Perceptual Ability Study Guide for the DAT

Angle Discrimination

Given four angles, labeled 1, 2, 3, and 4, you must determine the order of angles, ranked from smallest interior angle to largest interior angle.

The General Procedure

In these types of problems, you will often be given two angles of very similar size. Instead of determining the minuscule difference between those two, you can eliminate choices based on their ranking of the remaining two angles. For example, if angle 3 is clearly the smallest and one or two of the answer choices have angle 3 in any position except the first, then you can eliminate those choices and move to your next step. The same procedure works if an angle that is clearly larger than the others is present. By doing this, you can likely eliminate all answers except the correct one.

An alternate method of elimination choices is to see which angles are placed in which positions in the answers. If only angles 1 and 2 are placed in the “largest angle” position, then you can compare those two angles. When you decide which one is larger, you can eliminate the other choices that do not contain the largest angle. You can repeat this process until you have only one answer choice remaining.

In some instances, it may save time to first group the angles into obtuse (greater than 90 degrees) and acute (lesser than 90 degrees).

Examples

Try the following examples of this question type.

Example 1

Which of the orders represents the angles in order from least to greatest?

Since 4 is clearly the largest angle, the correct answer must have 4 in the last spot. We can, therefore, eliminate options A and B. We can also clearly see that 3 is the smallest angle, so it should go first. Therefore, we can eliminate C and are left with only option D. This way, we don’t have to compare angles 1 and 2, which are very similar.

Example 2

Which of the orders represents the angles in order from least to greatest?

As before, since 1 is clearly the largest angle, the correct answer must have 1 in the last spot. We can, therefore, eliminate options A and D. We can also clearly see that 4 is the next largest, so 4 should be in the next-to-last spot. There are only two choices, A and C, in which this is true. However, we have already eliminated A, so C must be the correct answer.

Paper Folding

In this section, you are presented with a piece of paper that is folded one, two, or three times in your direction. Once the paper is folded, the solid lines determine where the new folded paper’s boundaries are, and the dotted lines show where they originally were. A hole is then punched in the folded paper and you must infer all of the places there will be holes once the paper is unfolded.

The General Procedure

One effective strategy is to make a four-by-four grid for each sheet of paper. There will be 16 spaces on the fully unfolded paper. After you have drawn a grid, identify the line of symmetry for the fold that you are looking at (look at how you went from the previous picture to this one, and that is the line of symmetry). The hole will stay in the grid space where it is and will also be mirrored across the line of symmetry into the opposite grid space. Once you do this, move on to the next fold and repeat the process.

Examples

Look at these examples to fully understand this type of question.

Example 1

The correct answer is B. Using this grid box as a visual representation, we have space 5 already punched out. Going from fold 3 to 2, the bottom left of the grid is unfolded, so the bottom line of the box in fold 3 must be the line of symmetry. As such, there must be the original hole (in space 5), as well as one in the space below (9), since that is what is mirrored across the line of symmetry. Going from fold 2 to 1, the long side of the triangle opens up, so that is the line of symmetry. Mirroring the hole in space 9 across this line, we have space 14 punched out. Finally, going from fold 1 to the unfolded paper, we have a line of symmetry that is straight down the middle of the page. This means that we mirror every hole that we have (spaces 5, 9, and 14) across the centerline of the grid, and we get that this unfolded portion matches grid B since it also punches out spaces 15, 12, and 8.

Example 2

The correct answer is D. Using this grid box as a visual representation, we have space 11 and half of space 12 punched out. Going from fold 3 to 2, the line of symmetry is between the last two grid rows, so the hole in space 11 will be mirrored across this to punch out space 15 (though only half of the space is visible). Space 12 does not mirror across this line because that portion of the fold remains the same. Going from fold 2 to fold 1, the line of symmetry is along the long side of the triangle fold. Thus, the holes in spaces 11, 15, and 12 will be mirrored across. This means that space 11 mirrors to 16, and the half hole in space 12 fills in the rest of the way. Half of space 15 will also be mirrored across this line to punch out the remaining portion of this space. The final step is to go from fold 1 to the unfolded paper. The line of symmetry here will be the horizontal line in the middle of the paper, meaning we mirror all holes across this line. Doing this results in spaces 3, 4, 7, and 8 being punched out, and we see that grid D matches our unfolded paper.