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

It is currently 16 Sep 2019, 23:46

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

Six congruent circles are packed into an equilateral triangle so that

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58004
Six congruent circles are packed into an equilateral triangle so that  [#permalink]

Show Tags

New post 08 Mar 2018, 21:17
11
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

45% (02:00) correct 55% (01:42) wrong based on 124 sessions

HideShow timer Statistics

Image

Six congruent circles are packed into an equilateral triangle so that no circle is overlapping and such that circles are tangent to one another or the triangle at any point of contact, as shown above. What is the area of the part of the triangle that is NOT covered by circles?

(1) The radius of each circle is 2
(2) The area of the triangle is \(48+28\sqrt{3}\)


Attachment:
six_circles_packed_1.png
six_circles_packed_1.png [ 16.87 KiB | Viewed 1939 times ]

_________________
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58004
Re: Six congruent circles are packed into an equilateral triangle so that  [#permalink]

Show Tags

New post 08 Mar 2018, 21:22
Bunuel wrote:
Image

Six congruent circles are packed into an equilateral triangle so that no circle is overlapping and such that circles are tangent to one another or the triangle at any point of contact, as shown above. What is the area of the part of the triangle that is NOT covered by circles?

(1) The radius of each circle is 2
(2) The area of the triangle is \(48+28\sqrt{3}\)


Attachment:
six_circles_packed_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
_________________
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2972
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Six congruent circles are packed into an equilateral triangle so that  [#permalink]

Show Tags

New post 09 Mar 2018, 01:07
1
Bunuel wrote:
Image

Six congruent circles are packed into an equilateral triangle so that no circle is overlapping and such that circles are tangent to one another or the triangle at any point of contact, as shown above. What is the area of the part of the triangle that is NOT covered by circles?

(1) The radius of each circle is 2
(2) The area of the triangle is \(48+28\sqrt{3}\)


Attachment:
The attachment six_circles_packed_1.png is no longer available


Question: Area of uncovered part of triangle = Area of triangle - Area of six circles = ?

Statement 1: The radius of each circle is 2
Using this information the side of the equilateral triangle can be calculated (using 30-60-90 property) as mentioned in attachment, Hence
SUFFICIENT

Statement 2: he area of the triangle is \(48+28\sqrt{3}\)
sing this information the side of the equilateral triangle can be calculated as mentioned in attachment, Hence
SUFFICIENT

Answer: option D
Attachments

File comment: www.GMATinsight.com
Screen Shot 2018-03-09 at 1.40.56 PM.png
Screen Shot 2018-03-09 at 1.40.56 PM.png [ 204.67 KiB | Viewed 1547 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

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1240
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Six congruent circles are packed into an equilateral triangle so that  [#permalink]

Show Tags

New post 10 Mar 2018, 20:42
2
There is a simpler approach to it, by trying to draw it on paper.
see the Sketch attached.
Attachment:
WhatsApp Image 2018-03-11 at 09.09.28.jpeg
WhatsApp Image 2018-03-11 at 09.09.28.jpeg [ 99.73 KiB | Viewed 1455 times ]


GMATinsight wrote:
Bunuel wrote:
Image

Six congruent circles are packed into an equilateral triangle so that no circle is overlapping and such that circles are tangent to one another or the triangle at any point of contact, as shown above. What is the area of the part of the triangle that is NOT covered by circles?

(1) The radius of each circle is 2
(2) The area of the triangle is \(48+28\sqrt{3}\)


Attachment:
The attachment six_circles_packed_1.png is no longer available


Question: Area of uncovered part of triangle = Area of triangle - Area of six circles = ?

Statement 1: The radius of each circle is 2
Using this information the side of the equilateral triangle can be calculated (using 30-60-90 property) as mentioned in attachment, Hence
SUFFICIENT

Statement 2: he area of the triangle is \(48+28\sqrt{3}\)
sing this information the side of the equilateral triangle can be calculated as mentioned in attachment, Hence
SUFFICIENT

Answer: option D

_________________
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 937
Re: Six congruent circles are packed into an equilateral triangle so that  [#permalink]

Show Tags

New post 26 Oct 2018, 08:44
Bunuel wrote:
Image

Six congruent circles are packed into an equilateral triangle so that no circle is overlapping and such that circles are tangent to one another or the triangle at any point of contact, as shown above. What is the area of the part of the triangle that is NOT covered by circles?

(1) The radius of each circle is 2
(2) The area of the triangle is \(48+28\sqrt{3}\)

\(?\,\,\, = \,\,\,{S_\Delta } - 6 \cdot {S_ \circ }\)

The GMATH widget (a.k.a "GW") is defined in the figure below. It is formed combining an equilateral triangle (side length 4r) and three "legs" (length r each), where r is any positive number.

Image

With the GW in mind, the answer is (D) immediately:

(1) The value of r is given, hence the corresponding GW is unique, hence the triangle that circumscribes the GW is unique (dotted triangle in the figure shown in the bottom-left). Our FOCUS is unique.

(2) The equilateral triangle is given, hence the corresponding inscribed GW is unique (dotted GW shown in the bottom-right), hence r is unique. Our FOCUS is unique.


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMAT Club Bot
Re: Six congruent circles are packed into an equilateral triangle so that   [#permalink] 26 Oct 2018, 08:44
Display posts from previous: Sort by

Six congruent circles are packed into an equilateral triangle so that

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





cron

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