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. A. Pattern with small filled squares at top-left and bottom-right corners and bracket-shaped marks at top-right and bottom-left corners B. Pattern with diamond shapes at top-left and bottom-right corners and bracket-shaped marks at top-right and bottom-left corners C. Pattern with small filled squares at top-left and bottom-right, and at top-right, with bracket-shaped marks at bottom-left and bottom corners D. Pattern with a single central filled square and bracket-shaped marks at corners

GATE 2025 · General Aptitude · Paper Folding · medium

Answer: Option A — filled squares at two diagonally opposite corners and bracket shapes at the other two corners

1. Identify fold sequence from figures (I)-(III): After two folds the paper is a right triangle that is one-quarter of the original square. Each point of this small triangle corresponds to multiple points on the original square.
2. Map the cuts in figure (IV) to positions on the folded shape: Cut 1 passes through 2 layers (due to fold symmetry); it maps to 2 corner positions on the original square. Cut 2 similarly maps to 2 corner positions — the remaining two corners.
3. Compare to answer options: Option A shows: small filled squares at top-left and bottom-right corners, bracket (L-shape) marks at top-right and bottom-left corners. This is exactly consistent with the symmetric mapping of two types of cuts made at the two acute corners of the twice-folded triangle.