Mechanical Aptitude: Paper Folding

These questions are designed to test your geometric and spatial abilities.  In particular, the questions test your ability to form three-dimensional objects by folding a flat pattern.
The test will show a flat (two-dimensional) pattern with dotted fold lines, and several three-dimensional objects.  You will have to identify which of the three-dimensional objects can be made by folding the two-dimensional pattern along the dotted lines.

How Do You Improve Your Ability to Identify Which Objects Can Be Formed from the Patterns?
The paper folding questions are among the most difficult questions covered in this study guide, but there are a few tips that can help you.
First, it may help to count the number of faces in the pattern. 
Each region separated by dotted lines will form a separate face when the pattern is folded into a three-dimensional object.
For example, in the drawing below, the pattern has five separate regions.  When the pattern is folded, it creates a wedge-shaped object that also has five faces.  If you were to see this pattern on a test, you could immediately eliminate any objects that had greater or fewer than five faces.

Second, you can sometimes mentally piece together part of the object, and eliminate answers that are obviously wrong.
In the figure below, try to determine which of the objects can be made from the pattern shown.

ANSWER:  You can see that the pattern has two distinctively-shaped faces, 1 and 2.  If you fold the pattern into a physical object, the object must include each of those distinctive faces.  You can see that because answer choices A and C do not include two faces shaped like 1 and 2, these objects cannot be formed by folding the given pattern.  Therefore, you can eliminate these answer choices, leaving choice B as the only possible
If you are still having trouble with the practice problems in this section, it might help you to actually cut out the flat patterns in the practice section, and form them into shapes.

Practice Questions

1. Which shape can be formed by folding the given pattern?


2. Which shape can be formed by folding the given pattern?


3. Which shape can be formed by folding the given pattern?


4. Which shape can be formed by folding the given pattern?


5. Which shape can be formed by folding the given pattern?


Practice Answers

1. Only C can be formed by folding the given pattern.  You can eliminate choices A and B by examining the sawtooth-shaped face, and noticing that neither of the sawtooth-shaped faces in A or B matches the dimensions of the one given.  Of the remaining answer choices, C is the correct one because D is much too thin to match the pattern.

2. The answer is C.  The protrusion with the black square will form on the right, and the diagonal plane on choice A is too small.

3. The answer is D.  D has enough paper to make only one cubical protrusion, not two.

4. The answer is B.  When folded, the pattern will form two connected rectangular shapes.

5. The answer is A.  When folded, the pattern will form a smaller box on top of a larger box.  While choice D shows such an arrangement, the dimensions of the shape do not match those of the pattern.