mikemcgarry wrote:

Attachment:

2-to-1 rectangle with circle.JPG

In the diagram above, the sides of rectangle ABCD have a ratio AB:BC = 1:2, and the circle is tangent to three sides of the rectangle. If a point is chosen at random inside the rectangle, what is the probability that it is

not inside the circle?

(A) \(\frac{4-{\pi}}{4}\)

(B) \(\frac{4+{\pi}}{4}\)

(C) \(\frac{4+{\pi}}{8}\)

(D) \(\frac{8-{\pi}}{8}\)

(E) \(\frac{8+{\pi}}{8}\)

For a discussion of Geometric Probability, as well as a complete explanation of this particular question, see:

http://magoosh.com/gmat/2013/geometric- ... -the-gmat/Mike

Let the smaller side of square = 2x

Larger side will be = 4x

Radius of the circle will be = x

Area of the Square = 8\(x\)2

Area of the Circle = \(\pi\)\(x\)2

the probability that the point is inside the circle = Area of the Circle/ Area of the Square

= (\(\pi\)\(x\)2)/ (8\(x\)2)

= \(\pi\)/8

the probability that the point is

not inside the circle = 1 - the probability that the point is inside the circle

= 1- \(\pi\)/8

Answer D

Hope it helps

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