Perceptual Ability Study Guide for the DAT

View Recognition

In this type of question, you are presented with two of the three faces of a three-dimensional object (top, front, and end/side). From the two given faces, you must determine what the third face should be. The two given faces have no perspective, meaning they are flat and appear two-dimensional.

Another key piece of information given in the faces will be the types of lines that make up each face. Dotted lines indicate that there exists a change in geometry, or a change in length, width, and/or of a specific place in the figure, that we cannot see from the given view. Solid lines indicate a solid edge (a change in geometry) that is visible from our point of view. If a solid and dashed line overlap for a face, then the solid line will always take priority, and that is what will be represented. These problems will also always be presented with the following chart:

The General Procedure

The views all have patterns that connect with one another, which is what you will use to infer the third side. The vertical lines of the top and front view will match, the horizontal lines of the front and end view will match, and the vertical lines of the top view will also match the horizontal lines of the end view like so:

vertical top ⇔ vertical front
horizontal front ⇔ horizontal end
horizontal top ⇔ vertical end

This is the visual representation:

Using these patterns, you can deduce what the other face must be. If you are missing the end view, you can use the horizontal lines from the front view and the horizontal lines from the top view to deduce the gaps. if Similar patterns exist for the missing top and front views, like so:

It’s important to understand that the number of lines will match. So, for instance, if the top view has two horizontal lines, the end view will have two vertical lines. Likewise, if the top view has four vertical lines, the front view will have four vertical lines, and so on.

Examples

Here are some examples of this type of question.

Example 1

What is the front view of this shape?

Answer choices:

The resulting front view is B. This is because the left and right vertical sides of the top view give us the left and right vertical sides of the front view. Since there is a solid line halfway through the top view, we know that a change in geometry occurs, but we don’t know more beyond that from only the top view. Now, including the end view, we see the change in geometry must happen at the middle horizontal line on the end view as that is the only remaining line once we use the top and bottom horizontal lines from the end view to bound the front view. If we apply this information correctly, we should get the correct front view.

An alternative way to look at this problem is that our first step is to bound the left and right vertical lines of the front view by the left and right vertical lines of the top view and to bound the top and bottom horizontal lines of the front view by the top and bottom vertical lines of the end view like so:

As a note, we know that the lower side has to be on the left since the top view shows a change in geometry happening on the left side. There is no indication of a change in geometry on the right side.

Example 2

What is the top view of this shape?

Answer choices:

The correct top view is A. Our first step is to bound the left and right vertical lines of the top view by the left and right vertical lines of the front view and to bound the top and bottom horizontal lines of the top view by the left and right vertical lines of the end view like so:

Once the boundaries are defined, we repeat the same process and go from the outside lines to the inside lines, which should yield the resulting top view. An important thing to note is that from this top view, nothing is obstructed. So there should be no dashed lines like in the front view. So, the resulting top view is as follows: