GATE CS 2025 Set 1 — Question 9

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MCQ+2 / -0.67MediumPaper Folding, Cutting & PatternsSpatial AptitudeGeneral Aptitude

General Aptitude → Spatial Aptitude → Paper Folding, Cutting & Patterns

Last updated 5 September 2026

Question

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.

Correct answer (A) [figure] Solution Track where each part of the folded triangle (IV) lies in the original square. 1. Fold (II) is along the diagonal from the top-left to the bottom-right corner, giving the right triangle (III). Its two legs are original sides of the square and its hypotenuse is the diagonal fold. 2. Fold (III) is along the line from the right-angle corner to the midpoint of the hypotenuse. The result (IV) is a quarter-triangle whose bottom vertex is the centre of the square, whose two slanted edges are fold lines (half-diagonals), and whose top edge is an original side of the square (all four sides now lie on top of each other). Its two top corners are corners of the original square. Now unfold the cuts: Triangular notch in the middle of the top edge, pointing towards the edge: the top edge is an outer side, so the notch appears at the midpoint of every side of the square, each pointing outwards towards its side. Cut on the left slanted (fold) edge near the top-left corner: it is a right-angled piece whose long side lies on the 45° fold, so it opens out into a square sitting at a corner on a diagonal. This gives squares at two opposite corners. Small bar touching the right slanted (fold) edge near the top-right corner: reflecting a bar about a 45° fold produces a bent, L-shaped hook. This gives L-shaped hooks at the other two opposite corners. Checking the options: (A) Four edge triangles pointing outwards, squares at two opposite corners and L-hooks at the other two. Matches. (B) The corner squares are drawn as diamonds (rotated), which a cut whose long side lies along the 45° fold cannot produce. (C) The triangles at the top and bottom point the wrong way. (D) Has a square at the centre and no squares at the corners. Answer: (A) Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (A) [figure] Solution Track where each part of the folded triangle (IV) lies in the original square. 1. Fold (II) is along the diagonal from the top-left to the bottom-right corner, giving the right triangle (III). Its two legs are original sides of the square and its hypotenuse is the diagonal fold. 2. Fold (III) is along the line from the right-angle corner to the midpoint of the hypotenuse. The result (IV) is a quarter-triangle whose bottom vertex is the centre of the square, whose two slanted edges are fold lines (half-diagonals), and whose top edge is an original side of the square (all four sides now lie on top of each other). Its two top corners are corners of the original square. Now unfold the cuts: Triangular notch in the middle of the top edge, pointing towards the edge: the top edge is an outer side, so the notch appears at the midpoint of every side of the square, each pointing outwards towards its side. Cut on the left slanted (fold) edge near the top-left corner: it is a right-angled piece whose long side lies on the 45° fold, so it opens out into a square sitting at a corner on a diagonal. This gives squares at two opposite corners. Small bar touching the right slanted (fold) edge near the top-right corner: reflecting a bar about a 45° fold produces a bent, L-shaped hook. This gives L-shaped hooks at the other two opposite corners. Checking the options: (A) Four edge triangles pointing outwards, squares at two opposite corners and L-hooks at the other two. Matches. (B) The corner squares are drawn as diamonds (rotated), which a cut whose long side lies along the 45° fold cannot produce. (C) The triangles at the top and bottom point the wrong way. (D) Has a square at the centre and no squares at the corners. Answer: (A)

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GATE CS 2025 Set 1 — Question 9

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