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# Each circle has center O. The radius of the smaller circle i

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Joined: 07 Jan 2018
Posts: 560
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Kudos [?]: 485 [0], given: 84

Each circle has center O. The radius of the smaller circle i [#permalink]  13 Jun 2018, 22:09
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66% (00:47) correct 33% (01:40) wrong based on 3 sessions
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Each circle has center O. The radius of the smaller circle is 2 and the radius of the larger circle is 6. If a point is selected at random from the larger circular region, what is the probability that the point will lie in the shaded region?

A. $$\frac{1}{9}$$
B. $$\frac{1}{6}$$
C. $$\frac{2}{3}$$
D. $$\frac{5}{6}$$
E. $$\frac{8}{9}$$
[Reveal] Spoiler: OA
GRE Forum Moderator
Joined: 29 May 2018
Posts: 123
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Kudos [?]: 78 [1] , given: 3

Re: Each circle has center O. The radius of the smaller circle i [#permalink]  13 Jun 2018, 22:19
1
KUDOS
amorphous wrote:
Each circle has center O. The radius of the smaller circle is 2 and the radius of the larger circle is 6. If a point is selected at random from the larger circular region, what is the probability that the point will lie in the shaded region?

A. $$\frac{1}{9}$$
B. $$\frac{1}{6}$$
C. $$\frac{2}{3}$$
D. $$\frac{5}{6}$$
E. $$\frac{8}{9}$$

Total area of larger circle is 36*pi.

Area of smaller circle is 4*pi.

Now To get the area of shaded part ,we need to separate total area - smaller area = 32pi ( 36pi - 4pi).

Now to get the probability for the shaded part we need to take entire area of the maximum circle in the denominator.

Since p(a) = expected records / Total records.
i.e shaded / full circle => 32pi / 36pi => 8/9.

E.
Re: Each circle has center O. The radius of the smaller circle i   [#permalink] 13 Jun 2018, 22:19
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# Each circle has center O. The radius of the smaller circle i

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