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Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by sanju09 » Thu Apr 01, 2010 4:21 am
Hey all! I have seen the following problem somewhere (possibly on PS forum, choices weren't there though) an hour ago. But I am not finding it anywhere now. I don't remember the exact wordings, but it runs like

How many diagonals are there in a 21-sided polygon, when one vertex doesn't form any diagonal?

Please find it for me!
The mind is everything. What you think you become. -Lord Buddha



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by ajith » Thu Apr 01, 2010 5:34 am
sanju09 wrote:Hey all! I have seen the following problem somewhere (possibly on PS forum, choices weren't there though) an hour ago. But I am not finding it anywhere now. I don't remember the exact wordings, but it runs like

How many diagonals are there in a 21-sided polygon, when one vertex doesn't form any diagonal?

Please find it for me!
I did not Attempt that question because I could not imagine such a polygon. Can someone draw a pic for me [with lesser sides would do]
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by sanju09 » Thu Apr 01, 2010 5:38 am
ajith wrote:
sanju09 wrote:Hey all! I have seen the following problem somewhere (possibly on PS forum, choices weren't there though) an hour ago. But I am not finding it anywhere now. I don't remember the exact wordings, but it runs like

How many diagonals are there in a 21-sided polygon, when one vertex doesn't form any diagonal?

Please find it for me!
I did not Attempt that question because I could not imagine such a polygon. Can someone draw a pic for me [with lesser sides would do]
Can't we celebrate Apr 1 later?
The mind is everything. What you think you become. -Lord Buddha



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by ajith » Thu Apr 01, 2010 5:39 am
sanju09 wrote:
Can't we celebrate Apr 1 later?
No It has to be now!

https://www.beatthegmat.com/how-many-dia ... 45438.html

Fine ...

We will continue the celebrations on the relevant thread now!

I think I should delete this thread or move it to Lounge
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by sanju09 » Thu Apr 01, 2010 5:51 am
ajith wrote:
sanju09 wrote:
Can't we celebrate Apr 1 later?
No It has to be now!

https://www.beatthegmat.com/how-many-dia ... 45438.html

Fine ...

We will continue the celebrations on the relevant thread now!

I think I should delete this thread or move it to Lounge
believe me, it's a different thread. The one that I am searching hasn't got choices with it. Why delete or move?
The mind is everything. What you think you become. -Lord Buddha



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by ajith » Thu Apr 01, 2010 8:24 am
sanju09 wrote:
ajith wrote:
sanju09 wrote:
Can't we celebrate Apr 1 later?
No It has to be now!

https://www.beatthegmat.com/how-many-dia ... 45438.html

Fine ...

We will continue the celebrations on the relevant thread now!

I think I should delete this thread or move it to Lounge
believe me, it's a different thread. The one that I am searching hasn't got choices with it. Why delete or move?
https://www.beatthegmat.com/probability- ... %20polygon by any chance?
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by sanju09 » Fri Apr 02, 2010 3:54 am
ajith wrote:
sanju09 wrote:
ajith wrote:
sanju09 wrote:
Can't we celebrate Apr 1 later?
No It has to be now!

https://www.beatthegmat.com/how-many-dia ... 45438.html

Fine ...

We will continue the celebrations on the relevant thread now!

I think I should delete this thread or move it to Lounge
believe me, it's a different thread. The one that I am searching hasn't got choices with it. Why delete or move?
https://www.beatthegmat.com/probability- ... %20polygon by any chance?
[spoiler]now that's like a cute moderator[/spoiler]
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by arora007 » Fri Jul 30, 2010 8:42 am
How many diagonals does a polygon with 21 sides have, if one of its vertices does not connect to any diagonal?

a) 21
b) 170
c) 340
d) 357
e) 420
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by sanju09 » Sat Jul 31, 2010 12:53 am
arora007 wrote:How many diagonals does a polygon with 21 sides have, if one of its vertices does not connect to any diagonal?

a) 21
b) 170
c) 340
d) 357
e) 420
now, what is this favor for?

you mean again...

An n-sided convex polygon has nC2 different line segments that could possibly be drawn, out of which n are the sides of the polygon, and hence the total number of diagonals can be given by

nC2 - n = [n (n - 1)/2] - n = n (n - 3)/2

AB and BA are two different representations of the same line segment, call it AB or BA; the division by 2 is hence there in the resulting formula. If it's known that each of the n vertices has exactly (n - 3) one-way-read diagonals to its name, then the n vertices would have a total of n (n - 3) two-way-read diagonals or just n (n - 3)/2 diagonals to name. When one vertex does not participate in the diagonal formation, its share of exactly (n - 3) one-way-read diagonals is out from the total, and the remaining number of diagonals can be given by

[n (n - 3)/2] - (n - 3) = (n - 2) (n - 3)/2.

We have, n = 21, so our answer must be (21 - 2) (21 - 3)/2 = [spoiler]171, oopsy!! not in choices!!![/spoiler]
The mind is everything. What you think you become. -Lord Buddha



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