CAT 2022 Question Paper | Quant Slot 2

CAT 2022 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 3 : Regular polygons A and B have number of sides in the ratio 1 : 2 and interior angles in the ratio 3 : 4. Then the number of sides of B equals

Video Explanation

Explanatory Answer

The sum of internal angles of an n-sided polygon is given by (n - 2)180 degrees.
When the polygon is regular, each angle equals, \( \frac { ( n - 2 ) 180 } { n } \)
Number of sides of Polygon A and B are in the ratio 1 : 2
Let there be n sides in Polygon A, there will be 2n sides in Polygon B.
The ratio of internal angles of these Polygons is 3 : 4.
\( \frac { \frac { ( n - 2 ) 180 } { n } } { \frac { ( 2 n - 2 ) 180 } { 2 n } } = \frac { 3 } { 4 } \)
\( \frac { n - 2 } { n - 1 } = \frac { 3 } { 4 } \)
4(n - 2) = 3(n - 1)
4n - 8 = 3n - 3
n = 5
Number of sides in Polygon B = 2n = 2(5) = 10

The question is " Regular polygons A and B have number of sides in the ratio 1 : 2 and interior angles in the ratio 3 : 4. Then the number of sides of B equals "

Hence, the answer is '10'

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