This is an example of a question where we can use unique faces to quickly narrow down our answer choices. Before we begin, we must remember the golden rule of pattern folding: Patterns are always folded into the page.

Normally we would start with the most unique shape, which is highlighted by the blue star (see above). However, this shape is not visible in any of the option choices, meaning it ends up on the bottom of the folded object. Since this is not helpful, we can choose the next most unique shape, which is highlighted in red and labeled 1 through 4 (see above). In order for this shape to end up on the top of the folded object after the pattern is folded into the page, it must maintain its original orientation. In other words, the narrow end of the red face points right in the unfolded pattern, so it must point right in the folded object. Since face 1 points left, we can eliminate Option A.

Further, let's analyze the next most unique shape, which is highlighted in green and labeled 1 through 3 (see below).

This shape is an easily identifiable trapezoid. However, you might notice that the relative lengths of the parallel lines significantly differ between option choices. In the unfolded pattern, the short edge appears to be approximately half the length of the long edge. Only trapezoid 2 matches these proportions, whereas the short edge on trapezoids 1 and 3 are visibly shorter than half. Thus, Option C must be correct.

Questions like these are difficult because the shapes are complex and visually distracting. With these questions, much of the information is not useful and you typically only need to focus a single, complex shape. The complex shape for this pattern is highlighted in red (see below).

At a quick glance, it is easy to spot the characteristic F-shaped hole in the center of this image. We can compare this hole to the option choices. While Options A, B, and D match this pattern, Option C has an extra space in the center of the image, indicated by a red star (see above). Thus, Option C must be incorrect.

Let's take a closer look at our complex shape:

In the unfolded pattern, the red arm extends past the first column, labeled in yellow as A, and ends somewhere in the middle of the second column, labeled in yellow as B (see above). Similarly, the distance that the red arm extends in each option choice is indicated by the green dotted line (see above). Only the red arm in Option A extends far enough to line up with the center of column B, while Option B lines up with the edge of column B and Option D lines up with the space between the columns. Only the length of Option A's red arm matches the length in the unfolded pattern. Thus, Option A must be correct.

*Note: Because the lengths of the red arms in Option A and Option B are very close, you might want more proof that Option B is incorrect. Thus, you can analyze the width of columns A and B. In both the unfolded pattern and Option A columns A and B are slightly thicker than the red arm. In contrast, columns A and B are the same thickness as the red arm in Option B. Thus, Option B must be incorrect.

This is a rare example where it is easier to identify the correct answer than to eliminate incorrect options. The portion of the unfolded pattern that corresponds to the correct answer, Option B, can be quickly identified in the top right (see below):

To double check that the other answer choices are incorrect, we can use process of elimination for the possible orientations where the white face is on the bottom of the cube (this feature is common between the other options).

While the folded objects may look like hexagons, they are indeed cubes. The three visible faces are highlighted in Option B (see above). The bottom of the cube is highlighted in blue, the upper left face in green, and the upper right face in yellow. The three combinations whereby faces are connected to the white face are highlighted in red and labeled 1 through 3 (see above).

An easily identifiable shaded-pyramid pattern is highlighted in blue (see above). This pattern is not present in any of the answer choices, so we can eliminate combination 1.

The connecting edges are highlighted in complementary colors (e.g. blue edge connects to blue edge). The green edges can be connected using the cut-and-paste technique. Here, the faces are shown to connect to the bottom of the white face, making it easier to visualize the folded cube with the white face on top first, before flipping the cube upside down. The flipped cube has two shaded triangles in the bottom right corner of their respective faces, which are highlighted in blue (see above). This pattern is not present in any of the answer choices, so we can eliminate combination 2.

This combination places the face with the shaded triangle on the left side and a solid shaded face on the right side, both of which are highlighted in blue (see above). This pattern is not present in any of the answer choices, so we can eliminate combination 3.

Conclusion: None of the face combinations with the white square are valid. The only answer choice without the white square is Option B, which must be correct.

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