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

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GMAT Club Legend
Joined: 07 Jun 2014
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GRE 1: Q167 V156
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Circle A has area a Semicircle B has area a/2 [#permalink]  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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Manager
Joined: 23 Jan 2016
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Re: Circle A has area a Semicircle B has area a/2 [#permalink]  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.
Intern
Joined: 04 Jun 2016
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Re: Circle A has area a Semicircle B has area a/2 [#permalink]  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
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1650 [2] , given: 396

Re: Circle A has area a Semicircle B has area a/2 [#permalink]  16 Sep 2017, 04:21
2
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Expert's post
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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