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

It is currently 18 Apr 2014, 23:14

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 figure shown, if the area of the shaded region is 3

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Director
Director
Joined: 17 Oct 2005
Posts: 944
Followers: 1

Kudos [?]: 8 [0], given: 0

GMAT Tests User
In the figure shown, if the area of the shaded region is 3 [#permalink] New post 04 Feb 2006, 15:52
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

39% (02:25) correct 60% (01:38) wrong based on 46 sessions
Image
In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?

A. 4
B. 3
C. 2
D. \sqrt{3}
E. \sqrt{2}

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figure-shown-if-the-area-of-the-shaded-region-is-3-t-104668.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 31 Oct 2013, 02:55, edited 4 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesVeritas Prep GMAT Discount Codes
1 KUDOS received
VP
VP
Joined: 21 Sep 2003
Posts: 1071
Location: USA
Followers: 3

Kudos [?]: 26 [1] , given: 0

GMAT Tests User
 [#permalink] New post 04 Feb 2006, 15:56
1
This post received
KUDOS
Two times?

Smaller circle = pi*r^2
Larger circle = pi*R^2

Given ,

pi*R^2 - pi*r^2 = 3* pi*r^2

R^2 = 4*pi*r^2

R = 2*r

Ratio of circimference = 2*pi*R/2*pi*r = 2
_________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

VP
VP
Joined: 06 Jun 2004
Posts: 1065
Location: CA
Followers: 2

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

GMAT Tests User
 [#permalink] New post 04 Feb 2006, 16:32
Agree with Giddi's working :wink:
_________________

Don't be afraid to take a flying leap of faith.. If you risk nothing, than you gain nothing...

Director
Director
User avatar
Joined: 04 Jan 2006
Posts: 928
Followers: 1

Kudos [?]: 10 [0], given: 0

GMAT Tests User
 [#permalink] New post 04 Feb 2006, 16:43
I think it should be 1+ sqrt3 or 1 - sqrt3

Area of the shaded region is : Pi(R-r)^2 = 3 Pi r^2
(R-r)^2 = 3r^2
R-r =rsqrt3
or
R-r = -rsqrt3

If i See the options available for the PS, I might be able to answer it..

OA?
Senior Manager
Senior Manager
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 395
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 70 [0], given: 153

Re: In the figure shown, if the area of the shaded region is 3 [#permalink] New post 31 Oct 2013, 02:09
Let small circle radius = a
Big circle radius = (a+b)
Area of shaded region = PIE (a+b)^2 - PIE a^2 = PIE b (2a+b).............. (i)
Area of shaded region is thrice that of Area of smaller circle
So, 3 PIE a^2 = PIE b (2a+b)

3a^2 - 2ab - b^2 = 0
Solving above quadratic equation gives a = b
It means radius of bigger circle is twice than radius of smaller circle

Circumference = 2 PIE (radius) means
Circumference of bigger circle is twice than circumference of smaller circle
Attachments

cir.JPG
cir.JPG [ 11.93 KiB | Viewed 754 times ]


_________________

Kindly press "Kudos" to appreciate

Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17317
Followers: 2874

Kudos [?]: 18388 [0], given: 2348

GMAT Tests User CAT Tests
Re: In the figure shown, if the area of the shaded region is 3 [#permalink] New post 31 Oct 2013, 02:55
Expert's post
Image
In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?

A. 4
B. 3
C. 2
D. \sqrt{3}
E. \sqrt{2}

The area of the shaded region is area_{shaded}=\pi{R^2}-\pi{r^2} and the area of the smaller circle is area_{small}=\pi{r^2}. Given: \pi{R^2}-\pi{r^2}=3\pi{r^2} --> R^2=4r^2 --> R=2r;

Now, the ratio of the circumference of the larger circle to the that of the smaller circle is \frac{C}{c}=\frac{2\pi{R}}{2\pi{r}}=\frac{{2r}}{{r}}=2.

Answer: C.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figure-shown-if-the-area-of-the-shaded-region-is-3-t-104668.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Re: In the figure shown, if the area of the shaded region is 3   [#permalink] 31 Oct 2013, 02:55
    Similar topics Author Replies Last post
Similar
Topics:
Popular new posts PS - Area of shaded region vikramm 14 14 Oct 2005, 21:04
New posts Area of shaded region_PS brothers 4 28 Nov 2009, 03:18
New posts 1 area of shaded region xcusemeplz2009 7 10 Dec 2009, 20:08
New posts Experts publish their posts in the topic In the figure shown, if the area of the shaded region is 3 t monirjewel 6 11 Nov 2010, 08:09
New posts Experts publish their posts in the topic What is the area of the shaded region? joshoowa 2 01 Mar 2014, 19:44
Display posts from previous: Sort by

In the figure shown, if the area of the shaded region is 3

  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®.