Data Sufficiency

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.

IMO A.

for stmt 2 there can be more than one answer.

sum of interior angles (n-2)*180

what is OA?

We know that the sum of interior angles is given by the formula (n-2)*180,where n is the no of sides of the polygon

statement 1:

The sum of the interior angles of Polygon X is divisible by 16.
((n-2)*180)/16 is an integer
It can also be inferred from the question that n<9
((n-2)*45)/4 is an integer
The above statement is possible only for one value of n i.e n=6
So the polygon has 6 sides
Sufficient

statement 2:

The sum of the interior angles of Polygon X is divisible by 15.
((n-2)/180)/15 is an integer
(n-2)*12 is an integer ( for n<9)
n can be any number from 3 to 8
Insufficient

Hence the ans is A...Let me know if you have any doubts..