The question consists of a set of three figures X, Y and Z showing a sequence of folding of a piece of paper. Figure Z shows the…

Question

The question consists of a set of three figures X, Y and Z showing a sequence of folding of a piece of paper. Figure Z shows the manner in which the folded paper has been cut. Choose the figure which would most closely resemble the unfolded form of figure Z.

1. A.
2. B. (Correct answer)
3. C.
4. D.

Correct Answer

Option B — A square with two six-sided holes lying side by side along the horizontal centre line, meeting at a pinch point at the centre and reaching the left and right edges.

Detailed Solution & Explanation

The correct answer is option B.

Key Points

• Track the folds first. In figure X the sheet is folded along the horizontal centre line, taking the top half down onto the bottom half. In figure Y the result is folded again along the vertical centre line, taking the left half onto the right. The paper is now a quarter of its original size and four layers thick.
• In figure Z the cut is a shallow six-sided notch lying immediately below the horizontal fold, running from the vertical fold line across to the right-hand edge.
• Unfold in the reverse order:
  • Undoing the vertical fold mirrors the notch to the left, so it now stretches right across the sheet as two notches meeting at the centre.
  • Undoing the horizontal fold mirrors both notches upward. Because the cut sat *on* the fold line, each half-notch joins its reflection into one complete six-sided hole.
• The sheet therefore opens out with two six-sided holes side by side along the horizontal centre line, touching at the middle — which is option B.

Additional Information

• The single most useful rule here: a cut that touches a fold line opens into one whole shape, while a cut that sits clear of every fold opens into two separate shapes. Counting holes before comparing options settles most questions of this type.
• Each fold doubles the number of cut shapes. Two folds and one notch give 2 × 1 = 2 holes, which alone rules out option A with its four.
• Option A shows four holes in a pinwheel, the pattern you would get if the notch had straddled both fold lines rather than only the horizontal one.
• Option C adds a third hole rising to the top edge, which would require a second cut that figure Z simply does not show.
• Option D breaks the symmetry altogether. Folding guarantees the opened sheet is symmetric about every fold line used, so any option that is not symmetric left-to-right and top-to-bottom can be discarded on sight.