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# In the above figure, the smaller circle has a radius of 1, and the

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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In the above figure, the smaller circle has a radius of 1, and the  [#permalink]

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28 Dec 2017, 23:02
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Difficulty:

65% (hard)

Question Stats:

71% (02:03) correct 29% (01:32) wrong based on 62 sessions

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[GMAT math practice question]

Attachment:

ab.png [ 6.92 KiB | Viewed 1217 times ]

In the above figure, the smaller circle has a radius of 1, and the larger circle has a radius of 3. The center of the smaller circle moves randomly around inside the larger circle. What is the probability that the whole of the smaller circle lies inside the larger circle at any given time?

A. $$\frac{1}{4}$$
B. $$\frac{2}{5}$$
C. $$\frac{5}{6}$$
D. $$\frac{3}{8}$$
E. $$\frac{4}{9}$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 8007 Re: In the above figure, the smaller circle has a radius of 1, and the [#permalink] ### Show Tags 30 Dec 2017, 07:47 3 MathRevolution wrote: [GMAT math practice question] Attachment: The attachment ab.png is no longer available In the above figure, the smaller circle has a radius of 1, and the larger circle has a radius of 3. The center of the smaller circle moves randomly around inside the larger circle. What is the probability that the whole of the smaller circle lies inside the larger circle at any given time? A. $$\frac{1}{4}$$ B. $$\frac{2}{5}$$ C. $$\frac{5}{6}$$ D. $$\frac{3}{8}$$ E. $$\frac{4}{9}$$ Hi .. the smaller circle will remain completely inside larger circle till the smaller circle has its center atleast 1 from circumference of larger circle.. so it results in a smaller circle with radius 2 inside this larger circle with same center.. If the circle(red in clour) has its center in COMMON area of two concentric circles.. SEE attached figure so Probability will depend on the area of these two concentric circle.. probability that the whole of the smaller circle lies inside the larger circle at any given time = $$\frac{pi*2^2}{pi*3^2} = \frac{4}{9}$$ E.. OA is wrong and also the choices are not in ascending/descending order, a must in gmat Q Attachments circle inside circle.png [ 7.31 KiB | Viewed 1082 times ] _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8025 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: In the above figure, the smaller circle has a radius of 1, and the [#permalink] ### Show Tags 01 Jan 2018, 02:31 Attachment: 123.png [ 11.67 KiB | Viewed 998 times ] => In order for the whole of the smaller circle to lie inside the larger circle, the center of the smaller circle must lie inside a circle of radius 2 that is concentric with the larger circle. The ratio of the area of the circle of radius 2 to the area of the larger circle is $$\frac{4}{9}$$. Therefore, the answer is E. Answer : E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: In the above figure, the smaller circle has a radius of 1, and the  [#permalink]

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01 Jan 2018, 05:08
MathRevolution wrote:
Attachment:
123.png

=>
In order for the whole of the smaller circle to lie inside the larger circle, the center of the smaller circle must lie inside a circle of radius 2 that is concentric with the larger circle.
The ratio of the area of the circle of radius 2 to the area of the larger circle is $$\frac{4}{9}$$.

Hi MathRevolution

The OA for this question is wrong. Correcting it to E
Re: In the above figure, the smaller circle has a radius of 1, and the   [#permalink] 01 Jan 2018, 05:08
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