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# Twelve points are spaced evenly around a circle, lettered from A to L.

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4476
Twelve points are spaced evenly around a circle, lettered from A to L.  [#permalink]

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28 Feb 2017, 17:11
2
14
00:00

Difficulty:

95% (hard)

Question Stats:

19% (02:12) correct 81% (02:28) wrong based on 137 sessions

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Twelve points are spaced evenly around a circle, lettered from A to L. Let N be the total number of isosceles triangles, including equilateral triangles, that can be constructed from three of these points. A different orientation of the same lengths counts as a different triangle, because a different combination of points form the vertices. What is the value of N?

(A) 48
(B) 52
(C) 60
(D) 72
(E) 120

This is one of the easier problems from a set of 15 challenging GMAT Quant questions. To see the whole collection, as well as the OE with diagram for this particular question, see:
Challenging GMAT Math Practice Questions

Mike

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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4476
Re: Twelve points are spaced evenly around a circle, lettered from A to L.  [#permalink]

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04 Mar 2017, 14:36
5
umabharatigudipalli wrote:
Hi,

60 Isosceles triangles make sense, but would u help me out why did u subtract 8?

Uma

Dear Uma,

I'm happy to respond.

My friend, with all due respect, one of the most important qualities you can have in preparing for the GMAT, in B-school, and in your career in the business world, is initiative. Many people out there are simply good rule followers, but if you want to be manager, a leader, you need to demonstrate the ability to take advantage of resources and find out everything you can on your own. If, as a manager, you walk into your boss's office and ask for an explanation of something that you easily could have read yourself, your boss will not be impressed at all with you, and such things significantly matter when bosses consider raises and promotions. If you are comfortable with taking initiative and assuming responsibility for yourself, you will create positive impressions that will be rewarded time and time again.

For this problem, in my first post at the top of the problem, I included a link to a blog with the official explanation. I am going to ask you to go there, read the official explanation for this problem, and then ask me if there is anything that you don't understand. I will also suggest this blog:

I will also say: I recommend refraining from using casual language on GMAT Club (e.g. the letter "u" for "you"). You are here to prepare for the GMAT, to prepare for the beginning of what will be your professional career. Anyone reading what you have written in this public forum could someday be in a position to evaluate you in your career. If you aspire to an excellent performance, then you should strive to bring excellence to every single aspect of how you go about these preparations. As a wise man said: "How you do anything is how you do everything."

Does all this make sense?
Mike
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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
##### General Discussion
Math Expert
Joined: 02 Aug 2009
Posts: 8261
Twelve points are spaced evenly around a circle, lettered from A to L.  [#permalink]

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28 Feb 2017, 22:01
3
mikemcgarry wrote:
Twelve points are spaced evenly around a circle, lettered from A to L. Let N be the total number of isosceles triangles, including equilateral triangles, that can be constructed from three of these points. A different orientation of the same lengths counts as a different triangle, because a different combination of points form the vertices. What is the value of N?

(A) 48
(B) 52
(C) 60
(D) 72
(E) 120

This is one of the easier problems from a set of 15 challenging GMAT Quant questions. To see the whole collection, as well as the OE with diagram for this particular question, see:
Challenging GMAT Math Practice Questions

Mike

Hi...

I will just tell a logical method ...

There are 12 points at EQUAL interval..
So the isosceles triangle can have EQUAL sides of length.
Let's work on the central vertex.

A as the vertex between EQUAL sides..
The EQUAL sides can be 1 unit, two unit, 3 unit, 4 unit or 5 unit...
6 unit will be the diameter so not possible.
So A as central vertex can make 5 isosceles triangles.

Thus 12 vertices from A to L can make 12*5=60 such isosceles triangles.

However 4 units results in an equilateral triangle.
So we are counting the same triangle THREE times.
So actual different triangles with 4 unit as length = 12/3=4..
So we have 12-4=8 extra triangles counted..

Total = 60-8=52...

B
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Joined: 21 Jan 2017
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Re: Twelve points are spaced evenly around a circle, lettered from A to L.  [#permalink]

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04 Mar 2017, 07:51
Hi,

60 Isosceles triangles make sense, but would u help me out why did u subtract 8?

Uma
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: Twelve points are spaced evenly around a circle, lettered from A to L.  [#permalink]

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22 Aug 2018, 13:54
2
2
My solution is presented in the image attached.
Attachments

22Ago18_9y.gif [ 41.79 KiB | Viewed 4307 times ]

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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Posts: 935
Twelve points are spaced evenly around a circle, lettered from A to L.  [#permalink]

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27 Aug 2018, 04:38
Thank you for the kudos!!

If you have any other "conceptual" doubt, please feel free to post it in this forum and send to me a private message, including the link to that post.

I will be happy to help you understand the "theoretical subtleties" (there are many!) that belong to the GMAT content. And, yes, I will always be GMAT-focused, although I love the mathematics that goes far beyond the exam.

May I give you a suggestion? If you are that "rare type" of student who wants to understand the subject deeply, so that an outstanding performance is a "sub-product" of your knowledge and competence, try my method through a complete test drive you will obtain as soon as you register on my site (http://www.gmath.net).

It´s not (just a matter of) business (although I really "earn my living" teaching quant GMAT since 2000): I believe in the bold statement above. (Yes, bold in the two senses, LoL.)

Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Intern
Joined: 21 Feb 2017
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Twelve points are spaced evenly around a circle, lettered from A to L.  [#permalink]

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30 Nov 2018, 19:03
I solved this problem a little differently.

I remembered from another problem that the total number of equilateral triangles using evenly spaced points in a circle = (# of points on the circle)/3, which equals 4.

I then subtracted 4 from every answer and choose B because the remaining value, 48, was the only answer divisible by 3.
Twelve points are spaced evenly around a circle, lettered from A to L.   [#permalink] 30 Nov 2018, 19:03
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