GATE 2025 XH5 (Psychology) – Question 25

Reasoning and Comprehension · Quantitative reasoning · 2 marks · Numerical answer

In the following figure, four overlapping shapes (rectangle, triangle, circle, and hexagon) are given.

The sum of the numbers which belong to only two overlapping shapes is_______.

A rectangle, a triangle, a circle and a hexagon overlap. The circle contains the whole triangle. Regions are numbered: 5 and 7 are in the circle only, on either side of the triangle's top; 6 is in the triangle and circle; 2 (twice) is in the rectangle and circle but not the triangle; 3 inside the triangle is in the rectangle, triangle and circle; 3 on the far left is in the rectangle only; 1 is in the circle only, below the triangle; 9 is in the triangle, circle and hexagon; 8 is in the circle and hexagon but not the triangle; 4 is in the hexagon only.

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Correct answer: 18

Explanation

Look at each numbered region and count the shapes that contain it. The regions inside exactly two shapes are 6 (triangle and circle), the two regions marked 2 (rectangle and circle) and 8 (circle and hexagon). Regions 3 (inside the triangle) and 9 are in three shapes, and 1, 3 (far left), 4, 5 and 7 are in one shape only. The sum is $6 + 2 + 2 + 8 = 18$.