CAT 2022 Slot 2 QA Q3 Geometry

Question 3 of the Quantitative Ability (QA) section, CAT 2022 Slot 2, with CAT's official answer and a worked solution.

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

TITA: type in the answer. There are no options and no negative marking.

Answer: 10 Geometry TITA

Solution

  1. Let A have \(n\) sides and B \(2n\). Interior angles: \(180-\frac{360}{n}\) and \(180-\frac{180}{n}\).
  2. \(4\left(180-\frac{360}{n}\right)=3\left(180-\frac{180}{n}\right)\Rightarrow 180=\frac{900}{n}\Rightarrow n=5\).
  3. B has \(2n=10\) sides (pentagon 108 and decagon 144, ratio 3 : 4).

Same concept in other years

See every question on Regular polygons: exterior angle = 360°/n.

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