know R-r ,not R+r.

2. Not sufficient

$$kR/(kr-6) = -1$$
=> R+r = 6/k. but we dont know R-r

Together, its sufficient.

= pi*(R+r)(R-r) = pi*(6/k)(3k) = 18pi.

I have one question in the above explanation.

Shouldnt x be deducted only once in the equation ?? ..
(pi*R^2-x)-(pi*r^2-x) --> (pi*R^2)-(pi*r^2) - x

Look at the diagram:
Attachment:

Circles.JPG [ 13.02 KiB | Viewed 8135 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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12 May 2011, 03:59
5
Area 1 = OVerlap + ( pi*r^2 - Overlap)

Area 2 = OVerlap + ( pi*R^2 - Overlap)

So ( pi*R^2 - Overlap) - ( pi*r^2 - Overlap) = ?

= pi(R-r)(r+R)

(1)

R-r = 3k

Insufficient

(2)

kR = -kr +6

=> r+R = 6/k

Insufficient

(1) + (2)
So difference = pi* 3k * 6/k = 18pi

What is the OA ?
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##### General Discussion
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12 May 2011, 08:14
C1-C2 = pi* (R^2-r^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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12 May 2011, 15:49
@amit2k9, I think (2) should say :
(kR) / (kr – 6) = -1

@AnkitK, please confirm if what I've suggested is correct.
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12 May 2011, 17:04
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Let x be the overlapping area.

we were asked find difference in non overlapping areas = $$(pi*R^2-x)-(pi*r^2-x)$$

= pi*(R^2-r^2) = pi*(R+r)*(R-r)

1. Not sufficient.

we only know R-r ,not R+r.

2. Not sufficient

$$kR/(kr-6) = -1$$
=> R+r = 6/k. but we dont know R-r

Together, its sufficient.

= pi*(R+r)(R-r) = pi*(6/k)(3k) = 18pi.

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13 May 2011, 20:37
@subhashghosh:I regret the delay caused .OA is C only.Yes your approach is correct.
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14 May 2011, 09:05
1
yes , the explanation is a decent one.
we have (R-r) from 1 and (R+r) from 2. if we can eliminate the overlapped area from the equation , the question is solved.
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14 May 2011, 09:19
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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14 May 2011, 09:20
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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03 Mar 2012, 03:14
Spidy001 wrote:
Let x be the overlapping area.

we were asked find difference in non overlapping areas = $$(pi*R^2-x)-(pi*r^2-x)$$

= pi*(R^2-r^2) = pi*(R+r)*(R-r)

1. Not sufficient.

we only know R-r ,not R+r.

2. Not sufficient

$$kR/(kr-6) = -1$$
=> R+r = 6/k. but we dont know R-r

Together, its sufficient.

= pi*(R+r)(R-r) = pi*(6/k)(3k) = 18pi.

I have one question in the above explanation.

Shouldnt x be deducted only once in the equation ?? ..
(pi*R^2-x)-(pi*r^2-x) --> (pi*R^2)-(pi*r^2) - x
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Re: In the figure ,small circel with radius r intersects larger  [#permalink]

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13 Dec 2013, 04:38
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/(kr-6)=-1

What does 'k' stand for in the question stem?
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Joined: 02 Sep 2009
Posts: 52231
Re: In the figure ,small circel with radius r intersects larger  [#permalink]

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13 Dec 2013, 04:47
jlgdr wrote:
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/(kr-6)=-1

What does 'k' stand for in the question stem?

k is just some number.
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Re: In the figure ,small circel with radius r intersects larger  [#permalink]

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28 Oct 2018, 00:59
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Re: In the figure ,small circel with radius r intersects larger &nbs [#permalink] 28 Oct 2018, 00:59
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