DAT Review · Perceptual Ability Test
Keyholes (Apertures)
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In 30 seconds
Keyholes (also called "apertures") are the first question type in the PAT section. You're shown a 3D object and asked: "Through which of the five openings could this object pass if it were pushed through in a straight line without rotating?" The openings are flat, 2D cutouts — like the object needs to slide through a hole in a wall while maintaining one fixed orientation. There are typically 15 keyhole questions out of the 90 PAT questions, and you should budget about 40 seconds per question.
The key insight: you're NOT matching the opening to what the object "looks like" from a particular angle. You're finding the smallest aperture the object can fit through. This is a projection problem — imagine shining a light through the object and looking at the shadow cast on the wall. The correct opening must accommodate the object's maximum dimensions in that orientation.
The college version
Strategy/Review
The Three-Pass Algorithm
I teach a systematic three-pass approach that prevents the most common keyhole mistakes.
Pass 1 — Identify Extreme Dimensions. Before looking at the answer choices, mentally scan the object for its most extreme features. Where is it widest? Tallest? Does it have any protrusions, notches, or irregular features that would create unusual silhouettes? For example, an L-shaped block has maximum width at its base combined with a vertical extension — the extreme silhouette from the front might be tall-and-thin, while the extreme silhouette from the top might be an L-shape.
Pass 2 — Eliminate the Impossible. Run through all five answer choices and eliminate any that clearly cannot work. Watch for these elimination criteria: (a) an opening that is missing a necessary protrusion (a notch, a step, a bump that exists on the object), (b) an opening that has a feature the object doesn't have (an extra bump where the object is flat), (c) an opening whose proportions are clearly wrong (too narrow where the object is wide, too short where the object is tall), (d) an opening whose shape fundamentally cannot accommodate the object's cross-section (e.g., a circular hole for a square peg).
Pass 3 — Verify the Survivor(s). Once you've narrowed to 1-2 choices, mentally rotate the object into each candidate orientation and trace its silhouette against the opening. Ask: "Can I orient the object so that its projection fits inside this shape?" Remember that the object can be rotated to any angle — you're finding the orientation that produces the smallest possible projected outline.
Mental Rotation Technique. Rather than rotating the object itself, try rotating the opening mentally. Imagine picking up the answer choice shape and rotating it in 3D space until it aligns with a view of the object. For many students, this is actually easier than rotating the complex 3D object.
Top-Down vs. Side-View Thinking. For objects with distinct horizontal cross-sections, think about the "shadow" the object would cast from above (plan view) and from the side (elevation view). The correct opening is the shape formed by the object's maximal cross-section in some orientation — often the plan view or a diagonal between plan and elevation.
Common Traps
Trap 1 — The "Looks Like" Fallacy. The most dangerous trap in keyholes is choosing an opening that looks like an obvious view of the object. Imagine a simple cylinder with a cone on top. An opening shaped like a triangle with a circular base seems to match the side view — but the object's maximum width is the cylinder's diameter, and the cylinder can't pass through a triangular opening. The correct aperture would be a circle (the cylinder's cross-section), since you can orient the object so the cone enters first and the cylinder follows.
Trap 2 — Forgetting That the Object Can Rotate. Students often lock into one "natural" orientation and evaluate all choices against it. But the object can be rotated to any angle before passing through. A long, thin rectangular prism can pass through a surprisingly small hole if you tilt it diagonally. Always ask: "Is there ANY orientation where this works?"
Trap 3 — Overlooking Thin Protrusions. Small tabs, pegs, or thin extensions are easy to miss during visual scanning. An object that is mostly a rectangular block but has a small cylindrical peg on one face — if you forget the peg, you might choose a purely rectangular opening. The projection must account for every part of the object.
Trap 4 — Confusing Projection with Cross-Section. The opening isn't a cross-section slice through the middle of the object. It's the maximal outline from a particular viewing direction. A pyramid has a square cross-section near its base but a smaller square near its tip — the projection that matters is the largest one, because the entire object must pass through from front to back.
Trap 5 — Missing the "Straight Line" Constraint. The object must pass through in a straight line without rotating while passing through. You can rotate before entry, but once it starts going through, the orientation is fixed. This means curved or angled paths are not allowed — the projection must account for the entire depth of the object in one orientation.
Eli explains
The same idea, in plain words
Explain it like I’m 10
Imagine you have a toy block and a piece of paper with a hole cut in it. Your job is to figure out which hole the block can slide through — but you can turn the block any way you want BEFORE you push it through. Once you start pushing, you have to go straight and can't wiggle it.
Think of it like a shadow puppet. If you shine a flashlight at the block from different directions, you get different shadows. The "hole" has to be big enough for the whole shadow to fit inside it. Some shadows are bigger, some are smaller — you want to turn the block so its shadow is as small as possible, and then find the hole that matches that shadow.
The trick is that the shadow has to include EVERY part of the block. If the block has a bump, the shadow has a bump. If you see a hole with no bump, the block's bump would get stuck — wrong answer!
The most important rule: don't just pick the hole that "looks like" what you see. Turn the block in your head. Find the smallest shadow. Then match it.
Key takeaways
- Draw a simple L-bracket (two rectangular prisms joined at a right angle). Sketch the five possible openings: (a) an L-shape matching the front view, (b) a rectangle matching the side view, (c) a tall thin rectangle, (d) a square, (e) an irregular pentagon. Which can the bracket pass through? (Answer: only (a) — the maximal cross-section in any orientation is the L-shape; no rotation makes it a pure rectangle.)
- For a T-shaped object (vertical stem + horizontal crossbar), explain why a rectangular opening can NOT work even though the object looks rectangular from the side. (Answer: the crossbar creates a T-shaped projection in the plan view, and no rotation eliminates the crossbar's contribution to the maximal outline.)
- Take a triangular prism. From the side, it looks like a triangle. From the end, it looks like a rectangle. Which opening is correct? (Answer: the triangle, because the rectangular end view is smaller than the triangular side view — you can orient the prism so the triangular face goes through first, and the triangle is the largest cross-section in that orientation, which matches the triangular opening.)
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