canuckclint wrote: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.

minimum sides of a polygon = 3, maximum sides = 8

Statement I
The sum of the interior angles of Polygon X is divisible by 16
sum of the interior angles = (n-2)*180
sides=4, 2*180 = 360, not divisible by 16
sides=5, 3*180 = 540, not divisible by 16
sides=6, 4*180 = 720, divisible by 16
sides=7, 5*180 = 900, not divisible by 16
sides=8, 6*180 = 1080, not divisible by 16

Sufficient. Sides = 6

Statement II
The sum of the interior angles of Polygon X is divisible by 15
sum of the interior angles = (n-2)*180
sides=3, 1*180 = 180, divisible by 15
sides=4, 2*180 = 360, divisible by 15
sides=5, 3*180 = 540, divisible by 15
sides=6, 4*180 = 720, divisible by 15
sides=7, 5*180 = 900, divisible by 15
sides=8, 6*180 = 1080, divisible by 15

Insufficient.


Hence A.

OA?

It should be A)

The other way of looking at A) would for 16 we need 4 2's. 18 provides only 2 so we need 2 more 2's in n-2

The only value of n that could provide this is 6

(6-2) * 180/ 16 = integer (i.e. divisible by 16)

SUFF

B) 180 is divisible by 15 so for any value of 2<n< 8 it will work INSUFF

It should be A)

Stmt I)

The other way of looking at A) would be for 16 in dr to divide the nr exactly we need four 2's. 180 provides only two 2's (factorize 180) so we need two more 2's in n-2

The only value of n that could provide this is 6

(6-2) * 180/ 16 = integer (i.e. divisible by 16)

SUFF

Stmt II
180 is divisible by 15 so for any value of 2<n< 8 it will work INSUFF

Is this regular polygon, Because I was informed that , we can use (2n-4)*90-Sum of interior angles for regular polygon.

Please somebody correct me.