GATE CS 2026 Set 1 — Question 2
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General Aptitude → Spatial Aptitude → 2D & 3D Patterns
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Question
The figure shows two 4-tile patterns.
Either one or both of the patterns can be used any number of times and in any orientation to construct a new pattern. Which one of the options below cannot be constructed by using only these two 4-tile patterns assuming there are no overlaps among them?
Either one or both of the patterns can be used any number of times and in any orientation to construct a new pattern. Which one of the options below cannot be constructed by using only these two 4-tile patterns assuming there are no overlaps among them?
Correct answer
(C) [figure]
Solution
The problem asks which pattern cannot be constructed using the given 4-tile patterns (a square and a strip). Since each basic pattern consists of exactly 4 tiles, any constructed pattern must have a total number of tiles that is a multiple of 4.Let's analyze the number of tiles in each option:
- (A) A grid has tiles. Since 12 is divisible by 4, it is possible (e.g., using three strips horizontally).
- (B) A grid (or ) has tiles. Divisible by 4.
- (C) A grid has tiles. Since 15 is not divisible by 4, it is impossible to construct this pattern using only 4-tile shapes without overlap or gaps.
- (D) A grid has tiles. Divisible by 4.
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