CAT 2023 Question Paper | Quant Slot 3

CAT 2023 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 19 : In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is

Video Explanation

Explanatory Answer

Exterior angle + Interior angle = 180
Exterior angle + Exterior angle + 120 = 180
2(Exterior angle) = 60
Exterior angle = 30
In a polygon, the exterior angle is simply, \( \frac { 360 } { n } \)
\( \frac { 360 } { n } = 30 ; n = 12 \)
The number of diagonals \( = { } ^ { n } c _ { 2 } - n = { } ^ { 12 } c _ { 2 } - 12 = 54 \)

The question is " In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is "

Hence, the answer is '54'