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# The circumference of circle X is 1/2 the circumference of circle Y. Wh

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Math Expert
Joined: 02 Sep 2009
Posts: 44614
The circumference of circle X is 1/2 the circumference of circle Y. Wh [#permalink]

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13 Apr 2018, 01:26
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79% (00:45) correct 21% (00:51) wrong based on 13 sessions

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The circumference of circle X is 1/2 the circumference of circle Y. What is the area of circle X?

(1) The area of circle Y is $$100\pi$$ ft^2.
(2) The circumference of circle Y is $$20\pi$$ ft
[Reveal] Spoiler: OA

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Re: The circumference of circle X is 1/2 the circumference of circle Y. Wh [#permalink]

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13 Apr 2018, 01:39
Bunuel wrote:
The circumference of circle X is 1/2 the circumference of circle Y. What is the area of circle X?

(1) The area of circle Y is $$100\pi$$ ft^2.
(2) The circumference of circle Y is $$20\pi$$ ft

Since we know the relationship between R1 and R2 of the two circles..

2*pi*R2 = 0.5 * 2*pi*R1

Anything that gives R1 will give us R2.

Hence option (D) is our answer without solving for the actual values of anything.

Best,

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Re: The circumference of circle X is 1/2 the circumference of circle Y. Wh [#permalink]

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13 Apr 2018, 03:15
1 stmt gives 2 output
2 stmt gives correct radius which will be calcuated for Area of Circle X
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Re: The circumference of circle X is 1/2 the circumference of circle Y. Wh [#permalink]

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13 Apr 2018, 03:18
1
KUDOS
Expert's post
rohitf23 wrote:
1 stmt gives 2 output
2 stmt gives correct radius which will be calcuated for Area of Circle X

Yes statement 1 gives two output ..$$r^2 = 100...$$ r = 10 or -10
But we are looking at radius and it cannot be NEGATIVE so r = 10
suff
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Re: The circumference of circle X is 1/2 the circumference of circle Y. Wh [#permalink]

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13 Apr 2018, 05:40
1
KUDOS
Cx = 2 pi r
Cy = pi r

Statement 1
Ay=100 pi
also, Ay=C^2/4 pi ==> 100 pi = pi^2 r^2/4 pi ==>r = +/- 20, but radius will be positive so r=20

Statement 2

gives us the same info as statement 1

Cy=20 pi = pi r ==> r=20

Therefore ans is D
Re: The circumference of circle X is 1/2 the circumference of circle Y. Wh   [#permalink] 13 Apr 2018, 05:40
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