DAT Perceptual Ability
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DAT Perceptual Ability › DAT Perceptual Ability
In this question, a flat pattern is presented. This pattern is to be folded into a three-dimensional figure. The correct figure is one of the four given as answer choices. There is only one correct figure in each set. The outside of the folded shape is what is seen as the flat pattern. Select the three-dimensional shape that the flat pattern produces when folded.
Explanation
In this 3-D Form Development / Pattern Folding question, we need to figure out which face of the resulting L-shaped figure corresponds with the blue face on the flat diagram. We can ignore the answer choice that does not show any visible face as the blue one, because the only faces hidden from the shown view are larger than the rectangular face shown in the diagram. One would be the large square, and the other would be one of the large L-shaped faces.
Looking at the flat diagram, it's easy to see we have three similar rectangular faces to choose from, which correlate with the remaining three answer choices. If the L-shaped large faces are opposite one another, the rectangular shape shown underneath the large rectangle on the left of the flat diagram has to correlate to the one found on the far left of the folded shape. This isn't the blue rectangle, so the following answer choice is incorrect:
The rectangle that is directly adjacent to the right L-shaped face in the flat diagram has to share an edge/fold with it. This means that this has to be the top of the L-shape. Since it's not blue either, the following answer choice is also incorrect:
The only remaining answer choice is the correct one. The blue rectangle is the one underneath the rectangle adjacent to the L-shape. You can picture how if the white rectangle forms the top of the L-shape, the blue one is folded such that it becomes the height of the vertical section of the "L." This means that the following shape is the correct answer:
For this question, examine the for INTERIOR angles and rank each in terms of degrees from SMALL TO LARGE. Choose the answer choice that has the correct ranking.
4 - 2 - 3 - 1
4 - 2 - 1 - 3
2 - 4 - 3 - 1
2 - 4 - 1 - 3
Explanation
A three-dimensional object is shown in the question prompt, and outlines of five apertures or openings are shown as the answer choices. First, you imagine how the object looks from all directions (rather than form a single direction as shown). Then, pick from the five apertures outlined the opening through which the object could pass directly if the proper side were inserted first.
Here are the rules:
1. Prior to passing through the aperture, the irregular solid object may be turned in any direction. It may be started through the aperture on a side not shown.
2. Once the object is started through the aperture, it may not be twisted or turned. It must pass completely through the opening. The opening is always the exact shape of the appropriate external outline of the object.
3. Both objects are drawn to the same scale. Thus, it is possible for an opening to be the correct shape but too small for the object; however, in all cases, differences are large enough to judge by eye.
4. There are no irregularities in any hidden portion of the object; however, if the figure has symmetric indentations, the hidden portion is symmetric with the part shown.
5. For each object there is only one correct answer.
Explanation
This is the correct keyhole/aperture shape:
If the three-dimensional shape were positioned so that the front-most face were parallel with the keyhole, it would be able to fit through. Note how the triangular piece that juts up above the mostly-rectangular prism farthest away from the presented three-dimensional view would require the left sloped side of the triangular portion near the top of the keyhole, and the triangular piece sticking up from the front of the presented three-dimensional view would require the right sloped side of the triangle in the keyhole. The bottom right corner of the mostly-rectangular prism comes to a point, which is accommodated by a corresponding point in the keyhole. The right angle where the mostly-rectangular prism meets the left part of the shown three-dimensional shape is also represented in the keyhole.
The shape showns above are not correct because neither shows the right angle where the rectangular prism with a pointed bottom-right corner meets the left part of the shape. In addition, the shape on the right does not provide space for the pointed corner near the bottom-right of the presented view.
This shape is not correct because the two triangular pieces that jut above the mostly-rectangular prism are shown with a gap in between them. By looking at the presented three-dimensional shape, you can see that they do not have this large of a gap in between their spacing on the parallel sides of the rectangular prism.
This shape is not correct because it does not include space for the pointed corner of the shape similar to a rectangular prism. This is its bottom-right corner in the presented view.
Consider the following figure, which has been made by cementing together cubes of the same size. After being cemented, each group was painted on all sides except for the bottom on which it is resting. Not all cubes may be visible in the figure, but the only hidden cubes are those required to support other cubes.
In the figure shown above, how many cubes have only one of their sides painted?
1 cube
2 cubes
3 cubes
4 cubes
5 cubes
Explanation
A three-dimensional object is shown in the question prompt, and outlines of five apertures or openings are shown as the answer choices. First, you imagine how the object looks from all directions (rather than form a single direction as shown). Then, pick from the five apertures outlined the opening through which the object could pass directly if the proper side were inserted first.
Here are the rules:
1. Prior to passing through the aperture, the irregular solid object may be turned in any direction. It may be started through the aperture on a side not shown.
2. Once the object is started through the aperture, it may not be twisted or turned. It must pass completely through the opening. The opening is always the exact shape of the appropriate external outline of the object.
3. Both objects are drawn to the same scale. Thus, it is possible for an opening to be the correct shape but too small for the object; however, in all cases, differences are large enough to judge by eye.
4. There are no irregularities in any hidden portion of the object; however, if the figure has symmetric indentations, the hidden portion is symmetric with the part shown.
5. For each object there is only one correct answer.
Explanation
This is the correct keyhole/aperture shape:
If the three-dimensional shape were positioned so that the front-most face were parallel with the keyhole, it would be able to fit through. Note how the triangular piece that juts up above the mostly-rectangular prism farthest away from the presented three-dimensional view would require the left sloped side of the triangular portion near the top of the keyhole, and the triangular piece sticking up from the front of the presented three-dimensional view would require the right sloped side of the triangle in the keyhole. The bottom right corner of the mostly-rectangular prism comes to a point, which is accommodated by a corresponding point in the keyhole. The right angle where the mostly-rectangular prism meets the left part of the shown three-dimensional shape is also represented in the keyhole.
The shape showns above are not correct because neither shows the right angle where the rectangular prism with a pointed bottom-right corner meets the left part of the shape. In addition, the shape on the right does not provide space for the pointed corner near the bottom-right of the presented view.
This shape is not correct because the two triangular pieces that jut above the mostly-rectangular prism are shown with a gap in between them. By looking at the presented three-dimensional shape, you can see that they do not have this large of a gap in between their spacing on the parallel sides of the rectangular prism.
This shape is not correct because it does not include space for the pointed corner of the shape similar to a rectangular prism. This is its bottom-right corner in the presented view.
Consider the following figure, which has been made by cementing together cubes of the same size. After being cemented, each group was painted on all sides except for the bottom on which it is resting. Not all cubes may be visible in the figure, but the only hidden cubes are those required to support other cubes.
In the figure shown above, how many cubes have only one of their sides painted?
1 cube
2 cubes
3 cubes
4 cubes
5 cubes
Explanation
The pictures that follow are top, front, and end views of solid objects. The views are without perspective. That is, the points in the viewed surface are viewed along parallel lines of vision. The projection looking DOWN on it is shown in the upper left-hand corner (TOP VIEW). The projection looking at the object from the FRONT is shown in the lower left-hand corner (FRONT VIEW). The projection looking at the object from the END is shown in the lower right-hand corner. (END VIEW). These views are ALWAYS in the same positions and are labeled accordingly.
Note that lines that cannot be seen on the surface in some particular view are DOTTED in that view.
In these problems, two views are shown, with four alternatives to complete the set. You are to select the correct one. It is not always the end view that must be selected; sometimes it is the top view or the front view that is missing.
Explanation
To answer this question correctly, you need to understand the difference between solid lines and dashed lines on the DAT Perceptual Ability section. In this case, we're looking for the front view. The top view of this shape shows us that it is divided into three sections. Considering just this view, this could mean a variety of different things: the shape might be cube-like and each section might be a different step, for example, but we'd have no information about how the heights of each "step" would compare. In addition, the shape might not be a cube; angles might be involved. We can't tell solely from looking at the top view, though. The end view provides us with more information that allows us to narrow down our interpretation of the top view. Here, we see that the shape, when viewed from the end, involves an angle, and that there is a solid line at the bottom of the cube above the angular piece. This tells us that the cube is not connected to the shape that includes the angle. The cube's face isn't connected to the end face of the angled piece; it is separate. This tells us that the cube is farther away than the angled end face facing us directly in the end view. If one of its faces were connected to the angled end face, the diagram would not include a line separating the "cube" part of the shape from the angled part of the shape.
Now let's consider what the front of the shape has to look like. Notice that the "cube" part of the shape is on the left in all of the answer choices. This is important, as it tells us that we are looking at the flat, rectangular side of the larger part of the shape head-on, not at the angled sides. If we were looking at the angled sides, the "cube" part would have to be on the right side of the front-view diagram, and this isn't an option in any of the answer choices.
So, we know that the line forming the vertex of the angle shown in the End View diagram is behind the face of the shape we're directly looking at in the Front View. This tells us that this line must be dotted, not solid. Figuring this out allows us to ignore the following two answer choices because they use solid lines for their bottom-most shape-crossing line:
This leaves us with two remaining answer choices, each of which correctly uses a dotted line:
The only difference between these two answer choices is that the one on the left uses a dashed line to divide the "cube" shape from the rest of the shape, and the one on the right uses a solid line for this division. Which should it be? Consider how this "cube" shape will appear when we look at the shape head-on with the face shown as the bottom line of the Top View appearing first. Is the "cube" part of the shape in line with this face, or is it located further back in space? If the former is true, we need to use a dotter line to show that the cube shape does not continue for the entire volume of the shape, but that there is negative space located behind it. If the latter is true, we need to use a solid line to show that the negative space is in front of the cube. Looking at the Top View diagram, we can see that one face of the cube will be even with the face of the larger part of the shape at which we are looking in the Front View. This means that the negative space appears behind the cube, not in front of it, making the correct answer the shape that uses the dotted line:
A flat square of paper is folded one or more times. The broken lines indicate the original position of the paper. The solid lines indicate the position of the folded paper. The paper is never turned or twisted. The folded paper always remains within the edges of the original square. There may be from one to three folds in each item. After the last fold, a hole is punched in the paper. Your task is to mentally unfold the paper and determine the position of the holes on the original square. Choose the pattern of black circles that indicates the position of the holes on the original square. There is only one correct pattern for each item.
Explanation
In this question, a flat pattern is presented. This pattern is to be folded into a three-dimensional figure. The correct figure is one of the four given as answer choices. There is only one correct figure in each set. The outside of the folded shape is what is seen as the flat pattern. Select the three-dimensional shape that the flat pattern produces when folded.
Explanation
In this 3-D Form Development / Pattern Folding question, we need to figure out which face of the resulting L-shaped figure corresponds with the blue face on the flat diagram. We can ignore the answer choice that does not show any visible face as the blue one, because the only faces hidden from the shown view are larger than the rectangular face shown in the diagram. One would be the large square, and the other would be one of the large L-shaped faces.
Looking at the flat diagram, it's easy to see we have three similar rectangular faces to choose from, which correlate with the remaining three answer choices. If the L-shaped large faces are opposite one another, the rectangular shape shown underneath the large rectangle on the left of the flat diagram has to correlate to the one found on the far left of the folded shape. This isn't the blue rectangle, so the following answer choice is incorrect:
The rectangle that is directly adjacent to the right L-shaped face in the flat diagram has to share an edge/fold with it. This means that this has to be the top of the L-shape. Since it's not blue either, the following answer choice is also incorrect:
The only remaining answer choice is the correct one. The blue rectangle is the one underneath the rectangle adjacent to the L-shape. You can picture how if the white rectangle forms the top of the L-shape, the blue one is folded such that it becomes the height of the vertical section of the "L." This means that the following shape is the correct answer:
For this question, examine the for INTERIOR angles and rank each in terms of degrees from SMALL TO LARGE. Choose the answer choice that has the correct ranking.
4 - 2 - 3 - 1
4 - 2 - 1 - 3
2 - 4 - 3 - 1
2 - 4 - 1 - 3
Explanation