CogAT Paper Folding Analysis — Questions and Answers

Question 1: A square paper is folded once from left to right, then a single hole is punched near the center of the folded edge. When unfolded, how many holes appear?

1
2 (Correct answer)
3
4

Correct answer: 2

One fold creates two layers, so a single punch passes through both, making two holes.

Question 2: A paper is folded in half top to bottom, and a hole is punched exactly on the folded crease. After unfolding, where is the hole located?

Two holes, one in each half
One hole on the center crease line (Correct answer)
Four holes near the corners
No holes appear

Correct answer: One hole on the center crease line

Punching directly on the fold line places a single hole centered on the crease when unfolded.

Question 3: A square is folded in half twice (into quarters), then one hole is punched. How many holes appear when fully unfolded?

2
3
4 (Correct answer)
8

Correct answer: 4

Two folds create four layers, so one punch produces four holes.

Question 4: A paper folded once has a hole punched in the upper-left of the folded sheet. After a left-to-right unfold, how are the two holes arranged?

Mirror images across the fold line (Correct answer)
Stacked vertically
Both in the same spot
Diagonally opposite corners

Correct answer: Mirror images across the fold line

Unfolding reflects the punched hole across the fold line, producing a mirror-image pair.

Question 5: If a paper is folded into quarters and a corner of the folded square (the original center point) is cut off, what shape appears in the middle when unfolded?

A small square hole in the center (Correct answer)
A round hole at one corner
Four separate slits
No hole

Correct answer: A small square hole in the center

The folded corner that meets at the paper's center produces a square hole in the middle after unfolding.

Question 6: A paper folded in half left to right has two holes punched in a vertical line. How many holes appear after unfolding?

2
3
4 (Correct answer)
6

Correct answer: 4

Each of the two punches passes through both layers, creating four holes total.

Question 7: Which statement is true about a hole punched far from the fold line on a once-folded paper?

The two holes are spread far apart symmetrically (Correct answer)
The two holes are close to the crease
Only one hole forms
The holes overlap in the center

Correct answer: The two holes are spread far apart symmetrically

A punch far from the crease reflects to a position equally far on the other side, spreading the holes apart.

Question 8: A triangular flap is folded down over a square paper, then a hole is punched through both the flap and the sheet. When the flap is opened, how many holes show?

1
2 (Correct answer)
3
4

Correct answer: 2

The punch passes through the flap and the sheet beneath, leaving two holes when opened.

Question 9: A paper is folded in half three times, then one hole is punched. How many holes appear when unfolded?

4
6
8 (Correct answer)
16

Correct answer: 8

Three folds make eight layers, so one punch creates eight holes.

Question 10: A square is folded diagonally corner to corner, and a hole is punched in the middle of the long folded edge. After unfolding, the hole lies on which line?

The diagonal crease (Correct answer)
A vertical edge
The top edge
A horizontal midline

Correct answer: The diagonal crease

Punching on the diagonal fold places the single hole directly on the diagonal crease line.

Question 11: After folding a paper in half and punching a hole, the pattern shows two holes symmetric about a horizontal line. Which fold was used?

Top-to-bottom fold (Correct answer)
Left-to-right fold
Diagonal fold
No fold

Correct answer: Top-to-bottom fold

Symmetry across a horizontal line indicates the crease was horizontal, meaning a top-to-bottom fold.

Question 12: A paper folded into quarters has a small bite cut from the outer corner (away from the center). How many notches appear when unfolded?

1
2
3
4 (Correct answer)

Correct answer: 4

The outer corner of a quarter-folded sheet corresponds to all four corners, producing four notches.

Question 13: If unfolding a once-folded paper shows holes that nearly touch at the center, the punch was made:

Very close to the fold line (Correct answer)
Far from the fold line
On a corner
Through three layers

Correct answer: Very close to the fold line

Holes meeting near the center mean the original punch sat just beside the crease.

Question 14: A paper is folded in half left-to-right, then top-to-bottom, and one hole is punched in the inner corner where folds meet. When unfolded, the four holes form:

A small cluster near the center (Correct answer)
A line along one edge
A single hole
A wide ring near the corners

Correct answer: A small cluster near the center

Punching at the inner meeting corner places all four holes close together around the center.

Question 15: A paper is folded in half once and two holes are punched, both on the fold line. How many holes appear when unfolded?

1
2 (Correct answer)
3
4

Correct answer: 2

Holes punched on the crease do not duplicate, so two punches give two holes.

Question 16: Folding a square accordion-style into three equal panels, then punching one hole through all panels, yields how many holes?

2
3 (Correct answer)
4
6

Correct answer: 3

Three panels mean three layers, so one punch produces three holes.

Question 17: A square folded in half shows, when unfolded, a single hole on the crease and two holes off to the sides. The minimum number of punches made was:

1
2 (Correct answer)
3
4

Correct answer: 2

One punch on the fold gives the center hole and one punch off the fold gives the symmetric pair, totaling two punches.

Question 18: A paper folded into quarters has a hole punched midway along one folded edge (not at a corner). How many holes appear unfolded?

2
3
4 (Correct answer)
6

Correct answer: 4

Four layers and a single punch give four holes, mirrored across both fold lines.

Question 19: When a diagonally folded square is punched once off the crease, the two resulting holes are symmetric about:

The diagonal line (Correct answer)
A vertical line
A horizontal line
The center point only

Correct answer: The diagonal line

A diagonal fold reflects the punch across the diagonal, so the holes mirror about that diagonal.

Question 20: A paper folded in half top-to-bottom is punched once in the lower portion of the folded sheet. After unfolding, the two holes are:

Symmetric above and below the horizontal crease (Correct answer)
Side by side horizontally
In the same location
At opposite diagonal corners

Correct answer: Symmetric above and below the horizontal crease

A horizontal fold reflects the punch vertically, placing one hole above and one below the crease.

Question 21: If a folded-paper puzzle shows eight identical holes after unfolding, the paper was most likely folded:

Once
Twice
Three times (Correct answer)
Not at all

Correct answer: Three times

Eight holes from one punch require eight layers, which comes from three folds.

CogAT Paper Folding Analysis

A square paper is folded once from left to right, then a single hole is punched near the center of the folded edge.
When unfolded, how many holes appear?

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