Polygons 180(n-2) formula logic

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KICKGMATASS123: Master | Next Rank: 500 Posts; Posts: 113; Joined: Thu Feb 26, 2009 8:13 am; Location: New Jersey; GMAT Score:650

Polygons 180(n-2) formula logic

by KICKGMATASS123 » Wed May 20, 2009 5:26 pm

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.

Please explain this in detail i dont understand the approach to do this kind of question

Thanks
OA is A

Quote

Source: Beat The GMAT — Data Sufficiency | Wed May 20, 2009 5:26 pm

DeepakR: Master | Next Rank: 500 Posts; Posts: 158; Joined: Tue Sep 30, 2008 8:47 am; Thanked: 23 times; Followed by:1 members; GMAT Score:660

by DeepakR » Wed May 20, 2009 6:04 pm

Sum of interior angles of a polygon = (n-2) * 180
Where n is the number of sides. Given that n < 9

#1. It states that (n-2)*180/16 is an integer. This gets satisfied only for n=6
then 4*180/16 = 45. So n=6. Hence A is sufficient.

#2. It states that (n-2)*180/15 = integer. For this condition all the values of n like n=3,4,5 will satisfy. So we cant conclusively say the value of n. Hence B is insufficient.

Hence A.) alone is sufficient.

- Deepak