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SSC MTS Paper Folding & Cutting

Study Material — 8 PYQs (2024–2024) · Concept Notes · Shortcuts

SSC MTS Paper Folding & Cutting is a frequently tested subtopic — 8 previous year questions from 2024–2024 papers are included below with concept notes, key rules and shortcut tricks.

8 PYQs
2024–2024
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8 Key Points
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Previous Year Questions

SSC MTS Paper Folding & Cutting — Past Exam Questions

8 questions from actual SSC MTS papers · all shown free · click option to reveal solution

Exam Q 12024Previous Year Pattern

A circular piece of paper is folded in half to form a semicircle, then folded in half again. When unfolded, how many sections will the original circle be divided into?

Exam Q 22024Previous Year Pattern

A rectangular paper is cut into 3 equal vertical strips. Each strip is then cut into 2 equal horizontal pieces. How many total pieces of paper will result?

Exam Q 32024Previous Year Pattern

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 shape from above?

Exam Q 42024Previous Year Pattern

A rectangular paper is folded in half vertically, then folded in half horizontally. How many rectangular sections will appear when the paper is completely unfolded?

Exam Q 52024Previous Year Pattern

A square paper is folded in half to form a rectangle, then folded in half again to form a smaller square. If a small hole is punched through the folded paper, how many holes will appear when the paper is completely unfolded?

Exam Q 62024Previous Year Pattern

A rectangular paper (8cm × 6cm) is folded such that the top-right corner touches the bottom-left corner. The paper is then cut along the fold line. How many pieces result, and what is the shape of the largest piece?

Exam Q 72024Previous Year Pattern

A square paper is folded in half vertically, then in half horizontally, then in half diagonally. A single straight cut is made through all layers. After unfolding, which of the following is IMPOSSIBLE?

Exam Q 82024Previous Year Pattern

A rectangular paper (12cm × 8cm) is folded such that the top-left corner is brought to touch the bottom-right corner. The paper is then cut along the fold line. One of the resulting pieces is then folded in half along its longest dimension and cut again. How many total pieces exist after both cuts?

Concept Notes

Paper Folding & Cutting— Rules & Concept

Core ConceptRead this first — the foundation of the topic
Core Concept

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.

Exam PatternsWhat 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.

ShortcutsUse 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.

Worked ExampleSolve 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.

Exam TrapsCommon mistakes students make — avoid these

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.

Key Points to Remember

  • Each fold doubles the number of holes created by cuts
  • Holes appear symmetrically around all fold lines
  • Formula: Number of holes = 2^(folds) × number of cuts
  • Position of holes mirrors across each fold axis
  • Shape of cut remains same, only position multiplies
  • Count fold steps carefully before applying formula
  • Draw imaginary lines at fold positions to check symmetry
  • Work backwards from cut to unfold position step by step

Exam-Specific Tips

  • SSC CGL typically includes 1-2 paper folding questions per exam
  • Maximum folds shown in SSC questions is usually 3-4 folds
  • Most common cuts are circles, triangles, and small rectangles
  • Questions always provide exactly 4 answer options showing unfolded patterns
  • Each fold creates one axis of symmetry in the final pattern
  • Corner cuts are the most frequently tested cutting positions
  • Questions are worth 2 marks each in SSC CGL Tier-I
  • Time allocation should be maximum 1 minute per question
Practice MCQs

Paper Folding & Cutting — Practice Questions

3graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1medium

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 will be visible on the paper?

Practice 2medium

A square piece of paper is folded along a line parallel to one side, creating a rectangle. This rectangle is then folded diagonally. A triangular piece is cut from the folded paper. When unfolded, which of the following is NOT a possible outcome?

Practice 3medium

A square paper with a dot marked at its center is folded diagonally corner-to-corner twice (both diagonals). A small hole is then punched through the folded paper at a point that is 1 unit away from the center of the original square. When unfolded, how many holes will be visible?

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
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