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

 It is currently 05 Dec 2019, 22:07

### 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

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

# Six congruent circles are packed into an equilateral triangle so that

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59561
Six congruent circles are packed into an equilateral triangle so that  [#permalink]

### Show Tags

08 Mar 2018, 21:17
11
00:00

Difficulty:

75% (hard)

Question Stats:

47% (01:55) correct 53% (01:39) wrong based on 121 sessions

### HideShow timer Statistics

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 [ 16.87 KiB | Viewed 2270 times ]
Math Expert
Joined: 02 Sep 2009
Posts: 59561
Re: Six congruent circles are packed into an equilateral triangle so that  [#permalink]

### Show Tags

08 Mar 2018, 21:22
Bunuel wrote:

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

For other subjects:
ALL YOU NEED FOR QUANT ! ! !
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Six congruent circles are packed into an equilateral triangle so that  [#permalink]

### Show Tags

09 Mar 2018, 01:07
1
1
Bunuel wrote:

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

Attachments

File comment: www.GMATinsight.com

Screen Shot 2018-03-09 at 1.40.56 PM.png [ 204.67 KiB | Viewed 1852 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
Joined: 27 Oct 2017
Posts: 1310
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Six congruent circles are packed into an equilateral triangle so that  [#permalink]

### Show Tags

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 [ 99.73 KiB | Viewed 1760 times ]

GMATinsight wrote:
Bunuel wrote:

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

_________________
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: Six congruent circles are packed into an equilateral triangle so that  [#permalink]

### Show Tags

26 Oct 2018, 08:44
Bunuel wrote:

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.

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
Non-Human User
Joined: 09 Sep 2013
Posts: 13709
Re: Six congruent circles are packed into an equilateral triangle so that  [#permalink]

### Show Tags

26 Oct 2019, 15:23
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.
_________________
Re: Six congruent circles are packed into an equilateral triangle so that   [#permalink] 26 Oct 2019, 15:23
Display posts from previous: Sort by