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07 Feb 2013, 15:30
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D
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Difficulty:
15%
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Question Stats:
82% (02:08) correct
18%
(02:23)
wrong
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Attachment:
2-to-1 rectangle with circle.JPG [ 19.83 KiB | Viewed 10774 times ]
(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:
https://magoosh.com/gmat/2013/geometric- ... -the-gmat/
Mike
08 Feb 2013, 00:15
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mikemcgarry
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:
https://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
08 Feb 2013, 03:00
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mikemcgarry
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:
https://magoosh.com/gmat/2013/geometric- ... -the-gmat/
Mike
Let's assume the sides are 2 and 1
Hence area of rectangle = 2
Area of circle = \(\frac{{\pi}}{4}\)
Area Outside circle = \(2 - \frac{{\pi}}{4} = \frac{8 - {\pi}}{4}\)
Probability = \(\frac{Area Outside circle}{Area Of Rectangle}\)
= \(\frac{2 - [fraction]{\pi}}{4} = \frac{8 - {\pi}}{8}\)
