GATE 2026 EE GA Q.8: solution and answer

GATE 2026 · EEGA Q.8 · 2 marks · MCQ

Based on the relationship between each polygon and the number inside it, the value of ‘X’ is ______

GATE 2026 EE GA question 8: Four unshaded outline polygons in one horizontal row, each with a number written at its centre. — Figure from the GATE 2026 EE paper. It is part of the question.

(A)
720
(B)
596
(C)
24
(D)
240

Answer and solution

ANSWER

X = 6! = 720, so the answer is option (A).

Official answer: ASource: Official answer key, GATE 2026 EE (IIT Guwahati)

Count the sides of each polygon: triangle $= 3$ , rectangle $= 4$ , pentagon $= 5$ , hexagon $= 6$ .
Compare each number with its side count. Each number is the factorial of the number of sides, where $n! = 1 \times 2 \times \dots \times n$ .
Check the three given figures: triangle $3! = 3 \times 2 \times 1 = 6$ ; rectangle $4! = 4 \times 3! = 4 \times 6 = 24$ ; pentagon $5! = 5 \times 4! = 5 \times 24 = 120$ . All three match.
Another way to see the same rule: each number is the previous number multiplied by the new side count, so $6 \times 4 = 24$ and $24 \times 5 = 120$ .
Hexagon (6 sides): $X = 6! = 6 \times 5! = 6 \times 120 = 720$ .
$720$ is option (A).

KEY IDEA

The number inside each polygon is the factorial of its number of sides: $3! = 6$ , $4! = 24$ , $5! = 120$ , so the 6-sided hexagon holds $6! = 720$ .

WATCH OUT FOR

Looking only at the numbers and ignoring the shapes. From 6, 24, 120 alone you might guess "double the last number" ( $120 \times 2 = 240$ , option D) or reuse an earlier number (24, option C). The multiplier is not fixed: it goes up by one each time because it is the next polygon's side count, $\times 4$ then $\times 5$ then $\times 6$ .

From the GATE 2026 EE paper. Every question of this paper · Download the full paper · All 41 Reasoning questions, with notes

GATE 2026 EE GA Q.8: solution and answer

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