# DAT PAT Hole Punching Strategy: Symmetry

For each Hole Punching question in the Perceptual Ability (PAT) section of the DAT, a square piece of paper is folded one, two, or three times, and then one or more holes are punched at specific locations. You are then asked to unfold the paper mentally and determine the final locations of the hole(s).

The paper is always folded toward the front (out of the screen and toward you) to allow you to see the final positions of paper. The edges of the paper in the new position are represented by solid lines, and the original locations where the paper used to be are represented by dashed lines. The folds are not arbitrary; in fact, there are only four possible types of first folds, as follows:

However, note that each of these four first folds can occur on any edge; for example, the corner fold shown in the bottom right can be on any of the four corners, not just the bottom-left corner.

After the first fold, the paper may be folded one or more additional times. Since these occur after the first fold, a wide range of combinations exist, but all the folds still follow the same basic patterns. In the following example, you can see the paper folded diagonally in the first fold and then folded halfway down before a hole is punched.

Mentally unfolding the paper gives the following:

In the answer choices, punched holes are indicated by filled circles on a grid of 16 possible positions. These 16 positions represent the only possible final holes, and no partial holes will appear in the correct answer. Here, the correct answer includes two punched holes.

A helpful strategy for Hole Punching questions is to eliminate answer choices by looking at the symmetry of the first fold. Because the unfolding step will be the opposite of that initial fold, any position with a hole on one side of the line of symmetry created by the first fold will be mirrored by another position with the same hole.

Any answer choice that does not have the corresponding line of symmetry can be eliminated immediately regardless of any other factors. Note that, if the first fold does not bisect the paper into two equal parts, you should only look at the overlapping portion of the paper and can ignore any other sections. For example, if the first fold is a corner fold, the line of symmetry will be diagonal across that quadrant (one-fourth) of the paper, and the other three-fourths can be ignored when evaluating the paper’s symmetry:

Spend only five minutes on the Hole Punching section, which means taking an average of 20 seconds on each question. This will allow you spend more time on the other, more time-consuming perceptual ability questions on the DAT. This is a very short amount of time, though, so spend time practicing completing these questions both quickly and accurately.

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