A circular sheet of paper is folded along the lines in the directions shown. The paper, after being punched in the final folded state as shown and unfolded in the reverse order of folding, will look like _______. A. [Circle with two rectangular holes side by side in the centre and a rectangular hole at top centre] B. [Circle with two rectangular holes in the upper portion arranged horizontally] C. [Circle with two rectangular holes side by side in the centre and a rectangular hole at top centre — mirror variant] D. [Circle with one tall rectangular hole in the centre]

GATE 2021 · General Aptitude · Paper Folding · medium

Answer: The unfolded circular sheet looks like option A — with two rectangular holes side by side in the central area and one rectangular hole near the top, all symmetric about the fold axes.

  1. Identify fold axes and punch position: From the figure: Fold 1 is along the vertical centre line (left half onto right). Fold 2 is along the horizontal centre line (top half onto bottom). The punch after both folds is a small rectangle near the centre of the folded (quarter) sheet — this corresponds to a position in the top-right quadrant of the original circle.
  2. Undo Fold 2 (horizontal): reflect punch across horizontal axis: The single punch in the top-right of the folded sheet, when the horizontal fold is undone, creates a copy reflected below the horizontal axis. We now have 2 hole positions: one in the upper centre area and one in the lower centre area of the right half.
  3. Undo Fold 1 (vertical): reflect both holes across vertical axis: Each of the 2 holes gets a mirror copy on the left side of the circle. This yields 4 holes in total: two side-by-side rectangles in the horizontal centre band and one rectangle at the top centre. The arrangement matches option A: two rectangular holes side by side at centre and one rectangular hole at top.
  4. Match with answer options: With 2 folds, 1 punch yields up to 4 holes (2^2 = 4). Option A shows the correct symmetric arrangement of holes within the circular boundary matching the described fold-punch-unfold sequence.