January 19, 2019 January 19, 2019 07:00 AM PST 09:00 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. January 20, 2019 January 20, 2019 07:00 AM PST 07:00 AM PST Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52274

The points of a sixpointed star consist of six identical equilateral
[#permalink]
Show Tags
01 Jul 2015, 02:28
Question Stats:
69% (01:56) correct 31% (02:17) wrong based on 191 sessions
HideShow timer Statistics



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2723
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: The points of a sixpointed star consist of six identical equilateral
[#permalink]
Show Tags
01 Jul 2015, 02:44
Bunuel wrote: The points of a sixpointed star consist of six identical equilateral triangles, with each side 4 cm (see figure). What is the area of the entire star, including the center? A. \(36\sqrt{3}\) B. \(40\sqrt{3}\) C. \(44\sqrt{3}\) D. \(48\sqrt{3}\) E. \(72\sqrt{3}\) Attachment: The attachment 20150701_1424.png is no longer available Joining Diagonal of Inner Hexagon gives another set of six equilateral triangle making it a figure of a total 12 equilateral triangle of side 4 each Answer: Option D
Attachments
File comment: www.GMATinsight.com
Solution 12111.jpg [ 117.07 KiB  Viewed 5281 times ]
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne 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



Manager
Joined: 07 Apr 2015
Posts: 164

Re: The points of a sixpointed star consist of six identical equilateral
[#permalink]
Show Tags
01 Jul 2015, 05:42
How did you get to the part with sqrt 3?
Is there any other way to solve this?



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2723
Location: India
GMAT: INSIGHT
WE: Education (Education)

The points of a sixpointed star consist of six identical equilateral
[#permalink]
Show Tags
01 Jul 2015, 05:48
noTh1ng wrote: How did you get to the part with sqrt 3?
Is there any other way to solve this? Point 1) \(\sqrt{3}\) comes from the property of Area of Equilateral Triangle which is \((\sqrt{3}/4)*side^2\) Point 2) Another method is to Find Area of Bigger Equilateral Triangle of side (4+4+4 = 12) and adding three small Equilateral Triangles with it i.e. Total Area = \((\sqrt{3}/4)*12^2\) \(+ 3*(\sqrt{3}/4)*4^2\) i.e. Total Area = \((\sqrt{3}/4)*(144+3*16)\) i.e. Total Area = \((\sqrt{3}/4)*(192)\) i.e. Total Area = \((\sqrt{3})*(48)\) I hope it helps!
Attachments
File comment: www.GMATinsight.com
Sol(28).jpg [ 122.17 KiB  Viewed 5236 times ]
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne 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



Manager
Joined: 07 Apr 2015
Posts: 164

The points of a sixpointed star consist of six identical equilateral
[#permalink]
Show Tags
01 Jul 2015, 06:10
Ok, thank you!
I approached it in the same way you did it in your second choice, by figuring out the area of the big triangle and the one of the three smaller ones, but couldn't remember the Area formula for equilateral triangles so calculated the sides using Pythagorean Theorem.
Numerically I got to the same solution, but it obviously wasn't among the answer choices...



Math Expert
Joined: 02 Aug 2009
Posts: 7200

Re: The points of a sixpointed star consist of six identical equilateral
[#permalink]
Show Tags
01 Jul 2015, 06:34
Bunuel wrote: The points of a sixpointed star consist of six identical equilateral triangles, with each side 4 cm (see figure). What is the area of the entire star, including the center? A. \(36\sqrt{3}\) B. \(40\sqrt{3}\) C. \(44\sqrt{3}\) D. \(48\sqrt{3}\) E. \(72\sqrt{3}\) Attachment: 20150701_1424.png we have two inverted equilateral triangle with sides 12(4+4+4)... so the area of one of them is \(12^2*\sqrt{3}/4=36\sqrt{3}\).. apart from this there are three smaller equilateral triangles of sides 4.. so area of these 3 is \(3*4^2*\sqrt{3}/4\)=\(12\sqrt{3}\).. total=\(48\sqrt{3}\) ans D
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Manager
Joined: 26 Dec 2011
Posts: 114

Re: The points of a sixpointed star consist of six identical equilateral
[#permalink]
Show Tags
01 Jul 2015, 07:04
Bunuel wrote: The points of a sixpointed star consist of six identical equilateral triangles, with each side 4 cm (see figure). What is the area of the entire star, including the center? A. \(36\sqrt{3}\) B. \(40\sqrt{3}\) C. \(44\sqrt{3}\) D. \(48\sqrt{3}\) E. \(72\sqrt{3}\) Attachment: 20150701_1424.png We can do in different way  Area of large triangle of side 4+4+4 = 12 is (√3/4)*12^2 = 36√3 1 Then the area of remaining 3 small triangles not covered = 3*(√3/4)*4^2 = 12√3 2 So total area 1+2 = 36√3 + 12√3 = 48√3
_________________
Thanks, Kudos Please



Manager
Joined: 17 Mar 2014
Posts: 228
Location: India
Concentration: Operations, Strategy
GPA: 3.19
WE: Information Technology (Computer Software)

Re: The points of a sixpointed star consist of six identical equilateral
[#permalink]
Show Tags
01 Jul 2015, 08:07
total area of star = area of one vertical big triangle + area of 3 small remaining traingles = 36 root 3 + 12 root 3 = 48 root 3 So answer = D
_________________
Press +1 Kudos if you find this Post helpful



Retired Moderator
Joined: 29 Apr 2015
Posts: 842
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

Re: The points of a sixpointed star consist of six identical equilateral
[#permalink]
Show Tags
01 Jul 2015, 08:23
Bunuel wrote: The points of a sixpointed star consist of six identical equilateral triangles, with each side 4 cm (see figure). What is the area of the entire star, including the center? A. \(36\sqrt{3}\) B. \(40\sqrt{3}\) C. \(44\sqrt{3}\) D. \(48\sqrt{3}\) E. \(72\sqrt{3}\) Attachment: 20150701_1424.png First calculate the area of one big equiliteral triangle with 12^2*\(\sqrt{3}\)/4 = 36*\(\sqrt{3}\) Then the smaller outer equiliteral triangles of which are in total 3: 3 * 4^2*\(\sqrt{3}\)/4 = 12*\(\sqrt{3}\) In total we have 48 \(\sqrt{3}\) Answer D Answer D
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!
PS Please send me PM if I do not respond to your question within 24 hours.



Senior Manager
Joined: 15 Sep 2011
Posts: 324
Location: United States
WE: Corporate Finance (Manufacturing)

The points of a sixpointed star consist of six identical equilateral
[#permalink]
Show Tags
01 Jul 2015, 17:32
Since there are twelves equilateral triangles, the answer must be divisible by 12, and therefore some of the answer choices can be excluded, which ones that are not divisible by twelve.
A. \(36\sqrt{3}\) The area of 3, the area for each small triangle, is too small for an equaliteral triangle of side length 4. B. \(40\sqrt{3}\) Not divisible by 12. Out C. \(44\sqrt{3}\) Not divisible by 12. Out D. \(48\sqrt{3}\) The area of \(4\sqrt{3}\) is the area of the triangle with a side lenght of four. Correct answer. E. \(72\sqrt{3}\) If answer is above, E is out.
Thanks, A



Math Expert
Joined: 02 Sep 2009
Posts: 52274

Re: The points of a sixpointed star consist of six identical equilateral
[#permalink]
Show Tags
06 Jul 2015, 02:43
Bunuel wrote: The points of a sixpointed star consist of six identical equilateral triangles, with each side 4 cm (see figure). What is the area of the entire star, including the center? A. \(36\sqrt{3}\) B. \(40\sqrt{3}\) C. \(44\sqrt{3}\) D. \(48\sqrt{3}\) E. \(72\sqrt{3}\) Attachment: The attachment 20150701_1424.png is no longer available MANHATTAN GMAT OFFICIAL SOLUTION:You can think of this star as a large equilateral triangle with sides 12 cm long, and three additional smaller equilateral triangles with sides 4 inches long. Using the same 3 0 6090 logic you applied in problem #13, you can see that the height of the larger equilateral triangle is \(6\sqrt{3}\), and the height of the smaller equilateral triangle is \(2\sqrt{3}\). Therefore, the areas of the triangles are as follows: Large triangle: \(A = \frac{bh}{2} = \frac{12*6\sqrt{3}}{2}=36\sqrt{3}\) Small triangles: \(A = \frac{bh}{2} = \frac{4*2\sqrt{3}}{2}=4\sqrt{3}\) The total area of three smaller triangles and one large triangle is: \(36\sqrt{3}+3(4\sqrt{3})=48\sqrt{3}\). Answer: D. Attachment:
20150706_1435.png [ 8.44 KiB  Viewed 6409 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? Extrahard Quant Tests with Brilliant Analytics



Current Student
Status: Preparing for GMAT!!
Joined: 11 Oct 2015
Posts: 131
Location: India
Concentration: Entrepreneurship, International Business
GMAT 1: 660 Q47 V34 GMAT 2: 700 Q48 V38
GPA: 3.1
WE: General Management (Entertainment and Sports)

Re: The points of a sixpointed star consist of six identical equilateral
[#permalink]
Show Tags
27 Dec 2016, 09:59
Bunuel wrote: The points of a sixpointed star consist of six identical equilateral triangles, with each side 4 cm (see figure). What is the area of the entire star, including the center? A. \(36\sqrt{3}\) B. \(40\sqrt{3}\) C. \(44\sqrt{3}\) D. \(48\sqrt{3}\) E. \(72\sqrt{3}\) Attachment: 20150701_1424.png Area of 1 big triangle = \(12^2\)\(\frac{srt3}{4}\)=\(36\sqrt{3}\) Area of 3 small triangles= \(3*4^2\)\(\frac{srt3}{4}\)=\(12\sqrt{3}\) Area of total figure=\(48\sqrt{3}\) D
_________________
Yours, Siva Rama Krishna Meka



NonHuman User
Joined: 09 Sep 2013
Posts: 9422

Re: The points of a sixpointed star consist of six identical equilateral
[#permalink]
Show Tags
30 Jan 2018, 09:05
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: The points of a sixpointed star consist of six identical equilateral &nbs
[#permalink]
30 Jan 2018, 09:05






