Question 1

A square paper is folded diagonally to form a triangle. A small hole is punched through the folded paper at the center of the triangle. When the paper is unfolded, how many holes will be visible?

Accepted Answer

Folding a square diagonally creates 2 layers. Punching a hole through both layers creates 2 holes. When unfolded, these 2 holes are symmetrically placed on either side of the diagonal fold line.

Question 2

A rectangular paper is folded in half vertically (along the vertical midline). Then it is folded in half horizontally (along the horizontal midline). How many layers of paper exist at the corner of the final folded shape?

Accepted Answer

First fold (vertical): 2 layers. Second fold (horizontal): each of those 2 layers folds again, creating 2 × 2 = 4 layers at the corner where both folds meet.

Question 3

A square piece of paper is folded once along its diagonal. How many layers of paper will be visible if you look at the folded paper from above?

Accepted Answer

When a square is folded along its diagonal, one triangular half folds over the other, creating a double-layered triangle. From above, you see 2 layers of paper stacked together.

Question 4

A square piece of paper is folded diagonally once, then the resulting triangle is folded in half along its altitude from the right angle. When unfolded completely, how many distinct regions are created on the original square?

Accepted Answer

This question tests the ability to mentally track fold lines and visualize their intersection pattern when the paper is unfolded. Students must count the distinct regions created by all fold lines.

Question 5

A square paper with a dot marked at its center is folded along one diagonal, then along the other diagonal. The folded paper is now a small triangle. A small hole is punched through this triangle at a point that is 1/3 of the way from one vertex to the opposite side. When completely unfolded, how many holes appear on the original square?

Accepted Answer

This question tests the ability to track a single point through multiple folds and determine how many corresponding points exist on the unfolded paper due to symmetry.

Question 6

A square piece of paper is folded diagonally to form a triangle. This triangle is then folded in half by bringing the right angle vertex to meet the midpoint of the hypotenuse. A small triangular piece is cut from the folded paper at the folded right angle vertex. When the paper is completely unfolded, what is the shape of the hole created?

Accepted Answer

This question tests spatial visualization of nested folds and the ability to determine the shape of a hole after unfolding, considering the orientation and position of the cut.

Question 7

A square piece of paper is folded along its diagonal, then the resulting triangle is folded in half along its height (from the right angle to the hypotenuse). After unfolding completely, how many distinct regions will be visible on the paper?

Accepted Answer

This question tests the ability to mentally track fold lines and visualize the crease pattern that emerges after unfolding a twice-folded square paper.

Question 8

A rectangular strip of paper is folded in half three times, always folding along the length. After the three folds, the resulting shape is a small rectangle. A straight cut is made perpendicular to the length, passing through the middle of this small rectangle. When the paper is completely unfolded, how many separate pieces result?

Accepted Answer

This question tests understanding of how repeated parallel folds create layers and how a single cut through folded layers produces multiple pieces.

Question 9

A square sheet of paper is folded diagonally from top-left to bottom-right corner, creating a triangle. This triangle is then folded in half by bringing the right angle vertex to meet the hypotenuse midpoint. After unfolding completely, how many distinct regions are created on the original square sheet?

Accepted Answer

This question tests the ability to mentally track fold lines and visualize the crease pattern after unfolding. The first diagonal fold creates one crease. The second fold (right angle to hypotenuse midpoint) creates an additional crease on the folded triangle, which translates to two creases on the original square when unfolded. These creases intersect, dividing the square into distinct regions.

Question 10

A rectangular sheet (length 2× width) is folded in half lengthwise, then folded in half widthwise. A triangular cut is made from the folded corner (opposite to the fold edges) such that the cut removes a right triangle with legs of 1/4 the length and 1/4 the width of the original sheet. When unfolded, how many separate pieces result?

Accepted Answer

This question combines sequential folding with cutting, requiring students to track how a single cut on a multi-layered folded sheet produces multiple pieces when unfolded. The key is understanding that each fold doubles the layers, and a cut through all layers creates multiple corresponding cuts on the unfolded sheet.

Question 11

A square sheet is folded along a diagonal, then the resulting triangle is folded along its altitude from the right angle to the hypotenuse. A small square hole is punched at the center of the folded shape. Upon complete unfolding, how many holes appear on the original sheet, and what is their geometric arrangement?

Accepted Answer

This question tests the ability to track the position of a punch through multiple folds and visualize the symmetry of resulting holes. It requires understanding how fold lines act as axes of symmetry and how a single punch at a specific location on folded paper creates multiple holes with predictable geometric relationships.

Question 12

A rectangular sheet is folded in half three times in the same direction (always folding the shorter dimension). After three folds, a corner piece is cut off at 45 degrees. When completely unfolded, the original sheet has how many holes/cuts, and which corners are affected?

Accepted Answer

This question combines sequential folding in one direction with a corner cut, requiring students to track how repeated folds in the same direction create exponential layering and how a corner cut on the folded sheet translates to multiple cuts on the unfolded sheet. It tests understanding of fold accumulation and spatial mapping.

Question 13

A square sheet is folded by bringing the top-left corner to the center of the sheet, creating a crease. The sheet is then unfolded and folded again by bringing the bottom-right corner to the center. After both folds are made (without unfolding between them), a circular hole is punched at the center of the twice-folded sheet. Upon complete unfolding, how many holes appear and what is their arrangement?

Accepted Answer

This question tests the ability to track sequential folds without unfolding between them, and to visualize how a punch on a multi-layered folded sheet creates holes at multiple locations. It requires understanding that each fold changes the effective 'center' and that holes appear at positions corresponding to all layers at the punch location.

Question 14

A square piece of paper is folded diagonally from top-left to bottom-right corner, creating a triangular shape. The folded paper is then folded again along the midline parallel to the hypotenuse. After these two folds, a small equilateral triangle is cut from the vertex opposite to the hypotenuse. When the paper is completely unfolded, how many holes/cuts appear on the original square?

Accepted Answer

This is a hard paper folding and cutting question requiring spatial visualization of multiple fold layers and tracking how a single cut manifests across all layers when unfolded.

SSC CPO Paper Folding & Cutting

Paper Folding & Cutting— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Paper Folding & Cutting — Practice Questions

60-Second Revision — Paper Folding & Cutting