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# There is a n-polygon, what is the value of n?

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There is a n-polygon, what is the value of n? [#permalink]

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18 Feb 2016, 18:56
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There is a n-polygon, what is the value of n?

1) The sum of the inner angles is 900 degrees.
2) All the sides of the polygon have the same length.

* A solution will be posted in two days.

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Re: There is a n-polygon, what is the value of n? [#permalink]

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18 Feb 2016, 23:48
The formula 180(n-2) is valid only if it is a regular polygon.Which we get to know by statement 2.
Is there something that i am missing?
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Re: There is a n-polygon, what is the value of n? [#permalink]

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20 Feb 2016, 23:34
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

There is a n-polygon, what is the value of n?

1) The sum of the inner angles is 900o.
2) All the sides of the polygon have the same length.

In the original condition, there is 1 variable(n), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equatin, which is likely to make D the answer.
For 1), n=7 is derived from 180(n-2)=900, which is unique and sufficient.
For 2), the value of n is not unique and not sufficient.

 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: There is a n-polygon, what is the value of n? [#permalink]

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21 Feb 2016, 00:23
For solving equation 1 you have used the formula 180(n-2).My question is that we can use this formula when polygon is a regular one.
Otherwise this formula is not applicable.
From 2nd equ. we get to know that polygon is regular i.e all sides are equal. So,answer should be C.
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Re: There is a n-polygon, what is the value of n? [#permalink]

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21 Feb 2016, 09:37
1
mahakmalik wrote:
For solving equation 1 you have used the formula 180(n-2).My question is that we can use this formula when polygon is a regular one.
Otherwise this formula is not applicable.
From 2nd equ. we get to know that polygon is regular i.e all sides are equal. So,answer should be C.

Hi,
the formula is for any n sided polygon, be it regular or not..
Example a triangle will have (3-2)*180=180, irrespective of it being a equilateral triangle, isosceles triangle or scalene triangle..
ONE way to get it..
if you take any one vertices and join to all other vertices..
it will make n-2 triangles, the adjoining sides will be just a line..
these n-2 triangles will have (n-2)*180 degree..

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Re: There is a n-polygon, what is the value of n? [#permalink]

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21 Feb 2016, 22:14
Even if it's not a regular n-polygon, the number of triangles of n-polygon is (n-2). Also, the sum of interior angles of a triangle is 180.
Thus, in 1), (n-2)180=900, n=7 is derived, which is sufficient.

mahakmalik wrote:
For solving equation 1 you have used the formula 180(n-2).My question is that we can use this formula when polygon is a regular one.
Otherwise this formula is not applicable.
From 2nd equ. we get to know that polygon is regular i.e all sides are equal. So,answer should be C.

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There is a n-polygon, what is the value of n? [#permalink]

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13 Aug 2017, 10:35

The formula 180(n-2) holds good if the Polygon is Regular. If we combine 1 and 2 then answer can be found. so Answer is C

Correcting my stand on it. Answer is A . As sum of angles is 900 only one value of N will satisfy. And N is 7. So answer is A.
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Re: There is a n-polygon, what is the value of n? [#permalink]

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14 Aug 2017, 11:03
sisirkant wrote:

The formula 180(n-2) holds good if the Polygon is Regular. If we combine 1 and 2 then answer can be found. so Answer is C

Correcting my stand on it. Answer is A . As sum of angles is 900 only one value of N will satisfy. And N is 7. So answer is A.

The formula 180(n-2) holds good for any n-side polygon.
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Re: There is a n-polygon, what is the value of n?   [#permalink] 14 Aug 2017, 11:03
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