CAT 2024 Slot 3 QA Q7 Geometry

Question 7 of the Quantitative Ability (QA) section, CAT 2024 Slot 3, with CAT's official answer and a worked solution.

The midpoints of sides AB, BC, and AC in △ ABC are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of △ ABC is 1440 sq cm, then the area, in sq cm, of △ XYZ is

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

Answer: 90 Geometry TITA

Solution

  1. MP is a midline parallel to BC, so the median from A bisects it: X is the midpoint of MP. Likewise Y and Z are midpoints of MN and NP.
  2. So XYZ is the medial triangle of MNP, which is the medial triangle of ABC.
  3. Area \(= \frac{1440}{4 \times 4} = 90\).

Same concept in other years

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

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