Author 
Message 
TAGS:

Hide Tags

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4128

In the diagram above, the sides of rectangle ABCD have a rat [#permalink]
Show Tags
07 Feb 2013, 15:30
Question Stats:
77% (02:19) correct
23% (01:36) wrong based on 150 sessions
HideShow timer Statistics
Attachment:
2to1 rectangle with circle.JPG [ 19.83 KiB  Viewed 3233 times ]
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: http://magoosh.com/gmat/2013/geometric ... thegmat/Mike
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Mike McGarry Magoosh Test Prep





Director
Joined: 24 Aug 2009
Posts: 503
Schools: Harvard, Columbia, Stern, Booth, LSB,

Re: 2to1 rectangle with circle [#permalink]
Show Tags
08 Feb 2013, 00:15
2
This post received KUDOS
mikemcgarry wrote: Attachment: 2to1 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: http://magoosh.com/gmat/2013/geometric ... thegmat/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
_________________
If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth Game Theory
If you have any question regarding my post, kindly pm me or else I won't be able to reply



Moderator
Joined: 02 Jul 2012
Posts: 1223
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink]
Show Tags
08 Feb 2013, 03:00
2
This post received KUDOS
mikemcgarry wrote: Attachment: 2to1 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: http://magoosh.com/gmat/2013/geometric ... thegmat/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 = \(\frac{Area Outside circle}{Area Of Rectangle}\) = \(\frac{2  [fraction]{\pi}}{4} = \frac{8  {\pi}}{8}\)
_________________
Did you find this post helpful?... Please let me know through the Kudos button.
Thanks To The Almighty  My GMAT Debrief
GMAT Reading Comprehension: 7 Most Common Passage Types



Intern
Joined: 15 Jan 2013
Posts: 39
Concentration: Finance, Operations
GPA: 4

Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink]
Show Tags
08 Feb 2013, 09:08
Assume the sides of the rectangle to be 2 and 4. Diameter of the circle=AB=2 Radius of the circle=1 Area of circle= {\pi} Area of the rectangle = 2*4=8 Area of the rectangle outside circle = 8{\pi} So, probability= 8{\pi}/8



Manager
Joined: 08 Dec 2012
Posts: 66
Location: United Kingdom
WE: Engineering (Consulting)

Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink]
Show Tags
09 Feb 2013, 18:58
Let us assume the sides of the rectangle be 1 and 2, so the area of the rectangle is 2 which implies that the circle is inscribed within a square whose area is 1.
Area of circle inscribed within a square is \(\frac{pi}{4}\) times the area of square = \(\frac{pi}{4}\)
Probability of point not inside the circle = 1  probability of point inside the circle = 1  \((pi/4)/2\) = 1  \(\frac{pi}{8}\) = \(\frac{(8pi)}{8}\)
p.s how does one type the symbol of pi?



Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4128

Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink]
Show Tags
11 Feb 2013, 12:17
nave81 wrote: p.s how does one type the symbol of pi? Dear nave81  It's funny. I was wondering this same thing, and I had to quote a response of Bunuel in which he used the \({\pi}\) symbol to see what it looked like in the html text. Basically, you type {\pi}  (open curvy brackets)(backstroke)("pi")(close curvy brackets)  and then highlight that in the "math" delimiters  the m button, under the bold button in the rtf bar at the top of the editing window, does this. All math symbols need to be within the "math" delimiters. Does this make sense? Mike
_________________
Mike McGarry Magoosh Test Prep



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15939

Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink]
Show Tags
19 Aug 2015, 04:57
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Senior Manager
Joined: 31 Mar 2016
Posts: 411
Location: India
Concentration: Operations, Finance
GPA: 3.8
WE: Operations (Commercial Banking)

Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink]
Show Tags
08 Jun 2016, 11:16
Good question kudos given!
Probability = (Area of rectangle  Area of circle) / area of rectangle
b = breadth , l = length, r = radius. we know l = 2b so area of rectangle = l * b = 2b^2 . we can see the diameter of the circle = b hence radius = b/2 area will be π(b^2) / 4
Simplifying we get (8  π)/8




Re: In the diagram above, the sides of rectangle ABCD have a rat
[#permalink]
08 Jun 2016, 11:16








Similar topics 
Author 
Replies 
Last post 
Similar Topics:


3


In the figure above,ABCD is a rectangle. If the area of triangle AEB

arabella 
3 
03 Apr 2017, 23:51 



In the figure above, rectangle ABCD is attached to semicircle CFD. If

Bunuel 
1 
19 Nov 2015, 00:19 

8


In the figure above, ABCD is a rectangle inscribed in a circle. Angle

Bunuel 
8 
27 Mar 2017, 10:18 

4


In the figure above, ABCD is a rectangle inscribed in a circle. If the

Bunuel 
7 
25 May 2017, 19:01 

4


In the figure above, the perimeter of rectangle ABCD is 30

guerrero25 
4 
27 Mar 2017, 10:25 



