Paper cutting is a reasoning concept where a sheet of paper is folded and then cut at certain places. After the paper is unfolded, we must determine the final pattern or shape formed due to the cuts. This type of problem checks spatial understanding, logical thinking, and visualization skills.
How to Solve Paper Cutting Questions
Step 1: Understand the Given Sequence: Carefully look at the sequence of diagrams, and note down the way how paper is folded and/or cut. Pay attention to the direction and orientation of the fold and cut.
Step 2: Visualize the Folding and Cutting Operations: Mentally visualize the folding and/or cutting pattern. Try to visualize how the paper will look at each step.
Step 3: Determine the Final Shape: After visualization of each step, determine the final shape. Pay good attention to the sides, and corners of the shapes.
Step 4: Compare your visualization of the final shape with the options provided in the question, and select the one that matches your result.
Step 5: Verify Your Answer: Cross-verify your answer, do double-check because a minor cut can play a big role in such types of questions.
Solved Examples
Direction: Each of the following questions 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. These three figures are followed by four answer options from which you have to choose a figure that would most closely resemble the unfolded form of figure (Z).
Q1. Choose the figure from 1, 2, 3, or 4 which closely resembles figure Z.
Solution:
Visualizing the cutting Z -> start unfolding the figure Z -> From Z, move to Figure Y -> Then move to figure X.
Q2. Choose the figure from 1, 2, 3, or 4 which closely resembles figure Z.
Solution:
When we unfold Z, try to keep an eye on the pointed side of the cut. As the pointed side is facing the center then in all 4 quarters it should point to the center.
Q3. Choose the figure from A, B,C, and D which closely resembles Figure Z.
Solution:
Visualizing the cutting Z -> start unfolding the figure Z -> From Z, move to Figure Y -> Then move to figure X.
Keep and eye on the corner triangle, and on circle. These two will be present only on the two sides, then the central triangle will give a rhombus shape after opening.
Option D is the correct answer.
Q4. Choose the figure from 1,2,3 or 4 which closely resembles figure Z.
Solution:
Refer the above image, from figure Z follow the arrows and keep on visualizing the figure in your mind.
You will find Option 1 is the right answer.
Q5. Choose the figure from 1,2,3 or 4 which closely resembles figure Z.
Solution:
Try following the corners and the middle of the sides. You will observe, the missing corners of the final square.
Option 1 is the Correct.
Q6. Choose the figure from A, B, C, and D that closely resembles the last figure Z after being cut.
Solution:
When the paper is unfolded, we will witness 2 hearts. This rules out options C and D for the answer.
Since the paper was folded diagonally, the second heart must also be flipped vertically and rotated 90 degrees clockwise.
This further disqualifies option A for an answer. Option B is the correct answer.
Q 7. Choose the figure from A, B, C, and D that closely resembles the last figure Z after being cut.
Solution:
Visualize the image one by one as shown in the above image, you will easily be able to find the right answer.
Option C is the right answer.
Q8. Find a completely unfolded figure of Z.
Solution:
Firstly, concentrate on circle, then from Z go to Y and X.
Then concentrate on Center Rhombus.
Option 3 is the right answer.
Q 9. A square sheet of paper is folded and cut as shown below in the question figures. How it will appear when open, choose the correct option.
Solution:
By doing the careful examination, we can see there is no pattern at the corner. So, use the elimination method.
D is the right answer.
Q 10. A triangular sheet of paper is folded and cut as shown below in the question figures. How it will appear when open, choose the correct option.
Solution:
In the last figure, we can visualize that pattern will be in center only and that too triangular figures only.
Option A is the correct answer.
Practice Questions
Q1. A square sheet of paper is folded once vertically and then once horizontally. A small circular hole is punched in the folded sheet. When the paper is completely unfolded, how many holes will appear?
A. 2
B. 3
C. 4
D. 6
Q2. A rectangular sheet of paper is folded along its diagonal. A triangular cut is made on the folded edge. When the paper is unfolded, what pattern will be formed?
A. One triangle
B. Two symmetrical triangles
C. Four triangles
D. One rectangle
Q3. A square paper is folded from the left side to the right side. A small triangular piece is cut from the folded edge. What will the unfolded paper look like?
A. Two identical triangles on opposite sides
B. One triangle in the centre
C. Four triangles at the corners
D. Two triangles on the same side
Q4. A sheet is folded twice in different directions. A small square is cut from one corner of the folded paper. After unfolding the sheet completely, where will the cuts appear?
A. At one corner only
B. At two corners
C. At all four corresponding corners
D. In the centre only
Q5. A square sheet is folded along its vertical centre line and then along its horizontal centre line. A circular hole is punched near one corner of the folded sheet. How many identical holes will be visible after unfolding?
A. 2
B. 4
C. 6
D. 8