GATE DA 2025 | Question 4

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 overlap. The region inside the rectangle only is marked 1, inside the triangle only 2, inside the ellipse only 3, and inside the rectangle and the ellipse but outside the triangle 4; P marks the region inside all three shapes, Q the region inside the triangle and the ellipse but outside the rectangle, and R the region inside the rectangle and the triangle but outside the ellipse.

Option A: P = 6; Q = 5; R = 3 (correct)
Option B: P = 5; Q = 6; R = 3
Option C: P = 3; Q = 6; R = 6
Option D: P = 5; Q = 3; R = 6

Answer

(A)

Explanation

Each region carries the sum of the numbers of the shapes it lies in. The given label 4 confirms the rule: that region is inside the rectangle and the ellipse but outside the triangle, and \(1 + 3 = 4\).

P is inside all three shapes: \(P = 1 + 2 + 3 = 6\).
Q is inside the triangle and the ellipse only: \(Q = 2 + 3 = 5\).
R is inside the rectangle and the triangle only: \(R = 1 + 2 = 3\).

Answer: A