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GATE 2025 DA – Question 4

General Aptitude · Analytical Aptitude: Logical Reasoning and Deduction · 1 mark · Multiple choice

In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of P, Q, and R ?

A rectangle, a triangle and an ellipse overlapping. Each region carries a number: 1 in the rectangle only, 2 in the triangle only, 3 in the ellipse only, 4 in the part shared by the rectangle and the ellipse, and the unknown labels P, Q and R. P is in the part shared by all three shapes, Q in the part shared by the triangle and the ellipse outside the rectangle, and R in the part shared by the rectangle and the triangle outside the ellipse.
  1. P = 6; Q = 5; R = 3
  2. P = 5; Q = 6; R = 3
  3. P = 3; Q = 6; R = 6
  4. P = 5; Q = 3; R = 6

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Correct answer: (A) P = 6; Q = 5; R = 3

Explanation

The number written in a region is the sum of the numbers of the shapes that contain it. The part shared by the rectangle (1) and the ellipse (3) shows 4, which confirms this rule. P lies inside all three shapes, so $P = 1 + 2 + 3 = 6$. Q lies in the triangle and the ellipse only, so $Q = 2 + 3 = 5$. R lies in the rectangle and the triangle only, so $R = 1 + 2 = 3$.