There is an 8-polygons. what is the number of the diagonals of the 8-polygons ?
A. 20 B. 27 C. 32 D. 43 E. 45
is there any formula for this ?
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pappueshwar
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when it asks "how many different" they are normally asking for permutations combinations and here that is the case however there is a difference.
First you would solve for the number of combinations of two points out of 8 possible points.
8!/(8-2)!(2!) = 28
However, this accounted for the sides, as a connection between two points that are right next to each other on the shape will form a side, not a diagonal. Therefore you have to subtract the 8 sides from this calculation to get 20
The correct answer is A.
Best of Luck
First you would solve for the number of combinations of two points out of 8 possible points.
8!/(8-2)!(2!) = 28
However, this accounted for the sides, as a connection between two points that are right next to each other on the shape will form a side, not a diagonal. Therefore you have to subtract the 8 sides from this calculation to get 20
The correct answer is A.
Best of Luck
Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA
Master GMAT Instructor
The Princeton Review
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pappueshwar
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Brent@GMATPrepNow
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Another approach is to recognize that, for each of the 8 points, there are 5 possible points that we can connect to to create a diagonal.pappueshwar wrote:There is an 8-polygons. what is the number of the diagonals of the 8-polygons ?
A. 20 B. 27 C. 32 D. 43 E. 45
is there any formula for this ?
Aside: there are 5 possible points because we cannot create a diagonal by connecting 2 adjacent points.
These means that there are 40 possible diagonals (8x5=40).
However, we need to recognize that this method counts each diagonal twice. For example, it counts the diagonal AB and the diagonal BA as 2 separate diagonals.
So, to account for this duplication, we'll divide 40 by 2 to get 20[spoiler] (A)[/spoiler]
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
