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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, 22:02
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[GMAT math practice question]

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ab.png [ 6.92 KiB | Viewed 459 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. $$\frac{4}{9}$$
[Reveal] Spoiler: OA

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Re: In the above figure, the smaller circle has a radius of 1, and the [#permalink]

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30 Dec 2017, 06:47
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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
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circle inside circle.png [ 7.31 KiB | Viewed 320 times ]

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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, 01:31
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=>
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.
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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, 04:08
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 $$\frac{4}{9}$$.

Therefore, the answer is E.

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, 04:08
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In the above figure, the smaller circle has a radius of 1, and the

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