SSC CGL Reasoning · Paper Folding and Cutting

Other Folds and Transparent Sheets

Sheets folded along a diagonal, into thirds or only once before they are cut, and transparent sheets folded so that the pattern on one half lands on the other.

All Paper Folding and Cutting notes

Why this matters

Twelve questions in the bank, 4 from the 2023 shifts and 8 from the 2024 shifts, with 1 EASY, 10 MODERATE and 1 HARD. The rule is the same mirror in a fold line, but the fold lines are not the two centre lines, so the copies land in less familiar places.

Concept 1 of 2: Diagonal folds, thirds and single folds

Any fold makes a mirror line. Opening it puts a reflection of each cut on the other side of that line, at the same distance. That holds whether the line is a diagonal, a line one third of the way across, or the only fold made.

Definition

Count the layers: each fold doubles the layers under it. A cut through every layer makes one hole per layer.
Thirds: a strip folded into three equal parts has 3 layers, so each hole opens into 3, one in each third. The outer copies are reflections of the middle one in the two fold lines.
A diagonal fold: the reflection lies across the diagonal. A hole near one side of the diagonal opens into a pair facing each other across it.
A part with one layer: a hole punched where the paper is not folded over stays a single hole.
Fast route: count the holes first. Options with the wrong number are struck before you think about places.

Worked example

A strip of paper is folded into three equal parts, giving three layers, and one hole is punched through all of them. How many holes does the opened strip have, and where?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 23 Sep 2024, Shift 2 · Q6Moderate

Example 1 · Paper Folding and Cutting · Other Folds and Transparent Sheets

A square sheet of paper is folded along the dotted line successively along the directions shown and is then punched in the last as shown. How would the paper look when unfolded?

Using the centre lines for a diagonal fold

When the fold runs corner to corner, the copy is a reflection across that diagonal, not across a centre line. Find the actual fold line before you place any copy.

Counting layers that the punch did not go through

If part of the folded sheet has only one layer, a hole there makes one hole only. Check how many layers sit under each cut, not under the whole sheet.

Putting the outer copies in the same position as the middle one

In a strip folded into thirds, each outer copy is a reflection of the middle one, not a copy slid sideways. A hole near the left of the middle third opens next to the left fold line in the outer third.

Drill 8 more on diagonal folds, thirds and single folds

Concept 2 of 2: Folding a transparent sheet

A transparent sheet with a drawing on it is folded once. The folded half lands on the other half as its reflection in the fold line, and because the sheet is clear, you see that reflection on top.

Definition

The part of the drawing on the folded half is reflected in the fold line and lands on the other half.
A horizontal fold (top half down) turns that part upside down; left and right stay.
A vertical fold (left half over) reverses that part left to right; top and bottom stay.
The part of the drawing already on the half that stays still does not move.
Fast route: pick one end of the folded part, such as an arrowhead, and work out only where it lands.

Worked example

A transparent sheet has a dot near its top-left corner. Its left half is folded over onto its right half. Where is the dot now?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 17 Sep 2024, Shift 1 · Q15Easy

Example 2 · Paper Folding and Cutting · Other Folds and Transparent Sheets

A transparent sheet with a pattern is given below. Select the option that depicts the pattern that would appear when the given transparent sheet is folded at the middle horizontal line.

Sliding the folded part instead of reflecting it

The folded half lands upside down (for a horizontal fold) or reversed (for a vertical fold), not slid across unchanged. An arrow that still points the same way after the fold is wrong.

Moving the half that stays still

Only the folded half moves. A mark already on the half that does not move stays exactly where it was.

Measuring the distance from the edge, not the fold

A folded mark lands as far from the fold line as it started. A mark near the fold stays near it; a mark near the outer edge lands near the other outer edge.

Drill 2 more on folding a transparent sheet

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Watch out for (6)

Using the centre lines for a diagonal fold
→ Diagonal folds, thirds and single folds
Counting layers that the punch did not go through
→ Diagonal folds, thirds and single folds
Putting the outer copies in the same position as the middle one
→ Diagonal folds, thirds and single folds
Sliding the folded part instead of reflecting it
→ Folding a transparent sheet
Moving the half that stays still
→ Folding a transparent sheet
Measuring the distance from the edge, not the fold
→ Folding a transparent sheet

Test yourself on Paper Folding and Cutting

15 past SSC CGL questions from this chapter, timed at 9 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Take the Paper Folding and Cutting chapter test Drill all 12 questions