GATE CS 2026 Set 1 Q.2: Spatial Aptitude

The figure shows two 4-tile patterns.

Two 4-tile patterns: a 2 by 2 square of 4 tiles on the left, and a 4 by 1 vertical strip of 4 tiles on the right.

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?

A 2 by 4 rectangular grid of 8 unit tiles.

A 3 by 4 rectangular grid of 12 unit tiles.

A 3 by 5 rectangular grid of 15 unit tiles.

A 4 by 5 rectangular grid of 20 unit tiles.

Official answer and solution

Official answer: C
From: Official GATE 2026 answer key

Solution

Count the total number of unit tiles in each candidate rectangle and check whether it is divisible by 4 and tilable by $2 \times 2$ and $1 \times 4$ blocks.

Since both building blocks contain $4$ unit tiles and no overlaps are allowed, any pattern constructed from them must have a total number of unit tiles that is a multiple of $4$ :

Option (A) is a $2 \times 4$ grid ( $8$ tiles), which can be constructed using two $2 \times 2$ patterns (or two horizontal $1 \times 4$ patterns).
Option (B) is a $3 \times 4$ grid ( $12$ tiles), which can be constructed using three horizontal $1 \times 4$ patterns.
Option (C) is a $3 \times 5$ grid ( $15$ tiles). Since $15$ is not divisible by $4$ , it cannot be constructed without overlaps.
Option (D) is a $4 \times 5$ grid ( $20$ tiles), which can be constructed using five vertical $4 \times 1$ patterns.

Final answer

Option (C)

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2026 Computer Science and Information Technology - Session 1 (CS1)
Question: 2 of 65
Section: General Aptitude

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