IBPS Clerk Paper Folding & Cutting — Study Material & 12 Practice MCQs | ZestExam
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IBPS Clerk Paper Folding & Cutting
Study Material · Concept Notes · Shortcuts
This page covers IBPS Clerk Paper Folding & Cutting with complete concept notes, 12 graded practice MCQs, key points and exam-specific tips. Free to study.
When paper is folded and cut, the cuts create symmetric patterns when unfolded. Each fold creates a mirror effect. The number of holes depends on how many times the paper was folded
💡Key Rules
First, count the number of folds carefully. Each fold doubles the number of holes. One cut on a paper folded once = 2 holes. One cut on a paper folded twice = 4 holes.
Second, holes appear symmetrically around fold lines. Third, the position of holes mirrors across each fold line. Fourth, the shape of holes remains the same, only position changes.
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Exam Patterns
What examiners ask — read before attempting PYQs
SSC CGL typically asks 1-2 questions on this topic. Questions show 2-4 folding steps followed by cutting. You get 4 answer choices showing different unfolded patterns. The cuts are usually simple shapes - circles, triangles, or small squares.
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Shortcuts
Use these to save 30–60 seconds per question
Use the 'Fold Count Formula' - Number of holes = 2^(number of folds) × number of cuts. For symmetry, imagine drawing lines where folds occurred. Holes must appear symmetrically on both sides of these imaginary lines.
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Worked Example
Solve this step-by-step before moving on
1
Step 1
Count folds = 2 folds (vertical + horizontal)
2
Step 2
Count cuts = 1 cut (one circle)
3
Step 3
Apply formula = 2^2 × 1 = 4 holes
4
Step 4
Determine positions - Original cut was at top-right of folded paper. When unfolded, holes appear at all four corners (top-right, top-left, bottom-right, bottom-left) due to symmetry around both fold lines.
5
Step 5
Verify symmetry - Draw imaginary vertical and horizontal lines through center. Holes are symmetric around both lines.
Advanced Trick: For complex folding, trace the cut position backwards through each fold. Start from the final cut position and mirror it across each fold line in reverse order.
Common Mistake: Students often forget to account for all folds or miscalculate symmetry. Remember that each fold creates a new axis of symmetry. Also, don't confuse the number of paper layers with the number of holes. Focus on fold lines, not thickness.
Test Paper Folding & Cutting under exam conditions
A rectangular paper is folded in half vertically, then folded in half horizontally. If you unfold it completely, how many rectangular sections will the creases divide the paper into?
Practice 2easy
A circular piece of paper with a dot marked at its centre is folded in half. After unfolding, where will the crease line be positioned relative to the central dot?
Practice 3easy
A square piece of paper is folded once along its diagonal. After unfolding, how many triangular regions are created by the fold line?
Practice 4medium
A square piece of paper is folded diagonally once, then the resulting triangle is folded in half along its altitude from the right angle. After unfolding completely, how many distinct regions are created on the original square?
Practice 5medium
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?
Practice 6medium
A square paper is folded along one diagonal, then the resulting triangle is folded in half by bringing the right angle vertex to meet the midpoint of the hypotenuse. If a small hole is punched through the folded paper at a point that is 1/3 of the way along the hypotenuse from one end, how many holes appear on the unfolded square?
Practice 7medium
A rectangular piece of paper is folded in half along its length, then folded in half again along its width. Without unfolding, a straight cut is made from one corner of the folded rectangle to the opposite corner (a diagonal cut). How many separate pieces result when the paper is completely unfolded?
Practice 8hard
A rectangular paper (12 cm × 8 cm) is folded in half along its length, then folded in half again along the new length. A hole is punched through all layers at a point 2 cm from the top-left corner of the folded paper. When completely unfolded, how many holes appear and at what positions?
Practice 9hard
A square paper is folded along a diagonal, then the resulting triangle is folded along the line connecting the midpoint of the hypotenuse to the opposite vertex. If a small square of side 1 cm is cut from the corner of the folded paper (the corner opposite to the right angle), how many pieces result when the paper is completely unfolded?
Practice 10hard
A rectangular paper (20 cm × 10 cm) is folded in half three times: first along the 20 cm side, then along the new 20 cm side, then along the new 10 cm side. After the three folds, a rectangular hole of dimensions 2 cm × 1 cm is cut from the center of the folded paper. When completely unfolded, what is the total number of holes?
Practice 11hard
A square paper is folded along a diagonal to form a triangle. The triangle is then folded along the line from the right angle to the midpoint of the hypotenuse. Without unfolding, the folded paper is cut along a line parallel to the hypotenuse at a distance of 1/4 of the hypotenuse length from the hypotenuse. When completely unfolded, how many separate pieces are created?
Practice 12hard
A square sheet of paper is folded diagonally from top-left to bottom-right corner, creating a triangular shape. The folded triangle is then folded again along its altitude from the right angle to the hypotenuse, creating a smaller triangular shape. Finally, a small circular hole is punched through all layers at the midpoint of the hypotenuse of this final triangle. When the paper is completely unfolded, how many holes will be visible on the original square sheet?
60-Second Revision — Paper Folding & Cutting
Remember: Each fold doubles the hole count from cuts
Formula: Holes = 2^(number of folds) × cuts made
Trick: Holes must be symmetric around all fold lines
Method: Count folds first, then apply symmetry rules
Trap: Don't confuse paper thickness with number of holes
Speed tip: Eliminate options that violate symmetry immediately