Keyhole (Aperture):
- January 28, 2021
Keyhole
There are 15 questions in the keyhole subsection of PAT. It is recommended that you spend no more than 50 seconds on each question.
In this subsection, you will be shown a three-dimensional object, then you are presented with five options to choose from. The options are openings or apertures through which the three-dimensional object is supposed to pass from one side of the object if the proper side were inserted first.
Here are the rules for finding the right answer to the questions:
– You could turn the object in any direction before passing it through the opening.
– When you start passing the object through a hole from a certain side, you cannot twist or turn the object and you must be able to pass it completely through.
– There are no irregularities in any part of the object that is not visible, if there are visible indentations on the object, the parts that are not visible must be symmetric with the part shown.
– Both objects and apertures are drawn to scale and must be an exact fit, therefore, it is possible for an opening to be the correct shape, but too small for the object. But if the figure has symmetric indentations, the hidden portion is symmetric with the part shown.
– There is always one correct answer to the question.
The external outline of the object is the exact size and shape of the opening without being too big or too small or having extra protrusions.
So, the correct opening generally corresponds with one of three projections that can be drawn for the object: the top-bottom projection, the front-back projection, or the side projection. The most efficient way to find the correct answer is to determine the three main projections of the object and pick the choice that matches one of those. The following example illustrates this technique:
The correct choice is, therefore (C). Note how choice (D) is a distractor designed to trap test-takers who go for the obvious features of the object without paying attention to the finer aspects; this is a common perceptual ability trap.
You can first look at the choices you have to eliminate any choice that has any irregularities that don’t exist in the shape in question. In the following example, there is a square-like empty space in the circle, so option D cannot exist in any projection of the 3D shape. So choice D is wrong.
The front-back projection of the shape looks like a rectangle with a smaller rectangle on top, and left to right projection looks like a rectangle with another rectangle on the top right side, and the top-bottom projection looks like an incomplete circle.
If you can’t easily eliminate a choice, just move on and don’t waste too much time on that choice, see if you can eliminate other choices since the option you are trying to eliminate might be the answer.
One method for getting a proper visualization of the different projections of the shape is to try to imagine what two-dimensional shape would we have if we were to flatten the object against the wall relative to the top/bottom, front/back, or left/right sides. Whichever way you crush the original object, the part that remains will represent a correct aperture for the problem. For example, if you crush a can of soda from top to bottom, you are left with a circular disc. If you crush it from left to right or from front to back, though, you are instead left with a rectangular piece. Therefore, if your original object is a circular cylinder, the correct projection would be either a rectangle or a circle.
In the following video, we have illustrated what the process looks like when we crush an object to a wall, you can see what 2D shapes we have when we flatten the 3D object from the three-point of view. You can see how a cube becomes a rectangle when crushed from a side to a wall. When we smash it from top to bottom we have a square shape.
Another method is the flashlight method, if you hold a flashlight towards an object from one view, the shadow of that light will make the two-dimensional shape. To follow the soda can example, if you project light from the top view on a can of soda (cylinder shape), the shadow would be a circle that we are looking for in keyhole section questions. You obviously can’t do this process in real life to find the aperture for an object but this will help you have a better understanding of the apertures in this section.
Another method is identifying the lines in a 3D shape and deciding whether they are parallel, diverging, or converging, and also the relative length of the lines in an object.
For example, in the following question, option B cannot be correct because edges (shown by red color) in the object are not parallel, while the edges in option B are parallel.
Also, the length of the two blue lines is not identical. So option A can’t be left to right projection or front projection due to having non-parallel lines.
So when we are looking at an option, we should evaluate three aspects that could be wrong with an option:
First is the shape, a wrong shape, is when the keyhole has an obvious wrong indentation or feature that doesn’t exist in the 3D shape.
Second, there is size, this feature is assessed by using the relative length of lines in the shape.
The third is the position or a feature that is misplaced from what we see in the question.
In the example that we have, we can see the length of the two red arrows that are drawn between the circles, and the edge of the shape is different from what option B is showing. In option B we have a circle that is almost at the middle of the shape while we don’t see this positioning for circles in the 3D shape. So the position in option B is wrong.
In option D, the overall shape of the projection looks fine until we compare the placement of the indentations with the 3D shape. In the 3D shape, the middle indentation is taller between the two rectangles, the purple arrow in option D is pointing to this issue. So option D is wrong because of the wrong placement.
Options C and E are wrong because the only sensible view they could possibly be representing is the front view, but in the front view we are supposed to see two horizontal rectangular shapes with different elevations from the surface of the object as well as a vertical rectangle overlapping with the longer horizontal rectangle, but we do not see any of these elevations or indentations in these two options. In the following picture, we can see the difference between elevations. Have a look at the answer key to better understand these points that we talked about.
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