Author 
Message 
Senior Manager
Status: Countdown Begins...
Joined: 03 Jul 2016
Posts: 312
Location: India
Concentration: Technology, Strategy
GPA: 3.7
WE: Information Technology (Consulting)

A Circle, with its radius an integer, is inscribed in a square. [#permalink]
Show Tags
17 Jul 2017, 11:54
Question Stats:
38% (01:11) correct 62% (01:27) wrong based on 87 sessions
HideShow timer Statistics
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 GMAT Club Team == This is not a quality discussion. 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.
Official Answer and Stats are available only to registered users. Register/ Login.



Manager
Joined: 12 Sep 2016
Posts: 76
Location: India
GPA: 3.15

Re: A Circle, with its radius an integer, is inscribed in a square. [#permalink]
Show Tags
18 Jul 2017, 00:59
How is statement A sufficient?



Senior Manager
Status: Countdown Begins...
Joined: 03 Jul 2016
Posts: 312
Location: India
Concentration: Technology, Strategy
GPA: 3.7
WE: Information Technology (Consulting)

Re: A Circle, with its radius an integer, is inscribed in a square. [#permalink]
Show Tags
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..



Intern
Joined: 02 May 2016
Posts: 20
Location: Nigeria
Concentration: Strategy, Entrepreneurship
GPA: 3.52
WE: Operations (Retail Banking)

Re: A Circle, with its radius an integer, is inscribed in a square. [#permalink]
Show Tags
19 Jul 2017, 09:20
Bunuel please help with a detailed explanation.
Regards



Intern
Joined: 18 Aug 2015
Posts: 17
Location: United States
GPA: 3.38

A Circle, with its radius an integer, is inscribed in a square. [#permalink]
Show Tags
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?



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1345

A Circle, with its radius an integer, is inscribed in a square. [#permalink]
Show Tags
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
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



Current Student
Joined: 22 Sep 2016
Posts: 198
Location: India
GPA: 4

Re: A Circle, with its radius an integer, is inscribed in a square. [#permalink]
Show Tags
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.
_________________
Desperately need 'KUDOS' !!



Intern
Joined: 15 Oct 2016
Posts: 31

Re: A Circle, with its radius an integer, is inscribed in a square. [#permalink]
Show Tags
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



Senior Manager
Joined: 29 Jun 2017
Posts: 499
GPA: 4
WE: Engineering (Transportation)

Re: A Circle, with its radius an integer, is inscribed in a square. [#permalink]
Show Tags
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 GMAT Club Team == This is not a quality discussion. 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.
_________________
Give Kudos for correct answer and/or if you like the solution.




Re: A Circle, with its radius an integer, is inscribed in a square.
[#permalink]
07 Sep 2017, 02:13






