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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: 47161
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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15% (low)

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89% (00:49) correct 11% (01:00) wrong based on 36 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

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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
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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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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

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27 Apr 2018, 22:50
2πx=(1/2)*2πy
X=y/2

1) get value of y using πr^2
Then calculate x
Sufficient

II)get value of y using 2πr
Then calculate x
Sufficient

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Re: The circumference of circle X is 1/2 the circumference of circle Y. Wh &nbs [#permalink] 27 Apr 2018, 22:50
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# The circumference of circle X is 1/2 the circumference of circle Y. Wh

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