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

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If Polygon X has fewer than 9 sides, how many sides does [#permalink] New post 23 Nov 2007, 11:02
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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 [#permalink] New post 23 Nov 2007, 11:25
Answer is A.

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.
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 [#permalink] New post 23 Nov 2007, 11:59
jbs wrote:
Answer is A.

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!!
  [#permalink] 23 Nov 2007, 11:59
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