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Circle A has area a Semicircle B has area a/2

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Circle A has area a Semicircle B has area a/2 [#permalink] New post 30 Jun 2016, 18:20
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Question Stats:

66% (00:06) correct 33% (01:24) wrong based on 9 sessions
Circle A has area \(a\)
Semicircle B has area \(a/2\)

Quantity A
Quantity B
The circumference of Circle A
Twice the perimeter of semicircle B


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: Circle A has area a Semicircle B has area a/2 [#permalink] New post 04 Jul 2016, 20:50
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Both the circle A and Circle B have same circumference (As they have the same area). Now twice the perimeter of semicircle B will be 2 diameters more than perimeter of circle A. Hence answer B.
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Re: Circle A has area a Semicircle B has area a/2 [#permalink] New post 15 Sep 2017, 20:49
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Here A and 2*B circle has same area.hence same perimeter
Perimeter of 2*B circle=twice the perimeter of B=perimeter of A

So ans is (C)

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GMAT Club Legend
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Posts: 4749
GRE 1: Q167 V156
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Kudos [?]: 1650 [2] , given: 396

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Re: Circle A has area a Semicircle B has area a/2 [#permalink] New post 16 Sep 2017, 04:21
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saifulislampharmadu wrote:
Here A and 2*B circle has same area.hence same perimeter
Perimeter of 2*B circle=twice the perimeter of B=perimeter of A

So ans is (C)

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Circle A and B have the same area i.e. same radius.
However the option B is stated as = \(2 \times(\pi r +2r)\). Twice the perimeter of semicirle B is not Equal to perimeter of circle B since there is an additional term of the diameter in the perimeter.
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Re: Circle A has area a Semicircle B has area a/2   [#permalink] 16 Sep 2017, 04:21
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