GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 16 Nov 2018, 17:20

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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     November 17, 2018

     November 17, 2018

     07:00 AM PST

     09:00 AM PST

    Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • GMATbuster's Weekly GMAT Quant Quiz # 9

     November 17, 2018

     November 17, 2018

     09:00 AM PST

     11:00 AM PST

    Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

Two identical circles of area 36π overlap as shown above. If the dista

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50619
Two identical circles of area 36π overlap as shown above. If the dista  [#permalink]

Show Tags

New post 14 Sep 2018, 00:16
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

83% (01:45) correct 17% (01:46) wrong based on 18 sessions

HideShow timer Statistics

Image
Two identical circles of area 36π overlap as shown above. If the distance from point A to point B is 6, what is the area of the shaded region?


A. 6π

B. 12π

C. \(18\sqrt{3} – 6π\)

D. \(6π – 9\sqrt{3}\)

E. \(12π – 18\sqrt{3}\)


Attachment:
image020.jpg
image020.jpg [ 2.53 KiB | Viewed 521 times ]

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 22 Oct 2016
Posts: 15
GMAT 1: 590 Q47 V25
Reviews Badge
Re: Two identical circles of area 36π overlap as shown above. If the dista  [#permalink]

Show Tags

New post 14 Sep 2018, 01:03
distance between point A and B is given to assume an equilateral triangle with 6m sides, sinch area = 6^2xpie

Hence, Area of shaded region = 2(area of 60 deg sector - Area of Equilateral Triangle )
Ans = 12pie-18sqrt3
Intern
Intern
avatar
B
Joined: 04 Oct 2016
Posts: 8
Re: Two identical circles of area 36π overlap as shown above. If the dista  [#permalink]

Show Tags

New post 16 Sep 2018, 07:11
1
swapnilce.nitdgp wrote:
distance between point A and B is given to assume an equilateral triangle with 6m sides, sinch area = 6^2xpie

Hence, Area of shaded region = 2(area of 60 deg sector - Area of Equilateral Triangle )
Ans = 12pie-18sqrt3


Hi,
Can someone please provide a lil more detailed explanation...
Intern
Intern
avatar
Joined: 16 Sep 2018
Posts: 1
Re: Two identical circles of area 36π overlap as shown above. If the dista  [#permalink]

Show Tags

New post 16 Sep 2018, 09:16
mischiefmanaged wrote:
swapnilce.nitdgp wrote:
distance between point A and B is given to assume an equilateral triangle with 6m sides, sinch area = 6^2xpie

Hence, Area of shaded region = 2(area of 60 deg sector - Area of Equilateral Triangle )
Ans = 12pie-18sqrt3


Hi,
Can someone please provide a lil more detailed explanation...


ibb.co/iyL3zz (copy-paste this to see the picture I drew for you, it won't let me attach it for some reason...)

Basically, AB = 6 which happens to be = r (you can reverse engineer "r" looking at the area that is 36pi. Area of a circle = pi*r^2, therefore 36*pi means that r = 6).

You can now build an equilateral triangle with side = 6, and find its area since it's a 30-60-90 triangle.

You can also compute the "sector's area" using the formula in the image I posted (it's just a proportional fraction of the whole circle's area).

Now you can find the difference between the two, which will give you the area of half the shaded region. Multiply that by 2 and you get the result.
Intern
Intern
avatar
B
Joined: 10 Jun 2014
Posts: 39
Location: India
Concentration: Operations, Finance
GPA: 4
WE: Manufacturing and Production (Energy and Utilities)
Two identical circles of area 36π overlap as shown above. If the dista  [#permalink]

Show Tags

New post 16 Sep 2018, 11:39
For only one circle

Area = 36\(\pi\)
So Radius = 6
Distance between A to B = 6

So Origin,A & B form a equilateral Triangle
Area of \(\triangle\) = 9\(\sqrt{3}\)

\(\angle\) AOB= 60\(^{o}\) , Since Equilateral Triangle [ O= Origin]

Area of Circular segment OAB =(36\(\pi\) / \(360^{\circ}\)) x \(60^{\circ}\) = 6\(\pi\)

Shaded Portion by only one Circle = 6\(\pi\)-9\(\sqrt{3}\)

Shaded Portion by two circle = 12\(\pi\)-18\(\sqrt{3}\)
GMAT Club Bot
Two identical circles of area 36π overlap as shown above. If the dista &nbs [#permalink] 16 Sep 2018, 11:39
Display posts from previous: Sort by

Two identical circles of area 36π overlap as shown above. If the dista

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.