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GAN aptitude test

Paper folding test: the method, step by step

By the nodiexam team Updated

In a paper folding test you see a square sheet folded and punched, then pick the unfolded sheet. Open the folds in reverse order. Each time you open a fold, every hole on the part that was folded over gets a twin, mirrored across the fold line. Paper Folding shows a square sheet being folded, then one or two holes punched through it, and you pick which of five unfolded sheets shows the holes.

Paper folding is one of the sections on the GAN aptitude test, and a common part of other spatial tests. Programs list six sections: reading, numerical computation, numerical reasoning, paper folding, problem solving and mechanical comprehension. The method below works on every question. Practice it on paper first, then in your head.

How the questions work

  1. The pictures show a square sheet being folded, one fold per picture. A dashed outline shows where the folded part was before it moved, and an arrow shows the way it moved.
  2. The last picture shows where the holes were punched through the folded paper.
  3. The choices show five unfolded sheets. One shows exactly where the holes end up.

On this page, rows count from the top and columns from the left, 1 to 8, so each hole has an address such as row 2, column 6.

The method: open the folds in reverse

  1. Start with the punch. Mark each hole on the last picture.
  2. Open the last fold. Every hole that sits on the part that was folded over gets a twin on the other side of the fold line, at the same distance from the line.
  3. Open the fold before it in the same way, mirroring every hole you have so far, if it sits on that fold's folded part.
  4. Check the count. The number of holes equals the number of paper layers under each punch, added up.
  5. Check the choices for slips. A wrong choice often leaves out one fold, mirrors across the wrong line, or turns the pattern a quarter turn.

Example 1: one fold

Example 1: one foldFold 1: the left half is folded over from left to right, along a vertical line. Holes punched on the folded paper at row 2 column 6.1punch

Worked example. The left half is folded over onto the right half, and a hole is punched near the top of the folded sheet, in column 6 of 8.

  1. Only one fold to open: the vertical fold down the middle.
  2. The punch went through both layers. Mirror it across the middle line: column 6 is 2 columns right of the line, so its twin is 2 columns left of it, in column 3.
  3. Count: two layers, two holes.

The unfolded sheet has 2 holes in row 2, in columns 3 and 6.

Unfolded sheetExample 1: one fold, unfolded: 2 holes: row 2 at columns 3 and 6.

Example 2: two folds

Example 2: two foldsFold 1: the top half is folded over from the top down, along a level line. Fold 2: the left half is folded over from left to right, along a vertical line. Holes punched on the folded paper at row 6 column 7.12punch

Worked example. The top half is folded down. Then the left half of what is left is folded over to the right. One hole is punched near the lower right.

  1. Open fold 2 first, the vertical fold. The hole in column 7 gets a twin in column 2.
  2. Open fold 1, the level fold across the middle. Both holes in row 6 get twins in row 3.
  3. Count: four layers under the punch, four holes.

The unfolded sheet has 4 holes, in rows 3 and 6, columns 2 and 7: one near each corner, set in from the edges.

Unfolded sheetExample 2: two folds, unfolded: 4 holes: row 3 at columns 2 and 7; row 6 at columns 2 and 7.

Example 3: a slanted fold

Example 3: a slanted foldFold 1: the top left half is folded over from top left to bottom right, along the slanted line from bottom left to top right. Holes punched on the folded paper at row 6 column 7.1punch

Worked example. The top left half is folded over the slanted line that runs from the bottom left corner to the top right corner. One hole is punched near the lower right.

  1. A slanted fold mirrors across the slanted line. The twin's distance from the left edge equals the hole's distance from the bottom edge, and its distance from the top edge equals the hole's distance from the right edge.
  2. The hole is in the second column from the right and the third row from the bottom. So its twin is in the second row from the top and the third column from the left: row 2, column 3.

The unfolded sheet has 2 holes: one near the top left and one near the bottom right. A choice with the twin at row 6, column 2 mirrors across the vertical middle line instead, which is the usual slip.

Unfolded sheetExample 3: a slanted fold, unfolded: 2 holes: row 2 at column 3; row 6 at column 7.

Try these

Work each one on paper, then open the answers.

Drill 1Fold 1: the right half is folded over from right to left, along a vertical line. Holes punched on the folded paper at row 3 column 2, row 7 column 3.1punch
Drill 2Fold 1: the bottom half is folded over from the bottom up, along a level line. Fold 2: the right half is folded over from right to left, along a vertical line. Holes punched on the folded paper at row 2 column 2.12punch
Drill 3Fold 1: the left quarter is folded over from left to right, along a vertical line. Holes punched on the folded paper at row 4 column 4.1punch

Try it

  1. The first drawing: the right half folded over to the left, then two holes punched. Where are the holes when you open it?
  2. The second drawing: the bottom half folded up, then the right half folded over to the left, and one hole punched. Where are the holes?
  3. The third drawing: only the left quarter folded over, and one hole punched on the folded strip. How many holes, and where?
Show answers
  1. 4 holes: the two punches plus a twin of each across the middle line. Row 3 at columns 2 and 7, row 7 at columns 3 and 6.
  2. 4 holes, one near each corner: rows 2 and 7, columns 2 and 7.
  3. 2 holes in row 4: the punch in column 4 and its twin in column 1. The strip was a quarter of the sheet, so the twin lands near the left edge.

Keep practicing

The free GAN practice test has a full paper folding section with its own clock, and every question shows the method. The GAN study guide covers the other sections, and the GAN aptitude test overview explains how programs score the test.

Questions people ask

How do you solve paper folding questions fast?

Open the folds backward, last fold first. Each opened fold mirrors the holes that sit on the folded part across the fold line. Count the layers under the punch first: two layers give two holes, four give four. Then drop every choice with the wrong number of holes.

Do you rotate the paper in a paper folding test?

No. The sheet stays the way it was drawn. Opening a fold only mirrors holes across the fold line, so a choice that shows the right pattern turned a quarter turn is wrong.

How many holes will the unfolded sheet have?

One hole for every layer of paper the punch went through. Fold a sheet in half once and a punch makes 2 holes. Fold it in half twice and it makes 4. If part of the sheet was folded over only a narrow strip, a punch outside that strip goes through one layer and makes just 1 hole.

Is paper folding on the GAN test?

Yes. Every program page we checked that lists the GAN sections includes paper folding, and applicants at Pipe Fitters Local 597 and in an IBEW forum report that paper folding gave them trouble.

Sources

Facts on this page come from these pages. We checked each one on the date shown.