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If the center of a circle that has radius of 1 is located at random in

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Joined: 30 May 2018
Posts: 40
GMAT 1: 620 Q34 V42
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If the center of a circle that has radius of 1 is located at random in  [#permalink]

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New post 06 Apr 2019, 01:10
3
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

56% (01:58) correct 44% (01:53) wrong based on 16 sessions

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If the center of a circle that has radius of 1 is located at random in a rectangular region with dimensions 10 by 8, what is the
probability that the circumference of the circle will not exceed the rectangular region?

(A) 1/5
(B) pi/10
(C) 2/5
(D) pi/5
(E) 3/5
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If the center of a circle that has radius of 1 is located at random in  [#permalink]

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New post 06 Apr 2019, 02:02
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MBA20 wrote:
If the center of a circle that has radius of 1 is located at random in a rectangular region with dimensions 10 by 8, what is the
probability that the circumference of the circle will not exceed the rectangular region?

(A) 1/5
(B) pi/10
(C) 2/5
(D) pi/5
(E) 3/5


For circle to remain contained within the rectangle, the centre must be kept at a distance of min 1 unit from boundaries of rectangle

i.e. Centre of the circle may lie within the rectangle of dimension (8-2) and (10-2) i.e. 6*8 region

Probability = favourable Region / Total region = 6*8 / 10*8 = 3/5

Answer: Option E
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