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 648 times ]

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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

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