CAT 2022 Slot 3 QA Q22 Geometry

Question 22 of the Quantitative Ability (QA) section, CAT 2022 Slot 3, with CAT's official answer and a worked solution.

The lengths of all four sides of a quadrilateral are integer valued. If three of its sides are of length 1 cm, 2 cm and 4 cm, then the total number of possible lengths of the fourth side is
  1. A
    6
  2. B
    4
  3. C
    5
  4. D
    3

Answer: (C) 5 Geometry MCQ

Solution

  1. In a quadrilateral, each side must be less than the sum of the other three.
  2. If the fourth side \(x\) is the largest: \(x\lt1+2+4=7\).
  3. Side 4 must satisfy \(4\lt1+2+x\Rightarrow x\gt1\).
  4. So \(x\in\{2,3,4,5,6\}\): 5 lengths.

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