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# If A and B are each circles, what is the radius of the larger circle?

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Math Expert
Joined: 02 Sep 2009
Posts: 51121
If A and B are each circles, what is the radius of the larger circle?  [#permalink]

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09 Sep 2018, 07:04
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25% (medium)

Question Stats:

84% (01:12) correct 16% (01:27) wrong based on 31 sessions

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If A and B are each circles, what is the radius of the larger circle?

(1) The larger circle's circumference is 4 times the circumference of the smaller circle.
(2) The area of A minus the area of B is 20π

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Joined: 19 Apr 2017
Posts: 45
If A and B are each circles, what is the radius of the larger circle?  [#permalink]

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25 Sep 2018, 08:27
1
If A and B are each circles, what is the radius of the larger circle?
Larger Circle radius = R ; Smaller Circle radius = r

1) Larger circle's circumference is 4 times the circumference of the smaller circle.

$$2πR=4(2πr)$$
$$R=4r$$
To find the area we need exact value of r. As R=4 and r can be 1 or R=400 and r =100 we can get different areas for the proportional radii. So not sufficient

2) The area of A minus the area of B is $$20π$$
$$πR^2-πr^2=20π$$
$$R^2-r^2=20$$

From 1 and 2
Equate R=4r into $$R^2-r^2=20$$
Since this is a DS question you can stop here you would be able to find the exact values of r and R so answer is C.

But if its a PS question
$$4r^2-r^2=20$$
$$r^2=4/3$$
$$r=2/√3$$
Then
$$R=8/√3$$
ISB, NUS, NTU Moderator
Joined: 11 Aug 2016
Posts: 348
Re: If A and B are each circles, what is the radius of the larger circle?  [#permalink]

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25 Sep 2018, 08:37
1
NO, The answer can not be E, because statement says "The area of A minus the area of B is 20π"
since the value of the difference is +'ve, that means A is the bigger circle.

AvidDreamer09 wrote:
If A and B are each circles, what is the radius of the larger circle?
Larger Circle radius = R ; Smaller Circle radius = r

1) Larger circle's circumference is 4 times the circumference of the smaller circle.

$$2πR=4(2πr)$$
$$R=4r$$
To find the area we need exact value of r. As R=4 and r can be 1 or R=400 and r =100 we can get different areas for the proportional radii. So not sufficient

2) The area of A minus the area of B is $$20π$$
$$πR^2-πr^2=20π$$
$$R^2-r^2=20$$

From 1 and 2
Equate R=4r into $$R^2-r^2=20$$
Since this is a DS question you can stop here you would be able to find the exact values of r and R so answer is C.

But if its a PS question
$$4r^2-r^2=20$$.......=>(4r)^2-r^2=20
$$r^2=4/3$$
$$r=2/√3$$
Then
$$R=8/√3$$
$$πR^2=π8/√3)^2$$

I do however have a doubt
Am i wrong in thinking that Area A can be the bigger circle and area b is the smaller circle. No where in the question is the relation between large small a and b given. So if this question did come up in the test. Could the answer be E????

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Re: If A and B are each circles, what is the radius of the larger circle? &nbs [#permalink] 25 Sep 2018, 08:37
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# If A and B are each circles, what is the radius of the larger circle?

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