Practice PAT #9, Question 63-65
These questions are tricky because the structure includes an ambiguous cube, which is highlighted in yellow (see below). The surrounding cubes are labeled as cubes 1 through 3, for reference (see below).
You might be asking "why is this cube ambiguous?" The edges highlighted in yellow, blue, and green (see below) could indicate connecting edges between two cubes. However, the yellow edge could also indicate the top front edge of cube 1, the blue edge could be the top right edge of cube 2, and the green edge could be the top back edge of cube 3.
This creates two situations:
Ambiguous cube is present - Cube 1, 2, and 3 each have three sides exposed.
Ambiguous cube is absent - Cube 1, 2, and 3 each have four sides exposed.
As a result, it is critical to remember cube counting rule number 3:
Cubes are only assumed present if they are required...
...to support another cube in a hidden stack.
...for the overall structure to be connected.
Since the ambiguous cube is not required to support a stack of cubes or to connect the overall structure, we must assume that this cube is absent. The yellow, blue, and green edges must indicate free (i.e. non-connecting) edges on cubes 1, 2, and 3, respectively.