CAT 2003 Slot 1 — QA Question 27
PolygonsEasy
Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90° or concave if the internal angle is 270°. If the number of convex corners in such a polygon is 25, the number of concave corners must be
Answer & solution
Correct answer: 21
- A
20
- B
0
21
- D
22
Solution
Consider the polygon as shown in the figure. Here 4 corners A, D, G and J are the concave corners and remaining 8 corners are convex corners.
In general, for a polygon with sides parallel to either of the axes, if n is the number of concave corners and m is the number of convex corners, then we have,
m − n = 4
âµ m = 25
∴ n = 21
Hence, option (c).