Paper Folding for the DAT
/Learn key paper folding concepts and strategy, plus practice questions and answers
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Part 1: Introduction to paper folding
When you were a kid, there’s a good chance that you made a paper snowflake at some point. You folded a piece of paper up a few times and then used scissors to cut triangles and rectangles. When you unfolded the paper, it had an intricate design that looked like a snowflake! You probably didn’t know then, but making paper snowflakes was actually preparing you for one of the biggest tests of your life!
The paper folding section of the PAT really isn’t too much different than making a paper snowflake. A square paper is depicted, folded 3-4 times, and then hole punched. You must select the answer that shows where all the holes will be when the paper is unfolded. If this seems confusing, don’t worry. This guide will walk you through the format of this section and teach you practical strategies. Be sure to apply these strategies using the practice questions and answers at the end of the guide.
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Part 2: Rules and strategies
Figure 1: 4 types of folds and a hold punch for the DAT
This image depicts an example paper folding question. The solid lines represent the piece of paper, while dashed lines represent the original placement of the paper. The circle in the rightmost paper represents the hole punch. Your job is to mentally unfold the paper and decide where the hole punches will be. The answer choices to this question look like this:
Figure 2: hole punches in paper folding for the DAT
Darkened circles represent the location of the hole punches on the fully-unfolded paper, while unfilled circles depict unpunched areas. The answer to this particular question is D.
There will be 15 paper folding questions, each with a unique paper and different answer choices. To keep pace with the rest of the PAT, try to average 40 seconds or less per question.
Here are the rules for the paper folding section:
The paper will never be rotated or turned.
Sometimes you might look at a question and initially think that a fold makes the most sense if the paper was rotated. Don’t make this mistake! Even if that would be a logical explanation for the figure, remember this rule and try to understand the new fold from the previous one.
Each fold must stay within the parameters of the original paper.
In other words, there will not be any folds that go outside the dotted lines.
All papers begin as unfolded squares.
Although “Fold 0” is never depicted, each paper begins with no folds.
On the unfolded paper, each hole punch must appear in one of the 16 locations shown in the answer choices.
If a hole punch initially appears to be in between one of these 16 spots, that will not be the case when the paper is unfolded completely. The image below depicts the 16 locations that hole punches will appear on the unfolded paper.
Figure 3: hole punches for the DAT
Notice that the hole punches are arranged in a 4x4 grid. Using this grid, we can analyze the different types of folds you’ll encounter in this section. These folds are depicted in the image below. Folds can be horizontal, vertical, or diagonal. Horizontal and vertical folds will be along the lines of the grid or halfway between grid lines. A horizontal or vertical fold halfway between grid lines is referred to as a half fold. Diagonal folds will always evenly split grid squares. In other words, diagonal folds must run from one end of a grid square to the other at a 45° angle. These are the only types of folds that will appear on the PAT.
Figure 4: Various types of paper folds for the DAT
Here are two types of folds that you will not encounter and are not possible in this section. The first fold breaks the rule of staying within the original parameters of the paper. The second fold is a diagonal fold that stays within the parameters of the paper, but it does not evenly split the squares of the grid.
Figure 5: Impossible folds
Now that you have a basic understanding of the question format and rules, let’s go over some effective strategies to help you learn this section and do well on test day.
The first strategy is hands on. Get a piece of paper and a hole punch or push pin and do a practice question in real life. Although you cannot use this strategy on the actual PAT, this will help you visualize and understand paper folding questions. Here is a practice problem for you to apply this strategy:
Figure 6: Paper fold practice question for the DAT
After making the folds and hole punch yourself, you can see that the unfolded paper looks like the image below.
Figure 7: Paper Practice Answer
For the most part, you’ll only use this strategy a few times to get the hang of these types of questions. You can also use this strategy if you are ever struggling to understand the answer to a practice question.
Now let’s learn a strategy that you can actually use on test day. This strategy requires you to use the scratch paper and marker provided for the PAT section. For each paper folding question, start by drawing a diagram like this on your paper:
Figure 8: Diagram first
Notice that this 4x4 grid has 16 spaces in the same location as the 16 hole punches in the answer choices. Start with the most folded paper (hole-punch image) and work your way to the least folded paper (fold 1 image), marking the location of the hole punches on the diagram. By the time you’ve finished, you simply select the answer that matches the diagram. Here is a practice question with a step-by-step walkthrough of this strategy:
Figure 9: Diagram practice question
Starting with the hole-punch image, mark the quadrant that matches the location of the hole punch.
Figure 10: Diagram second for the DAT
Now, working backwards, we can see that the smaller square of paper was folded to create the triangle in the fold 3 image. In order to create the triangle without rotating the paper, the fold must have been along a diagonal line.
Figure 11: Folds 2 to 3 explained
To fill out the diagram, reflect the hole punch across the fold line. The updated diagram now looks like this:
Figure 12: Diagram third
Let’s do this process again using the fold 1 and 2 images. After fold 1, the paper was folded in half from left to right. To mentally unfold the image and fill out the diagram, reflect the location of the hole punches across the fold line. The diagram now looks like this:
Figure 13: Folds 1 to 2 explained
Figure 14: diagram fourth for the DAT
Finally, we are left with the fold 1 image. Remember that all papers start as an unfolded square. This means that fold 1 was a fold from top to bottom, as depicted below.
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