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Circles X and Y are concentric. If the radius of circle X is three

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Circles X and Y are concentric. If the radius of circle X is three [#permalink]

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New post 26 Jun 2013, 02:11
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Circles X and Y are concentric. If the radius of circle X is three times that of circle Y, what is the probability that a point selected inside circle X at random will be outside circle Y?

(A) 13

(B) \(\frac{\pi}{3}\)

(C) \(\frac{\pi}{2}\)

(D) 5/6

(E) 8/9
[Reveal] Spoiler: OA

Last edited by guerrero25 on 26 Jun 2013, 02:26, edited 1 time in total.
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Circles X and Y are concentric. If the radius of circle X is three [#permalink]

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guerrero25 wrote:
Circles X and Y are concentric. If the radius of circle X is three times that of circle Y, what is the probability that a point selected inside circle X at random will be outside circle Y?

(A) 13

(B) \(\frac{\pi}{3}\)

(C) \(\frac{\pi}{2}\)

(D) 5/6

(E) 8/9


Say the radius of the smaller circle (Y) is 1, then the radius of the larger circle would be 3.

The area of X = \(\pi{R^2}=9\pi\);
The area of Y = \(\pi{r^2}=\pi\).

The probability = (Favorable)/(Total) = \(\frac{9\pi-\pi}{9\pi}=\frac{8}{9}\).

Answer: E.
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Re: Circles X and Y are concentric. If the radius of circle X is three [#permalink]

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New post 14 Oct 2013, 00:54
Small circle radius = a, so area = PI a ^ 2

Large circle radius = 3a, so area = 9. PI a ^ 2

Area of shaded region = 9PI a^2 - PI a^2 = 8 PI a^2

So, probability = ( 8 PI a^2 ) / (9 PI a^2 )

= 8/9 = Answer = E
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Re: Circles X and Y are concentric. If the radius of circle X is three [#permalink]

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New post 20 Jan 2018, 07:58
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Re: Circles X and Y are concentric. If the radius of circle X is three   [#permalink] 20 Jan 2018, 07:58
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