GATE CS 2025 Set 1 Q.9: Spatial Aptitude

A square paper, shown in figure (I), is folded along the dotted lines as shown in the figures (II) and (III). Then a few cuts are made as shown in figure (IV). Which one of the following patterns will be obtained when the paper is unfolded?

Note: The figures shown are representative.

Four sequential paper-folding diagrams: (I) square sheet; (II) square folded along main diagonal from bottom-left to top-right; (III) resulting right triangle folded along its altitude; (IV) folded triangle with an upward triangle cut near the top edge, a right-triangle cut on the left slanted fold, and a horizontal rectangular cut near the right slanted fold.

Unfolded square pattern (A) with outward-pointing triangles on all four side midpoints, L-shaped rectangular cutouts in the top-right and bottom-left corners, and axis-aligned square cutouts in the top-left and bottom-right corners.

Unfolded square pattern (B) with outward-pointing triangles on all four side midpoints, L-shaped rectangular cutouts in the top-right and bottom-left corners, and diamond-shaped (45-degree rotated square) cutouts in the top-left and bottom-right corners.

Unfolded square pattern (C) with inward-pointing triangles at the top and bottom midpoints, outward-pointing triangles at the left and right midpoints, L-shaped cutouts in the top-right and bottom-left corners, and axis-aligned square cutouts in the top-left and bottom-right corners.

Unfolded square pattern (D) with outward-pointing triangles on all four side midpoints, L-shaped cutouts in the top-right and bottom-left corners, and a single square cutout in the center of the sheet.

Official answer and solution

Official answer: A
From: Official GATE 2025 answer key

Solution

Reflect the three cuts in figure (IV) across the second fold line from (III) and then across the main diagonal fold line from (II).

Trace each of the three cuts in figure (IV) as the paper is unfolded:

Outer-edge triangle cut (along the top edge of (IV)): Because all four outer edges of the square are folded onto this boundary with the same orientation toward the perimeter, unfolding produces four triangles at the midpoints of the four sides of the square, each pointing outward toward its respective edge (eliminating (C)).
Left diagonal fold cut: In (IV), a right-angled triangle with horizontal and vertical legs is cut along the fold line of step (III). Reflecting this right-angled triangle across its hypotenuse (the 45-degree fold line in (IV)) combines the two right triangles into an axis-aligned square (with horizontal and vertical sides) in the top-left and bottom-right corners (eliminating (B) and (D)).
Right diagonal fold cut: The horizontal rectangular slot near the right slanted fold line reflects across the diagonal fold from step (II) into a vertical rectangular slot meeting it at the corner, creating the two L-shaped rectangular pairs in the top-right and bottom-left corners.

Thus pattern (A) is obtained.

Final answer

Option (A)

Common trap

Choosing (B) by assuming a triangular notch on a slanted fold unfolds into a rotated diamond, without noticing that the notch in (IV) already has horizontal and vertical legs.

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

Source

Paper: GATE 2025 Computer Science and Information Technology - Session 1 (CS1)
Question: 9 of 65
Section: General Aptitude

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