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# If Polygon X has fewer than 9 sides, how many sides does

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Director
Joined: 10 Feb 2006
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If Polygon X has fewer than 9 sides, how many sides does [#permalink]  23 Nov 2007, 10:02
If Polygon X has fewer than 9 sides, how many sides does Polygon X have?

(1) The sum of the interior angles of Polygon X is divisible by 16.

(2) The sum of the interior angles of Polygon X is divisible by 15.
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Manager
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For any polygon, sum of interior angles = (n-2)*180.

Given: n<9

A) (n-2)*180 is divisible by 16. Only one value of 'n' (n = 6) is possible.
Sufficient.

B) (n-2)*180 is divisible by 15. 180 is divisible by 15. Therefore there are multiple possible values for 'n'.
Insufficient.
Senior Manager
Joined: 06 Aug 2007
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jbs wrote:

For any polygon, sum of interior angles = (n-2)*180.

Given: n<9

A) (n-2)*180 is divisible by 16. Only one value of 'n' (n = 6) is possible.
Sufficient.

B) (n-2)*180 is divisible by 15. 180 is divisible by 15. Therefore there are multiple possible values for 'n'.
Insufficient.

Same strategy...only A is sufficient..since (n-2)*180 is always divisible by 15.

1. (N-2)*180/16 = (N-2)*45/4

SO (N-2) should be divisible by 4 and only when N= 6 its possible!!
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