January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. 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.
Author 
Message 
TAGS:

Hide Tags

Manager
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 139
Location: India
Concentration: Finance, International Business
WE: Information Technology (Investment Banking)

In the figure above, three segments are drawn from the opposite vertic
[#permalink]
Show Tags
17 Sep 2011, 23:08
Question Stats:
38% (00:57) correct 62% (01:02) wrong based on 230 sessions
HideShow timer Statistics
In the figure above, three segments are drawn from the opposite vertices of a hexagon to form six triangles. These segments all bisect each other at point A. Are all of the triangles equilateral? (1) All six sides of the hexagon are the same length. (2) The three segments drawn between the opposite vertices are the same length are are bisected by point A. Attachment: File comment: Question
img_1.JPG [ 44.87 KiB  Viewed 2333 times ]
Official Answer and Stats are available only to registered users. Register/ Login.




Retired Moderator
Joined: 15 Jun 2012
Posts: 1010
Location: United States

Re: In the figure above, three segments are drawn from the oppos
[#permalink]
Show Tags
27 Aug 2013, 14:21
I try to visualize the question as following: Note: if all six triangles in a hexagon are equilateral, then the hexagon has all equal sides and six 120 degrees internal angles. The hexagon is regular. If the hexagon has only six equal sides, the hexagon may not be regular. Thus, six triangles may not be equilateral. Answer is C. Hope it helps.
Attachments
Hexagon.jpg [ 58.69 KiB  Viewed 3426 times ]
_________________
Please +1 KUDO if my post helps. Thank you.
"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."
Chris Bangle  Former BMW Chief of Design.




Intern
Joined: 06 Aug 2011
Posts: 5

Re: In the figure above, three segments are drawn from the opposite vertic
[#permalink]
Show Tags
17 Sep 2011, 23:40
Given: The segments bisects each other at point A.
In this question, we need to know two things.
1. Whether the segments(diagonals) are of same length. 2. Whether the angles formed by the edges of the hexagon are same.
I. All six sides are of same length. > Not Sufficient. This info doesn't tell us whether the triangles are equilateral.
II. The three segments(diagonals) are of same length. Not Sufficient. We do not know whether the lengths of the edges are equal.
I & II, both are sufficient. It is because 
1. When the six edges are equal, the angle formed by one edge at the centre is 180  2x, x is the angle which is opposite to the side formed by half of a segment in a particular triangle.
2. Let's take 180  2x = Y.Now there are 6 angles, each measuring Y and 6Y = 360 => Y = 60 degree.
Then its easy to say the triangle are equilateral.



VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1015

Re: In the figure above, three segments are drawn from the opposite vertic
[#permalink]
Show Tags
21 Sep 2011, 22:38
a gives that all triangles are similar,however the hexagon side and the two bisected sides don't have relation specified. not sufficient.
b no mention about the hexagon sides. not sufficient.
a+b
all sides are equal.hence equilateral.
C it is.



Senior Manager
Joined: 03 Mar 2010
Posts: 374

Re: In the figure above, three segments are drawn from the opposite vertic
[#permalink]
Show Tags
22 Sep 2011, 00:44
This question is from 800score. I did this few days ago. Here you can check illustrative solution in flash http://www.800score.com/explanations/GMAT_MATH_T1_Q25_Hard.html
_________________
My dad once said to me: Son, nothing succeeds like success.



Intern
Status: Finance Analyst
Affiliations: CPA Australia
Joined: 10 Jul 2012
Posts: 16
Location: Australia
Concentration: Finance, Healthcare
GMAT 1: 470 Q38 V19 GMAT 2: 600 Q44 V34
GPA: 3.5
WE: Accounting (Health Care)

In the figure above, three segments are drawn from the oppos
[#permalink]
Show Tags
Updated on: 27 Aug 2013, 02:25
Attachment: File comment: Image
Hexagon.png [ 4.42 KiB  Viewed 3650 times ]
In the figure above, three segments are drawn from the opposite vertices of a hexagon to form six triangles. These segments all bisect each other at point A. Are all of the triangles equilateral? (1) All six sides of the hexagon are the same length. (2) The three segments drawn between the opposite vertices are the same length are are bisected by point A.
_________________
Our deepest fear is not that we are inadequate. Our deepest fear is that we are powerful beyond measure. It is our light not our darkness that most frightens us.
Your playing small does not serve the world. There's nothing enlightened about shrinking so that other people won't feel insecure around you.
It's not just in some of us; it's in everyone. And as we let our own light shine, we unconsciously give other people permission to do the same.
As we are liberated from our own fear, our presence automatically liberates others.
—Marianne Williamson
Originally posted by vaishnogmat on 26 Aug 2013, 21:18.
Last edited by Bunuel on 27 Aug 2013, 02:25, edited 1 time in total.
RENAMED THE TOPIC.



Intern
Joined: 31 Jan 2013
Posts: 17
WE: Consulting (Energy and Utilities)

Re: Equilateral triangles in Hexagon?
[#permalink]
Show Tags
26 Aug 2013, 23:00
Experts kindly correct me if my thinking process is incorrect.
From the properties of hexagon, if all the interior angles are equal and if all the sides are equal, then it's a regular hexagon and a regular hexagon could be divided into six equilateral triangles. Hence by proving our hexagon as regular hexagon, we should get our answer.
Option 1: Although it is given that all six sides of the hexagon are equal, with no information about the angles or the positioning of the bisectors, we couldn't conclusively say it's a regular hexagon. hence, not sufficient.
Option 2: Not sufficient
Option 1 & 2: Will prove the hexagon is definitely a regular hexagon.



Manager
Joined: 26 Feb 2013
Posts: 154

Re: In the figure above, three segments are drawn from the oppos
[#permalink]
Show Tags
29 Aug 2013, 02:30
pqhai wrote: I try to visualize the question as following:
Note: if all six triangles in a hexagon are equilateral, then the hexagon has all equal sides and six 120 degrees internal angles. The hexagon is regular. If the hexagon has only six equal sides, the hexagon may not be regular. Thus, six triangles may not be equilateral.
Answer is C.
Hope it helps. I couldn't visualize this and hence couldn't come up with a proper draw, but this helps, thanks.



Intern
Joined: 20 Nov 2012
Posts: 15

Re: In the figure above, three segments are drawn from the oppos
[#permalink]
Show Tags
10 Dec 2013, 08:51
hey guys. i found an excellent explanation of this problem http://www.800score.com/explanations/GM ... _Hard.html



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13331
Location: United States (CA)

Re: In the figure above, three segments are drawn from the oppos
[#permalink]
Show Tags
04 Feb 2015, 11:52
Hi All, The explanation/drawings offered by pqhai for this question are spoton, so I won't rehash any of that work here. Instead, I'll focus on a 'key' element to dealing with DS questions: to get the correct answer, you have to be clear on what you KNOW and what you DON'T KNOW. This prompt starts us off with a hexagon, which is a 'weird' shape (and is not likely to show up on Test Day). Before dealing with this shape, I'm going to start with an easier example: If you're given a triangle, what do you really KNOW about the triangle? 1) You know it has 3 sides 2) You know that its 3 angles add up to 180 degrees 3) You know that the length of the sides are related (through the triangle inequality theorem) 4) You know that the biggest side is 'across' from the biggest angle, the smallest is across from the smallest. What do you NOT KNOW: 1) You DON'T KNOW the lengths of the sides. 2) You DON'T KNOW the angles 3) You DON'T KNOW if it's a right triangle, isosceles, equilateral, etc. Etc. Now, take that same perspective with this prompt. We're given a hexagon, so what do you really KNOW about it? 1) A hexagon has 6 sides 2) A hexagon has 720 degrees What do we NOT KNOW: 1) We don't know if the sides are the same length. 2) We don't know any of the angles. Realizing those points, working through the rest of the question isn't that tough. Most of the 'work' is really about drawing pictures and considering the various possibilities. In all DS questions, make note of the things that you don't know (and the possibilities that can occur) and you'll be better able to get to the correct answer (and have proof of it). GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



Manager
Joined: 07 Feb 2017
Posts: 188

Re: In the figure above, three segments are drawn from the oppos
[#permalink]
Show Tags
03 Nov 2018, 07:50
QUOTE: (2) The three segments drawn between the opposite vertices are the same length are are bisected by point A.
WHAT?



Senior Manager
Joined: 08 Aug 2017
Posts: 288

Re: In the figure above, three segments are drawn from the oppos
[#permalink]
Show Tags
03 Nov 2018, 22:41
Hello, How I took this question is as below. Given: A hexagon which is divided by 3 segments which bisect each other at point A. And this 3 segment make 6 triangles. Question: Are these triangles are equilateral. Statement 1 All the sides of hexagon are equal. then angle substanded at A in front of all sides will be equal. Now suppose if length of any of 3 segments remain unequal, will length of hexagon side will remain same? I think NO. So when it is given that all sides are equal in hexagon, other two sides made by intersection of segments have to be equal to side of hexagon. In this way all triangles must be equilateral. Statement 2 All segments are equal in length. Now, in this case two sides made by segments will be equal. Third side (Hexagon's side) could be or couldn't be equal to sides drawn by segments. A seems correct answer. Now please tell me where I did wrong. subhajeet wrote: In the figure above, three segments are drawn from the opposite vertices of a hexagon to form six triangles. These segments all bisect each other at point A. Are all of the triangles equilateral? (1) All six sides of the hexagon are the same length. (2) The three segments drawn between the opposite vertices are the same length are are bisected by point A.



Manager
Joined: 07 Feb 2017
Posts: 188

Re: In the figure above, three segments are drawn from the oppos
[#permalink]
Show Tags
04 Nov 2018, 07:18
gmatzpractice wrote: QUOTE: (2) The three segments drawn between the opposite vertices are the same length are are bisected by point A.
WHAT? Typo: (2) The three segments drawn between the opposite vertices are the same length AND are bisected by point A. (1) is not sufficient. Imagine it's a beach ball.




Re: In the figure above, three segments are drawn from the oppos &nbs
[#permalink]
04 Nov 2018, 07:18






