Target Test Prep 20% Off Flash Sale is on! Code: FLASH20

Redeem
Target Test Prep
5-Day Free Trial
5-day free, full-access trial TTP

Available with Beat the GMAT members only code

MORE DETAILS
Target Test Prep
Magoosh
Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

MORE DETAILS
Magoosh

A triangle is formed by connecting three randomly chosen ver

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

A triangle is formed by connecting three randomly chosen ver

by Max@Math Revolution » Wed Dec 05, 2018 12:57 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

[Math Revolution GMAT math practice question]

A triangle is formed by connecting three randomly chosen vertices of a hexagon. What is the probability that at least one of the sides of the triangle is also a side of the hexagon?

A. 4/5
B. 5/6
C. 7/8
D. 8/9
E. 9/10
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Wed Dec 05, 2018 3:46 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

A triangle is formed by connecting three randomly chosen vertices of a hexagon. What is the probability that at least one of the sides of the triangle is also a side of the hexagon?

A. 4/5
B. 5/6
C. 7/8
D. 8/9
E. 9/10
Let the 6 vertices = A, B, C, D, E and F.

P(the triangle includes AT LEAST 1 side of the hexagon) = 1 - P(the triangle includes NO sides of the hexagon).

From the 6 vertices, the number of ways to choose 3 to form a triangle = 6C3 = (6*5*4)/(3*2*1) = 20.
Of these 20 triangles, only 2 include no sides of the hexagon:
Triangle ACE
Triangle BDF
Thus:
P(the triangle includes no sides of the hexagon) = 2/20 = 1/10.
P(the triangle includes at least 1 side of the hexagon) = 1 - 1/10 = 9/10.

The correct answer is E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

A triangle is formed by connecting three randomly chosen ver

by fskilnik@GMATH » Wed Dec 05, 2018 6:30 pm
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

A triangle is formed by connecting three randomly chosen vertices of a regular (or at least convex) hexagon. What is the probability that at least one of the sides of the triangle is also a side of the hexagon?

A. 4/5
B. 5/6
C. 7/8
D. 8/9
E. 9/10
Image

$$? = 1 - {{\,\,\# \,\,\Delta \,\,\,{\rm{no}}\,\,\,{\rm{sides}}\,\,\,{\rm{in}}\,\,\,{\rm{hexag}}\,\,\,} \over {\# \,\,\Delta \,\,{\rm{total}}}} = 1 - {2 \over {C\left( {6,3} \right)}} = 1 - {2 \over {20}} = {9 \over {10}}$$

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

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

by Max@Math Revolution » Thu Dec 06, 2018 11:46 pm
=>

Since the hexagon has 6 vertices, and we need to choose 3 of them to form the vertices of the triangle, the total number of triangles that can be formed is 6C3 = 20.
Note that only the following 2 triangles do not include an edge of the hexagon:

Image

Therefore, the number of the triangles satisfying the original condition is 18 = 20 - 2.
Thus, the probability that the triangle will include an edge of the hexagon is 18/20 = 9/10.

Therefore, the answer is E.
Answer: E
Top
Post new topic Post Reply
• Page 1 of 1