CAT 2022 Slot 3 QA Q7 Geometry

Question 7 of the Quantitative Ability (QA) section, CAT 2022 Slot 3, with CAT's official answer and a worked solution.

Suppose the medians BD and CE of a triangle ABC intersect at a point O. If area of triangle ABC is 108 sq. cm., then, the area of the triangle EOD, in sq. cm., is

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

Answer: 9 Geometry TITA

Solution

  1. O is the centroid, so \(OD=\frac13BD\).
  2. D is the midpoint of AC, so \([ABD]=\frac12\cdot108=54\); E is the midpoint of AB, so \([EBD]=\frac12\cdot54=27\).
  3. Triangles EOD and EBD share the vertex E with bases on line BD: \([EOD]=\frac13\cdot27=9\).

Shortcut. Area of the triangle formed by two midpoints and the centroid is \(\frac1{12}\) of the whole triangle.

Same concept in other years

See every question on Medians and centroid: 2:1 split and equal-area pieces.

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