gmattesttaker2 wrote:Hello,
Can you please assist with this:
In a polygon, a diagonal is defined as the line that joins a vertex to any other vertex except the two adjacent vertices. How many diagonals does a seven-sided polygon have?
OA: 14
Thanks a lot,
Sri
A 7-sided polygon has 7 vertices.
Any combination of 2 NON-ADJACENT vertices can serve to form a diagonal.
From the 7 vertices, the number of combinations of 2 that can be formed = 7C2 = (7*6)/(2*1) = 21.
These 21 combinations include the 7 sides of the polygon.
Subtracting the 7 sides of the polygon from the 21 combinations that can be formed, we get:
21-7 =
14 diagonals.
An alternate approach is to WRITE IT OUT.
Let the 7 vertices be A, B, C, D, E, F and G.
Any non-adacent pair of vertices can serve to form a diagonal.
Options:
AC, AD, AE, AF
BD, BE, BF, BG
CE, CF, CG
DF, DG
EG
Total options = 14.
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
