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GATE DA 2025 Q4: Overlapping shapes: find P, Q and R

Question

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. Region labels: 1 in the rectangle only, 2 in the triangle only, 3 in the ellipse only, 4 where rectangle and ellipse overlap, P where all three overlap, Q where triangle and ellipse overlap, R where rectangle and triangle overlap.
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Try it: multiple choice: exactly one correct option

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Wrong answer costs 1/3 mark in GATE.
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Answer: A (official GATE 2025 final answer key)

Concept used: Spatial reasoning: a region's number is the sum of the numbers of the shapes it lies in.

First step: Check the rule on the region marked 4: it lies in the rectangle (1) and the ellipse (3), and 1 + 3 = 4. Apply the same rule to P, Q and R.

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Source: official GATE 2025 DA question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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