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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. P = 6, Q = 5, R = 3 B. P = 5, Q = 6, R = 3 C. P = 3, Q = 3, R = 6 D. P = 3, Q = 5, R = 6

GATE 2025 · General Aptitude · Geometry · medium

Answer: P = 6, Q = 5, R = 3 (Option A)

  1. Identify regions and their shape memberships: From the figure, three numbers (1, 2, 3) are placed in distinct regions. Region labeled 1 lies inside the rectangle only. Region labeled 2 lies inside the triangle only, near its apex that overlaps with the rectangle. Region labeled 3 lies inside the ellipse only. Overlap zones between shapes are also counted per shape.
  2. Count total regions per shape: Reading the figure: the rectangle is the largest shape and covers regions containing labels summing to P = 6 sub-divisions. The triangle covers regions summing to Q = 5. The ellipse is the smallest enclosed area, covering regions summing to R = 3. This matches option A: P = 6, Q = 5, R = 3.