Non Verbal Reasoning · Reflections, Folding & Cutting
Paper Folding — Questions & Answers
Paper folding questions show a sheet folded one or more times and punched or cut, and ask how it looks when opened. Every fold is a mirror line, so each hole appears once for every layer of paper.
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How to approach
Each fold doubles the layers: 1 fold = 2 layers, 2 folds = 4, 3 folds = 8 — so one punch makes that many holes.
Unfold one fold at a time, starting with the last: mirror every hole across that fold line.
A cut on a folded edge opens into one whole shape that straddles the crease.
5 solved Paper Folding questions
A circular sheet is folded as shown (dashed part folded over in the direction of the arrow) and then punched. How will it look when opened?
Solution — answer A
The paper is folded twice, so it has 4 layers and every punch goes through all of them: it appears 4 times on the opened sheet, mirrored across every fold line.
4 steps · reveal one at a timeStep 1: Count the Folds
The problem describes a circular sheet being folded. The verified solution confirms that the paper is folded twice. This initial folding action determines the number of layers created.
Step 2: Layers and Punches
Because the paper is folded twice, it results in 2×2=4 layers. When a punch is made, it goes through all four layers. This means each punch will create four marks on the original sheet.
Step 3: Placement of Marks
When the sheet is opened, the four punch marks will be visible. These marks are not random; they are mirrored across every fold line. This symmetrical arrangement helps determine the final pattern.
Step 4: The answer
So the answer is (A) Figure A. This figure correctly shows the punch mark appearing four times, symmetrically mirrored across the fold lines, as established by the folding and punching process.
A square sheet is folded as shown (dashed part folded over in the direction of the arrow) and then cut / punched. How will it look when opened?
Solution — answer D
The paper is folded once, so it has 2 layers and every punch goes through all of them: it appears 2 times on the opened sheet, mirrored across every fold line. A cut on a folded edge opens into one full shape across that crease; a cut on the outer edge or a corner leaves a notch in the sheet's outline.
4 steps · reveal one at a timeStep 1: Analyze the Fold
The problem describes a square sheet folded once. This means the folded paper has 2 layers. Any cut or punch made will go through both layers of the paper.
Step 2: Effect of Punches
Because the punch goes through 2 layers, it will appear twice on the opened sheet. These two shapes will be mirrored across the fold line, creating a symmetrical pattern.
Step 3: Cuts on Edges
The type of cut also matters. A cut made on a folded edge will open into one full shape across that crease. However, a cut on an outer edge or a corner will simply leave a notch in the sheet's outline.
Step 4: The answer
So the answer is (D) Figure D. This figure correctly shows the result of the initial fold and subsequent cuts, with shapes appearing twice and mirrored, and specific cuts forming full shapes or notches as described.
A square sheet was folded and punched once, then opened; the opened sheet looks like the figure. Which of these shows how it was folded (dashed: the whole sheet and its creases) and where it was punched?
Solution — answer C
Open each option in your head: mirror the hole across every crease. Only option C gives exactly 4 holes in the places shown.
5 steps · reveal one at a timeStep 1: Analyze the Problem
The task is to determine which folding pattern and punch location creates the final opened sheet with its specific hole pattern. We need to work backward or simulate the folding and punching process for each possibility.
Step 2: How Holes Appear
When a sheet is folded and punched, the hole isn't just in one spot. Each fold acts like a mirror. When you unfold the sheet, the original punched hole is reflected across each crease, creating multiple holes.
Step 3: Test Each Option
To check each option, imagine the sheet being unfolded. For every crease, you must mirror the punched hole (or holes already formed) across that crease. This reveals where all the holes would appear on the fully opened sheet.
Step 4: Count the Holes
Continue mirroring across all creases until the sheet is fully open. The correct option will be the one where the mirrored holes exactly match the number and position of holes shown in the opened sheet, which is 4 holes.
Step 5: The answer
So the answer is (C) Figure C. Only Figure C, when unfolded by mirroring the punch across its creases, results in exactly 4 holes in the correct positions as shown in the final opened sheet.
A circular sheet is folded as shown (dashed part folded over in the direction of the arrow) and then cut / punched. How will it look when opened?
Solution — answer A
The paper is folded twice, so it has 4 layers and every punch goes through all of them: it appears 4 times on the opened sheet, mirrored across every fold line. A cut on a folded edge opens into one full shape across that crease; a cut on the outer edge or a corner leaves a notch in the sheet's outline.
4 steps · reveal one at a timeStep 1: Analyze the Fold
The circular sheet is folded twice. This means that any cut or punch you make will go through 4 layers of paper. Understanding this is crucial for predicting how the final opened sheet will appear.
Step 2: Punches and Symmetry
Because a punch goes through 4 layers, it will appear 4 times on the opened sheet. Each appearance will be mirrored across every fold line, creating a symmetrical pattern on the final sheet.
Step 3: Cuts and Edges
A cut made on a folded edge will open up into one complete shape across that crease. In contrast, a cut made on the outer edge of the folded paper or on a corner will result in a notch in the sheet's outline when opened.
Step 4: The answer
So the answer is (A) Figure A. This figure correctly shows the result of the described folding and cutting, with shapes appearing 4 times and mirrored across the fold lines, and any edge cuts forming full shapes or notches as expected.
The transparent sheet below is folded along the dashed middle line, in the direction of the arrow. Which figure shows how it looks after folding?
Solution — answer B
The sheet is transparent, so after folding you see both halves at once. The half that stays does not change; the half that is folded over lands on top as a mirror image across the fold line.
4 steps · reveal one at a timeStep 1: Identify the Action
The problem describes a transparent sheet being folded along a dashed middle line. This means one part of the sheet will move and overlap the other.
Step 2: Effect of Transparency
Since the sheet is transparent, you will be able to see both parts of the original figure after it is folded. Nothing will be hidden from view.
Step 3: Analyze the Folded Image
The part of the sheet that stays in place will look exactly the same. The part that is folded over will appear as a mirror image of itself, reflected across the dashed fold line, on top of the stationary half.
Step 4: The answer
So the answer is (B) Figure B. This figure correctly shows the original stationary half combined with the mirror image of the folded half.
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