Find all School-related info fast with the new School-Specific MBA Forum

It is currently 31 Jul 2014, 20:27

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the diagram above, the sides of rectangle ABCD have a rat

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 1961
Followers: 473

Kudos [?]: 1878 [0], given: 29

In the diagram above, the sides of rectangle ABCD have a rat [#permalink] New post 07 Feb 2013, 14:30
Expert's post
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

81% (01:57) correct 19% (01:19) wrong based on 68 sessions
Attachment:
2-to-1 rectangle with circle.JPG
2-to-1 rectangle with circle.JPG [ 19.83 KiB | Viewed 1138 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- ... -the-gmat/

Mike :-)
[Reveal] Spoiler: OA

_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesVeritas Prep GMAT Discount Codes
1 KUDOS received
Director
Director
avatar
Joined: 24 Aug 2009
Posts: 510
Schools: Harvard, Columbia, Stern, Booth, LSB,
Followers: 8

Kudos [?]: 355 [1] , given: 241

Re: 2-to-1 rectangle with circle [#permalink] New post 07 Feb 2013, 23:15
1
This post received
KUDOS
mikemcgarry wrote:
Attachment:
2-to-1 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- ... -the-gmat/
Mike :-)



Let the smaller side of square = 2x
Larger side will be = 4x
Radius of the circle will be = x
Area of the Square = 8x2
Area of the Circle = \pix2

the probability that the point is inside the circle = Area of the Circle/ Area of the Square
= (\pix2)/ (8x2)
= \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

1 KUDOS received
Moderator
Moderator
User avatar
Joined: 02 Jul 2012
Posts: 1226
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 61

Kudos [?]: 638 [1] , given: 116

GMAT Tests User Premium Member
Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink] New post 08 Feb 2013, 02:00
1
This post received
KUDOS
mikemcgarry wrote:
Attachment:
2-to-1 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- ... -the-gmat/

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
Intern
avatar
Joined: 15 Jan 2013
Posts: 39
Concentration: Finance, Operations
GPA: 4
Followers: 0

Kudos [?]: 15 [0], given: 6

Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink] New post 08 Feb 2013, 08:08
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
Manager
avatar
Joined: 08 Dec 2012
Posts: 64
Location: United Kingdom
GMAT 1: 710 Q0 V0
WE: Engineering (Consulting)
Followers: 1

Kudos [?]: 44 [0], given: 31

Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink] New post 09 Feb 2013, 17:58
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{(8-pi)}{8}


p.s how does one type the symbol of pi?
Expert Post
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 1961
Followers: 473

Kudos [?]: 1878 [0], given: 29

Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink] New post 11 Feb 2013, 11:17
Expert's post
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

Image

Image

Re: In the diagram above, the sides of rectangle ABCD have a rat   [#permalink] 11 Feb 2013, 11:17
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic In the figure above ABCD is a rectangle and point K is the c HerrGrau 13 30 May 2014, 07:29
1 Experts publish their posts in the topic In the rectangle above, A is the midpoint of the side, and DeeptiM 6 15 Aug 2011, 01:57
1 ABCD forms a rectangle with sides x and y. z is the bmwhype2 5 15 Feb 2008, 03:55
Experts publish their posts in the topic Figure ABCD is a rectangle with sides of length x centimete dynocomet 6 15 Jul 2007, 18:45
1 Rectangle ABCD is inscribed in a circle as shown above. What cloaked_vessel 9 26 Mar 2005, 08:12
Display posts from previous: Sort by

In the diagram above, the sides of rectangle ABCD have a rat

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.