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

It is currently 21 Aug 2014, 04:33

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

Three congruent circles overlap in such a way that each circ

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 09 Feb 2013
Posts: 121
Followers: 1

Kudos [?]: 205 [0], given: 17

Three congruent circles overlap in such a way that each circ [#permalink] New post 11 Mar 2013, 23:48
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

80% (01:54) correct 20% (01:38) wrong based on 137 sessions
Attachment:
2.jpg
2.jpg [ 8.43 KiB | Viewed 2419 times ]
Three congruent circles overlap in such a way that each circle intersects the centers of both of the other circles, as shown below. If the radius of each of the circles is 8, what is the area of the central section where all three circles overlap?

A. 16\sqrt{3}

B. 32(\pi-\sqrt{3})

C. 16(\pi+\sqrt{3})

D. 32\pi

E. 32(\pi+\sqrt{3})
[Reveal] Spoiler: OA

_________________

Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.


Last edited by Bunuel on 12 Mar 2013, 01:53, edited 1 time in total.
Edited the question.
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19036
Followers: 3360

Kudos [?]: 24445 [3] , given: 2677

Re: Three congruent circles overlap in such a way that each circ [#permalink] New post 12 Mar 2013, 02:10
3
This post received
KUDOS
Expert's post
emmak wrote:
Attachment:
The attachment 2.jpg is no longer available
Three congruent circles overlap in such a way that each circle intersects the centers of both of the other circles, as shown below. If the radius of each of the circles is 8, what is the area of the central section where all three circles overlap?

A. 16\sqrt{3}

B. 32(\pi-\sqrt{3})

C. 16(\pi+\sqrt{3})

D. 32\pi

E. 32(\pi+\sqrt{3})


I'd go with approximation with this question. Look at the diagram below:
Attachment:
Circles.png
Circles.png [ 21.94 KiB | Viewed 2395 times ]
Notice that triangle ABC is equilateral (all sides are radii of the circles, for example AB and AC are radii of the lower circle and BC is radius of both upper circles). This implies that angle A is 60 degrees, thus the area of sector ABC (yellow region in the lower circle) is 1/6th of the area of the circle, so it's area is \frac{8^2\pi}{6}\approx{34}.

Now, the area of the region we need to find must be more than this but not too much. Only B fits.

Answer: B.

Hope it's clear.
_________________

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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 20 Jan 2013
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 2

Re: Three congruent circles overlap in such a way that each circ [#permalink] New post 13 Mar 2013, 19:19
The area of the overlapping section should be little less than the half of the area of the circle , and only B fits
Expert Post
3 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4668
Location: Pune, India
Followers: 1072

Kudos [?]: 4776 [3] , given: 163

Re: Three congruent circles overlap in such a way that each circ [#permalink] New post 13 Mar 2013, 19:43
3
This post received
KUDOS
Expert's post
emmak wrote:
Attachment:
2.jpg
Three congruent circles overlap in such a way that each circle intersects the centers of both of the other circles, as shown below. If the radius of each of the circles is 8, what is the area of the central section where all three circles overlap?

A. 16\sqrt{3}

B. 32(\pi-\sqrt{3})

C. 16(\pi+\sqrt{3})

D. 32\pi

E. 32(\pi+\sqrt{3})


To get the exact answer, we can just follow Bunuel's solution a little further.

Area of overlap = Area of sector ABC + 2 (Area of sector ABC - Area of triangle ABC) (or you can also look at it as Area of overlap = 3*Area of sector ABC - 2*Area of triangle ABC)

Area of overlap = \frac{64\pi}{6} + 2(\frac{64\pi}{6} - \frac{\sqrt{3}*64}{4})
Area of overlap = 32(\pi - \sqrt{3})
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 2083
Followers: 179

Kudos [?]: 35 [0], given: 0

Premium Member
Re: Three congruent circles overlap in such a way that each circ [#permalink] New post 24 Jun 2014, 11:22
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

Re: Three congruent circles overlap in such a way that each circ   [#permalink] 24 Jun 2014, 11:22
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic Most Efficient Way for Dealing with Overlapping Sets? TooLong150 6 06 Oct 2013, 05:41
5 Each of three charities gmat1220 9 14 May 2011, 19:38
overlapping circles xcusemeplz2009 1 10 Dec 2009, 21:08
The area of circle A is three times more than the circle of keeeeeekse 6 27 Sep 2006, 05:14
On an xy plane, a circle is placed in such a way that any alimad 8 30 Aug 2006, 05:27
Display posts from previous: Sort by

Three congruent circles overlap in such a way that each circ

  Question banks Downloads My Bookmarks Reviews Important topics  


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®.