it has to be C
coz with st 1 we can have polygon of side 4 or 5 or 7 so on so forth
but with 2nd st we know that it is quadrilateral

Given p = polygon and x = prime
Polygon can be 3-sided (triangle), 4-sided (square / rectangle), 5-sided (pentagon) and so on ...
quadrilateral is a 4 sided polygon
so essentially the question is asking whether the polygon has 4 sides or their interior angles sum to 360 degrees.

1. polygon's interior angles sum to 180 x
sum of interior angles = (no. of sides - 2) * 180
given X = prime

if x = 2, Sum of angles = 180 * 2 = 360 degrees (hence no of sides = 4) Yes a quadrilateral
but if x = 3, sum of angles = 180 * 3 = 540 (number of sides = 5) NOT a quadrilateral.
Hence insufficient

2. polygon has 2x sides
if x = 2, no of sides = 4 (YES a quadrilateral)
if x = 3, no of sides = 6 (NOT a quadrilateral)
Hence insufficient

Taking 1+2 together, still insufficient
hence E

What's the OA?

Taking 1+2 together, still insufficient
hence E

it has to be C .from st1 we are getting the sides as 4 ,5 ,7,9
and from st 2 we know that sides are even hence sides have to be 4
hence C
make sense ?

1) n-2 = x 180x

4-2= 2
5-2= 3
6-2= 4 no good , not prime
7-2= 5

number of sides can vary so not suff

2) 2*x = sides

2 * 2= 4
2 * 3= 6
2 * 5= 10
2 * 7= 14

again number of sides can vary so not suff

together

4 sides when x=2 is only consistent answer.

suff. answer c