How many triangles and quadrilaterals altogether can be formed using the vertices of a 7-sided regular polygon?

This topic has expert replies
Junior | Next Rank: 30 Posts
Posts: 11
Joined: 21 Jul 2020

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

How many triangles and quadrilaterals altogether can be formed using the vertices of a 7-sided regular polygon?

A 35
B 40
C 50
D 65
E 70

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3007
Joined: 22 Aug 2016
Location: Grand Central / New York
Thanked: 470 times
Followed by:32 members
sambati wrote:
Tue Aug 04, 2020 1:54 pm
How many triangles and quadrilaterals altogether can be formed using the vertices of a 7-sided regular polygon?

A 35
B 40
C 50
D 65
E 70
• Number of triangles can be formed from a polygon with 7 sides = 7C3 = (7*6*5) / (1*2*3) = 35;

• Number of quadrilaterals can be formed from a polygon with 7 sides = 7C4 = (7*6*5*4) / (1*2*3*4) = 35;

Total Number of ways that triangles and rectangles can be formed from a polygon with 7 sides = 35 + 35 = 70.

Correct answer: E

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: GMAT Prep Phoenix | GRE Prep West Palm Beach | GMAT Prep Asia | SAT Prep St. Louis | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 5664
Joined: 25 Apr 2015
Location: Los Angeles, CA
Thanked: 43 times
Followed by:24 members
sambati wrote:
Tue Aug 04, 2020 1:54 pm
How many triangles and quadrilaterals altogether can be formed using the vertices of a 7-sided regular polygon?

A 35
B 40
C 50
D 65
E 70
Solution:

There are 7C3 = (7 x 6 x 5) / (3 x 2) = 35 ways to choose 3 vertices from the 7 vertices of the polygon to form a triangle. Likewise, there are 7C4 = (7 x 6 x 5 x 4)/(4 x 3 x 2) = 35 ways to choose 4 vertices from the 7 vertices of the polygon to form a quadrilateral. Therefore, there is a total of 35 + 35 = 70 triangles and quadrilaterals that can be formed.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage