BTGmoderatorDC wrote:

In the figure above, polygon N has been partially covered by a piece of paper. How many sides does N have?

(1) x + y = 45
(2) N is a regular polygon

OA C

Source: Veritas Prep

Target question: How many sides does N have?

Statement 1: x + y = 45
Since all angles in a triangle add to 180°, we know that the missing angle is 135°


There are plenty of polygons that have at least one angle measuring 135°. Here are two:

Case a:

In this case, the answer to the target question is polygon N has 3 sides


Case b:

In this case, the answer to the target question is polygon N has 4 sides

Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: N is a regular polygon
This definitely doesn't help (we have no idea what the measurement of each angle is)
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that ONE angle measures 135°
Statement 2 tells us that all of the angles are EQUAL (that's what "regular" means)
At this point, we have LOCKED IN the shape. That is, there is ONLY ONE regular polygon in which all of the angles are 135°
So, if we did some more work, we COULD determine the number of sides of N, which means we COULD answer the target question with certainty
The combined statements are SUFFICIENT

Answer: C

Aside: Here's how we'd determine the number of sides:
Useful rule: the sum of the angles in an n-sided polygon = (n - 2)(180º)
So, in a REGULAR n-gon, the measurement of EACH angle = (n - 2)(180º)/n

We can write: (n - 2)(180)/n = 135
Multiply both sides by n to get: (n - 2)(180) = 135n
Expand left side to get: 180n - 360 = 135n
Rearrange to get: 45n = 360
Solve: n = 360/45 = 8
So, polygon N has 8 sides

Cheers,
Brent