Understanding Top-Front-End Dotted Lines

In the Perceptual Ability Test (PAT) of the DAT, Top-Front-End or view recognition questions are some of the most challenging. You are presented with two projections of an object and are expected to determine the third. However, Top-Front-End projections are not mere outlines but also contain lines that represent where the visible and hidden edges of each figure would appear. Hidden edges of the object that cannot be seen when viewing it straight on are represented by dotted or dashed lines, whereas visible edges that can be seen when viewing it straight on are represented by solid lines, like in this example:

The top views of both of the above objects are the same. They show that the object possesses some kind of step, but it’s not clear which half is higher from the top view alone. This information is conveyed in the front views. In the first case, since the front view contains a solid line, the lower step must be in front. In the second case, however, the higher step is in front, hiding the lower step from view. Hence, a dotted or dashed line is used to indicate the presence of the step; it is something that is present in the shape but not visible when looking from the direction indicated.
The correct interpretation of solid and dashed lines can be very helpful in more challenging problems. Sometimes it can be very difficult to construct a full 3D image of the object from the two projections given; in these situations, it may be much easier to focus on some finer features and determine whether solid or dotted lines will be present in certain regions. The following example illustrates this point:

In this question, you are asked to select the correct top view. The 3D appearance of the object is not immediately obvious from the two given projections. However, in the front view, you can see a substructure represented by dotted lines. The dotted lines show that the substructure is present but not visible from the front view. However, since the substructure is connected to the top of the object, you can expect to see it in solid lines in the top view. Only choice (C), which shows a horizontally centered, visible structure, fits that prediction.