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A Circle, with its radius an integer, is inscribed in a square.
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17 Jul 2017, 11:54
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A Circle, with its radius an integer, is inscribed in a square. What is the probability that a point randomly chosen inside the square will lie outside the circle? 1. Side of the square is a prime number. 2. Another square inscribed in the circle has side \(\sqrt{2}\) Source : Selfmade. == Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
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Re: A Circle, with its radius an integer, is inscribed in a square.
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18 Jul 2017, 00:59
How is statement A sufficient?



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Re: A Circle, with its radius an integer, is inscribed in a square.
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18 Jul 2017, 02:00
darn wrote: How is statement A sufficient? Question says circle's radius is an integer. Now the side of square is 2*radius. So the side is an even number. If, the side is a prime number, then the side must be 2. Because 2 is the only even prime number and hence radius must be 1. Hope this helps..



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Re: A Circle, with its radius an integer, is inscribed in a square.
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19 Jul 2017, 09:20
Bunuel please help with a detailed explanation.
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A Circle, with its radius an integer, is inscribed in a square.
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19 Jul 2017, 11:44
I am a bit confused why you would need a statement to figure this out at all.
If the circle is in the square, then we have the area of the square and the triangle.
Circle = x2 Triangle = π(1/2)x2
Let's say x=2 Ac=4 At=3.14
Probability =.86/2
Does that seam right?



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A Circle, with its radius an integer, is inscribed in a square.
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19 Jul 2017, 12:25
RMD007 wrote: A Circle, with its radius an integer, is inscribed in a square. What is the probability that a point randomly chosen inside the square will lie outside the circle?
1. Side of the square is a prime number.
2. Another square inscribed in the circle has side \(\sqrt{2}\)
You don't need any statements to answer the question. The area of the circle is π r^2, and the area of the square is (2r)^2 = 4r^2, since the diameter of the circle is equal in length to a side of the square, if the circle is inscribed in the square. To find the probability a point chosen randomly from within the square is inside the circle, we just work out what fraction of square the circle takes up  we divide the area of the circle by the area of the square. So a random point in the square is also in the circle with probability π*r^2 / 4*r^2 = π/4, and the probability that point is not in the circle is thus 1  (π/4). The length of the radius doesn't matter. edit  had included another comment, but misread statement 2
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Re: A Circle, with its radius an integer, is inscribed in a square.
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02 Aug 2017, 02:52
RMD007 wrote: A Circle, with its radius an integer, is inscribed in a square. What is the probability that a point randomly chosen inside the square will lie outside the circle? 1. Side of the square is a prime number. 2. Another square inscribed in the circle has side \(\sqrt{2}\) Source : Selfmade. If a circle is inscribed in a square, is it mandatory for the circle to touch the sides of the square? Shouldn't this be mentioned? This way, the answer should be E.
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Re: A Circle, with its radius an integer, is inscribed in a square.
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02 Aug 2017, 04:26
RMD007 wrote: A Circle, with its radius an integer, is inscribed in a square. What is the probability that a point randomly chosen inside the square will lie outside the circle? 1. Side of the square is a prime number. 2. Another square inscribed in the circle has side \(\sqrt{2}\) Source : Selfmade. The original problem statement is good enough to answer this question. We do not need the 2 statements at all, because in such a symmetric arrangement all the peripherial lengths will be proportionate to each other. The required probability = 1  Probability that the point will lie both inside the square and the circle = 1  pi*r^2/(2r)^2= 1  pi/4 = 0.215



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Re: A Circle, with its radius an integer, is inscribed in a square.
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07 Sep 2017, 02:13
1) Side of square is prime Clearly side = a ( prime ) which is = 2r as circle is inscribed P( reqd) = {a^2  (πa^2)/4 }/a^2 => (4π)/4 Definite Ans A/D 2) A square is again inscribed in circle of side √2 => radius =√(2+2) = 2 and side =4 again P reqd = ( 4x4 π4 )/16 p(reqd) = (4π)/4 So D is the AnswerBunuel HOWEVER QUES SHOULD CLEARLY SPECIFY THAT WE HAVE TO TAKE A POINT INSIDE OF FIRST SQUARE AND OUTSIDE OF CIRCLE. THIS COULD BE MISUNDERSTOOD AS A POINT MAY BE TAKEN INSIDE OF THE INNER SQUARE THEN ANS WOULD HAVE BEEN DIFFERENT.== Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
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Re: A Circle, with its radius an integer, is inscribed in a square.
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