LR13 — Paper Cutting and Folding

🧠 AFCAT Reasoning · LR13 ✈️ AFCAT Level

📌 AFCAT Pattern (LR13): Paper Cutting and Folding contributes 2–3 questions per paper. A square paper is folded (one or more times), then a cut or punch is made. You must visualise what the paper looks like when fully unfolded. Key principle: cuts/holes appear symmetrically based on the folds.

1. Folding Principles

Fold Types and Symmetry

1 fold: Creates 2 symmetrical halves; cut appears in 2 places when unfolded
2 folds: Creates 4 symmetrical quadrants; cut appears in 4 places
3 folds: Creates 8 sections; cut appears in 8 places
General rule: n folds → 2ⁿ cuts/holes appear when unfolded

Fold Types

Vertical fold: Left half folds onto right (or vice versa)
Horizontal fold: Bottom half folds onto top (or vice versa)
Diagonal fold: Triangle shape; creates diagonal symmetry
After folding: the cut point is mirrored across the fold line

2. The Reflection Method

When paper is folded and punched, the hole appears at the punch location AND its mirror image across the fold line. For multiple folds: apply mirror for each fold in REVERSE ORDER (unfold last fold first, then second-to-last, etc.).

Worked Example — Single Fold

Square paper. Fold: right half onto left half (vertical fold, fold line = vertical centre). Punch: one hole in the upper-left area of the folded paper.
Unfolding: The punch goes through both layers. Hole 1 = original punch location (left side of paper). Hole 2 = mirror image across vertical centre (right side of paper, same height). Both holes are at equal distances from the centre line. Result: 2 holes, symmetrically placed on left and right.

Worked Example — Double Fold

Square paper. Fold 1: fold bottom half onto top (horizontal fold). Fold 2: fold right half onto left (vertical fold). Punch: one hole in top-left corner of folded paper.
Unfold step 1 (reverse fold 2 — vertical): Hole appears at top-left AND top-right.
Unfold step 2 (reverse fold 1 — horizontal): Each hole doubles → 4 holes: top-left, top-right, bottom-left, bottom-right (corners). Result: 4 holes at corners.

📝 AFCAT PYQPaper Folding — AFCAT Pattern

Q1. A square paper is folded once horizontally (top on bottom). A triangular cut is made at the folded edge (bottom). When unfolded, which pattern appears? (AFCAT I 2025)

(a) One triangle at centre
(b) Diamond/rhombus at centre
(c) Two separate triangles at top and bottom
(d) One rectangle cut

Answer: (b) Diamond/rhombus at centre
The paper is folded: top half onto bottom. The cut is at the folded edge. When unfolded: the triangular cut on the folded edge (which is the centre of the original paper) AND its mirror image combine to form a diamond/rhombus shape at the centre. The cut goes through both layers at the fold line, creating a symmetric shape when unfolded.

Q2. A square is folded along the diagonal (corner to corner). A circle is punched in the triangular section. How many circles appear when unfolded? (AFCAT II 2024)

(a) 1
(b) 2
(c) 4
(d) 3

Answer: (b) 2
One fold = 2 layers = punch goes through both = 2 holes when unfolded. The two holes are mirror images across the diagonal fold line. General rule: 1 fold → 2 holes. The diagonal fold means the second hole appears at the mirror location across the diagonal.

⚡ Quick Reference — LR13

Fold-to-Hole Formula

1 fold → 2 holes/cuts
2 folds → 4 holes/cuts
3 folds → 8 holes/cuts
n folds → 2ⁿ holes (if all layers punched)

Unfolding Method

Unfold in REVERSE order of folding
Each unfold: reflect existing holes across fold line
Vertical fold: reflect left-right
Horizontal fold: reflect top-bottom

AFCAT Strategy

Draw the fold lines on paper
Mark punch location precisely
Unfold step by step (reverse)
Eliminate options with wrong number of holes first

📝 AFCAT Mock Tests 🎯 Reasoning Quiz ✈️ Telegram