GMAT-Quants

In a Polygon,all but one vertices are connected to each other by straight lines and 78 diagonals are formed.How many sides does the polygon have ?

A. 15

B.17

C.12

D.16

E.18

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1. Jonny Charger says:

   February 27, 2009 at 1:54 am

   None of the above. This is a bad question. By defenition a polygon is a plane geometric figure constructed by intersecting straight line segments forming a closed path or circuit. Therefore, the figure described as having all but one vertice connected by straigt lines would not be a polygon.

   The relationship between a polygon and its diagonals is n(n-3)/2 = D with n being the number of sides and D being the number of diagonals. The closest figure to the one described would be a 14-sided figure with 77 diagonals.
2. Tron says:

   February 27, 2009 at 3:17 am

   It says.. ‘all but one’ vertices are connected to each other by straight lines.

   The answer is A
3. PR says:

   February 27, 2009 at 10:06 am

   Its A… yu can obtain it by solving [(n(n-3))/2]-[n-3]=78!!
4. A Chakraverty says:

   February 27, 2009 at 10:15 am

   Ans. A

   Say, number of sides of polygon = n
   Total no. of lines (sides + diagonals) = nC2
   Since one point is not joined to any other point to form a diagonal.
   Total number of lines drawn from one point in a polygon of n sides
   = (n-1)
   therfore, total no. of diagonals from one point = (n-1) – 2 = n-3
   total no. of diagonals in a polygon = nC2 – n
   No. of diagonals, when one pt. is excluded = nC2 – n – (n-3)
   Thus, nC2 – n – (n-3) = 78
   On solving, n = 15
5. syed says:

   February 27, 2009 at 12:47 pm

   a
6. khyati says:

   February 27, 2009 at 11:38 pm

   A
7. Dharm says:

   February 28, 2009 at 7:27 am

   option A