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

It is currently 22 Jun 2018, 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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The figure above shows an equilateral triangle with three circles. Eac

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46280
The figure above shows an equilateral triangle with three circles. Eac [#permalink]

Show Tags

New post 08 Mar 2018, 21:26
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

62% (02:33) correct 38% (02:19) wrong based on 39 sessions

HideShow timer Statistics

Image
The figure above shows an equilateral triangle with three circles. Each point of contact between two circles or between a circle and the triangle is a point of tangency. If the triangle has a height of 18, what is the combined area of the two smaller circles?

A. 4π
B. 8π
C. 16π
D. 36π
E. 44π

Attachment:
Equilateral_triangle_circle_packing_1 (1).png
Equilateral_triangle_circle_packing_1 (1).png [ 13.97 KiB | Viewed 952 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

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46280
Re: The figure above shows an equilateral triangle with three circles. Eac [#permalink]

Show Tags

New post 08 Mar 2018, 21:27
Bunuel wrote:
Image
The figure above shows an equilateral triangle with three circles. Each point of contact between two circles or between a circle and the triangle is a point of tangency. If the triangle has a height of 18, what is the combined area of the two smaller circles?

A. 4π
B. 8π
C. 16π
D. 36π
E. 44π

Attachment:
Equilateral_triangle_circle_packing_1 (1).png


23. Geometry




24. Coordinate Geometry




25. Triangles




26. Polygons




27. Circles




28. Rectangular Solids and Cylinders




29. Graphs and Illustrations




For other subjects:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
_________________

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

Expert Post
1 KUDOS received
SVP
SVP
User avatar
P
Joined: 08 Jul 2010
Posts: 2114
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
The figure above shows an equilateral triangle with three circles. Eac [#permalink]

Show Tags

New post 09 Mar 2018, 00:31
1
2
Bunuel wrote:
Image
The figure above shows an equilateral triangle with three circles. Each point of contact between two circles or between a circle and the triangle is a point of tangency. If the triangle has a height of 18, what is the combined area of the two smaller circles?

A. 4π
B. 8π
C. 16π
D. 36π
E. 44π

Attachment:
The attachment Equilateral_triangle_circle_packing_1 (1).png is no longer available


The radius of an In-Circle in an equilateral triangle = (1/3)* Height of equilateral triangle(DERIVATION IS ATTACHED HERE)

therefore Radius of the bigger circle = (1/3)*18 = 6

Now The Height of Triangle ADE = 18-(2*radius of bigger circle) = 18 - 12 = 6

Now the radius of the smaller circle = (1/3)* Height of equilateral triangle ADE = (1/3)*6 = 2

i.e. Area of Both the smaller circle = 2* πr^2 = 2*π*2^2 = 8π

Answer: option B
Attachments

File comment: www.GMATinsight.com
Screen Shot 2018-03-09 at 1.08.46 PM.png
Screen Shot 2018-03-09 at 1.08.46 PM.png [ 496.21 KiB | Viewed 629 times ]


_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Expert Post
examPAL Representative
User avatar
S
Joined: 07 Dec 2017
Posts: 435
Re: The figure above shows an equilateral triangle with three circles. Eac [#permalink]

Show Tags

New post 09 Mar 2018, 02:11
Bunuel wrote:
The figure above shows an equilateral triangle with three circles. Each point of contact between two circles or between a circle and the triangle is a point of tangency. If the triangle has a height of 18, what is the combined area of the two smaller circles?

A. 4π
B. 8π
C. 16π
D. 36π
E. 44π



Since there is only one way to draw an equilateral triangle with an inscribed circle, we can trust the drawing.
That is, we'll visually estimate the answer and look for the closest answer choice.
This is an Alternative approach.

The height of the triangle is 18 so its base is 18\(\sqrt{2}\) (because this is a 30-60-90 triangle) which is about 20*1.4 = 28
Then the area is about 18*28/2 = 18*14 = 140+80+32=252
Dividing our equilateral triangle into 9 identical smaller triangles, we can SEE that the two small circles are about half the area of 2 of the small triangles.
That is, about (1/2)*(2/9) of the total area or 252/9 which is a bit more than 25, say 30.
Option (B) is the only relevant choice.

** Note that with regular polygons and area-related questions it is almost always easier to estimate the answer instead of looking for an extremely complicated Precise geometrical solution.
Attachments

equi.png
equi.png [ 38.58 KiB | Viewed 594 times ]


_________________

David
Senior tutor at examPAL
Signup for a free GMAT course
Image
Image
We won some awards:
Image
Join our next webinar (free)
Save up to $250 on examPAL packages (special for GMAT Club members)

Manager
Manager
avatar
S
Joined: 04 Apr 2015
Posts: 110
Re: The figure above shows an equilateral triangle with three circles. Eac [#permalink]

Show Tags

New post 09 Mar 2018, 11:19
GMATinsight wrote:
Bunuel wrote:
Image
The figure above shows an equilateral triangle with three circles. Each point of contact between two circles or between a circle and the triangle is a point of tangency. If the triangle has a height of 18, what is the combined area of the two smaller circles?

A. 4π
B. 8π
C. 16π
D. 36π
E. 44π

Attachment:
Equilateral_triangle_circle_packing_1 (1).png


The radius of an In-Circle in an equilateral triangle = (1/3)* Height of equilateral triangle(DERIVATION IS ATTACHED HERE)

therefore Radius of the bigger circle = (1/3)*18 = 6

Now The Height of Triangle ADE = 18-(2*radius of bigger circle) = 18 - 12 = 6

Now the radius of the smaller circle = (1/3)* Height of equilateral triangle ADE = (1/3)*6 = 2

i.e. Area of Both the smaller circle = 2* πr^2 = 2*π*2^2 = 8π

Answer: option B



Radius =1/3 of the height is obvious since circumcenter,incenter of equilateral triangle lie on the same point. Since circumcenter divides the triangle in 2:1 ratio, the radius should be 1/3 of the height
Re: The figure above shows an equilateral triangle with three circles. Eac   [#permalink] 09 Mar 2018, 11:19
Display posts from previous: Sort by

The figure above shows an equilateral triangle with three circles. Eac

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


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®.