Perceptual Ability Study Guide for the DAT

Cube Counting

In this section, you will be given a stack of connected, identical cubes. You are told to assume that all of the sides of the cube, except the bottom, that are exposed to the air are painted. You will then be asked to determine how many cubes from the stack will have 1, 2, 3, 4, or 5 painted sides.

For this type of question, there may be a floating cube, but if a floating cube is present, then the gap must be clearly visible to the viewer, and the faces of the other cubes around the gap must also be visible. If you have a cube above the ground level, and it is not clearly floating, there will be another cube underneath it, visible or not.

The General Procedure

One effective strategy is to look at the front face of the stack. Then, draw each layer of cubes on the graph paper provided to you, and inside each of them, label how many painted sides the cube has. This will give you a quick, comprehensive tool to look back on to determine exactly how many cubes have 2, 3, or more open faces. This concept can seem abstract, so here is a concrete example:

The first step is to separate this figure into separate layers like so, from front to back:

Once all of the layers are separated, label how many sides each one has painted, like so:

Now that we have this information, we can use it to solve any further questions by simply counting how many of each box we have.

Examples

These are some examples to try.

Example 1

Drawing out the layers and filling them in yields this:

From this picture, we can clearly see that there are exactly 5 cubes that have 2 sides painted, which means that B is the answer.

Example 2

As before, we will start by drawing out the layers of the figure and labeling each cube with the number of sides that are painted. It is important to note that any cube touching the empty space will have one extra painted side. Utilizing this information, the corresponding layers are as follows:

Counting the number of cubes with 4 painted sides, we get 7 cubes, so the correct answer is C.