NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 00:47 It is currently 25 Apr 2024, 00:47
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
G
mikemcgarry
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4452
Own Kudos [?]: 28571 [17]
Given Kudos: 130
In the diagram above, the sides of rectangle ABCD have a rat [#permalink] New post   07 Feb 2013, 15:30
1
Kudos
16
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

82% (02:09) correct 18% (02:22) wrong based on 298 sessions
Hide Show timer Statistics
Attachment:
2-to-1 rectangle with circle.JPG
2-to-1 rectangle with circle.JPG [ 19.83 KiB | Viewed 9965 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:
https://magoosh.com/gmat/2013/geometric- ... -the-gmat/

Mike :-)
ShowHide Answer
Official Answer
D
User avatar
B
fameatop
Senior Manager
Senior Manager
Joined: 24 Aug 2009
Posts: 388
Own Kudos [?]: 2260 [2]
Given Kudos: 276
Concentration: Finance
Schools:Harvard, Columbia, Stern, Booth, LSB,
Send PM
Re: 2-to-1 rectangle with circle [#permalink] New post   08 Feb 2013, 00:15
2
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:
https://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 = 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
User avatar
MacFauz
VP
VP
Joined: 02 Jul 2012
Posts: 1011
Own Kudos [?]: 3119 [4]
Given Kudos: 116
Location: India
Concentration: Strategy
Schools: Ross '16 (D) McCombs '16 (D) Kenan-Flagler '16 (WA) Olin '16 (M$) Tepper '16 (D)
GMAT 1: 740 Q49 V42
GPA: 3.8
WE:Engineering (Energy and Utilities)
Send PM
Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink] New post   08 Feb 2013, 03:00
4
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:
https://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 = \(\frac{Area Outside circle}{Area Of Rectangle}\)

= \(\frac{2 - [fraction]{\pi}}{4} = \frac{8 - {\pi}}{8}\)
User avatar
agrchandan
Intern
Intern
Joined: 15 Jan 2013
Posts: 12
Own Kudos [?]: 79 [0]
Given Kudos: 6
Concentration: Finance, Operations
GPA: 4
Send PM
Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink] New post   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
User avatar
nave
Manager
Manager
Joined: 08 Dec 2012
Posts: 55
Own Kudos [?]: 1328 [0]
Given Kudos: 31
Location: United Kingdom
WE:Engineering (Consulting)
Send PM
Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink] New post   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 - \(\frac{pi}{8}\) = \(\frac{(8-pi)}{8}\)


p.s how does one type the symbol of pi?
User avatar
G
mikemcgarry
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4452
Own Kudos [?]: 28571 [1]
Given Kudos: 130
Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink] New post   11 Feb 2013, 12:17
1
Bookmarks
Expert Reply
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 :-)
User avatar
Senthil7
Senior Manager
Senior Manager
Joined: 31 Mar 2016
Posts: 325
Own Kudos [?]: 195 [0]
Given Kudos: 197
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE:Operations (Commercial Banking)
Send PM
GMAT ToolKit User
Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink] New post   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
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32662
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink] New post   15 Jan 2023, 12:39
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 Club Bot
gmatclubot
Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink]
15 Jan 2023, 12:39
Moderators:
Bunuel
Math Expert
92901 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions