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# Is the radius of circle with center O an integer?

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Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129061 [0], given: 12190

Is the radius of circle with center O an integer? [#permalink]

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21 Aug 2017, 23:38
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Is the radius of circle with center O an integer?

(1) The circumference of the circle is $$16\pi$$
(2) The ratio of the circumference of the circle to the area of the circle is 1/4
[Reveal] Spoiler: OA

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Kudos [?]: 129061 [0], given: 12190

Director
Joined: 18 Aug 2016
Posts: 512

Kudos [?]: 140 [0], given: 123

GMAT 1: 630 Q47 V29
Re: Is the radius of circle with center O an integer? [#permalink]

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21 Aug 2017, 23:44
Bunuel wrote:
Is the radius of circle with center O an integer?

(1) The circumference of the circle is $$16\pi$$
(2) The ratio of the circumference of the circle to the area of the circle is 1/4

(1) 2*pi*r = 16*pi
r=8
Sufficient

(2) 2/r = 1/4
r=8
Sufficient

D
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Kudos [?]: 140 [0], given: 123

Intern
Joined: 06 Feb 2017
Posts: 27

Kudos [?]: 8 [0], given: 24

Schools: ISB '19, IIMA
Re: Is the radius of circle with center O an integer? [#permalink]

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22 Aug 2017, 00:08
statement 1: The circumference of the circle is 16π
that means, 2*π*r = 16π, hence radius = 8, an integer --> sufficient

statement 2: The ratio of the circumference of the circle to the area of the circle is 1/4
(2*π*r)/(π*r^2) = 1/4
on solving we get: radius = 8, an integer --> sufficient
Hence option D

Kudos [?]: 8 [0], given: 24

Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129061 [0], given: 12190

Re: Is the radius of circle with center O an integer? [#permalink]

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24 Aug 2017, 01:47
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Bunuel wrote:
Is the radius of circle with center O an integer?

(1) The circumference of the circle is $$16\pi$$
(2) The ratio of the circumference of the circle to the area of the circle is 1/4

Is the radius of circle with center O an integer?

(1) The circumference of the circle is $$16\pi$$ --> $$circumference=2\pi{r}=16\pi$$ --> $$r=8=integer$$. Sufficient.

(2) The ratio of the circumference of the circle to the area of the circle is 1/4 --> $$\frac{circumference}{area}=\frac{2\pi{r}}{\pi{r^2}}=\frac{1}{4}$$ --> $$r=8=integer$$. Sufficient.

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Kudos [?]: 129061 [0], given: 12190

Re: Is the radius of circle with center O an integer?   [#permalink] 24 Aug 2017, 01:47
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# Is the radius of circle with center O an integer?

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