Spatial reasoning tests: six question types, worked through

A spatial reasoning test asks you to picture shapes and move them in your mind. The Dental Admission Test sets out six kinds of spatial question in detail. This guide works through one of each, using the practice on this site that asks the same kind of question.

What the Perceptual Ability Test asks

The American Dental Association runs the Dental Admission Test. Its 2026 candidate guide lists four sections. One is the Perceptual Ability Test: 90 questions in 60 minutes, which is 40 seconds a question on average. The questions come in six types, which the ADA describes like this.

  • Apertures: decide whether a solid can pass through an opening.
  • View recognition: picture how an object looks from another side.
  • Angle discrimination: rank a set of angles from smallest to largest.
  • Paper folding: unfold a folded, punched sheet in your mind.
  • Cube counting: work out how much of each cube in a stack is exposed.
  • Spatial relations, also called 3D form development: find the solid a flat pattern folds into.

The ADA publishes instructions and one sample question for each type. The practices on this site are original. They are not DAT questions, and some of their rules differ. Each example says where.

Where else these tasks appear

Researchers use the same kinds of task. The Educational Testing Service lists a Paper Folding Test and a Surface Development Test under visualization, and a Cube Comparisons Test under spatial orientation, in its Kit of Factor-Referenced Cognitive Tests, 1976 edition. Two more research tasks have guides of their own here: the mental rotation test and the cross section test.

Six worked examples

Each example below is a real question from a practice on this site, drawn by that practice. Try each one before you read the steps.

Example 1: apertures (Match the opening, Standard)

This one is from Match the opening. In the DAT you may turn the solid any way before it starts through the opening, but not once it is moving. Here the solid always travels along the arrow, and you may only turn it in quarter turns around the arrow first.

The question as the practice draws it.

Which opening can the whole solid pass through?

  • A
  • B
  • C
  • D
  1. Look along the arrow. At each place across the solid, only the tallest column counts, in whichever row it stands. From left to right they are 3, 2 and 1 cubes tall, so the outline has six squares.
  2. No single row of columns across the arrow makes that outline. The rows alone cover four, five and one squares.
  3. Opening B has the whole outline with no turn. The other three have the same area but a different shape.
The answer as the practice shows it: the whole outline inside the opening.

The answer is B.

Example 2: view recognition (Cube views, level 4)

This one is from Cube views. The DAT gives two of a solid's top, front and end views, drawn flat, and asks you to choose the third. In the Find the missing view mode here, you get the top and front views of a stack of cubes and choose the right view.

Top view

Back

Front

Front view

The two given views as the practice draws them.

Which right view fits both? The front is on its left.

  • 1
  • 2
  • 3
  • 4
  1. The front view gives the tallest stack in each column, left to right: 1, 2 and 2.
  2. Take the top view one row at a time, from the front row to the back row. Each row is as tall as the tallest front-view column it has a stack in: 2, 1 and 2.
  3. The right view has the front on its left, so its columns are 2, 1 and 2 high. That is option 1.

The answer is option 1.

Example 3: angle discrimination (Angle ranking, Standard)

This one is from Angle ranking. The DAT's sample shows four angles and asks you to choose their order from a list. Here you tap the four angles in order, smallest first.

Put these angles in order from smallest to largest.

  • A
  • B
  • C
  • D
  1. Sort them against a square corner first. Sharper: A and D. Close to square: B. Wider: C.
  2. Then compare inside each group. D opens wider than A.
  3. Smallest to largest: A, D, B and C.
  • A64 degrees
  • D78 degrees
  • B91 degrees
  • C104 degrees
The answer as the practice shows it: each angle turned to start from the same line.

The answer is A, D, B, C.

Example 4: paper folding (Paper folding, Easy)

This one is from Paper folding, which sets the same task as the DAT on a 4 by 4 grid. Every DAT question has more than one fold. Fold the bottom half up, then the right half over to the left. Then punch one hole.

1. Flat paper
2. Fold bottom half up
3. Fold right half left, then punch
The question as the practice draws it.

Which pattern shows the holes on the open sheet?

  • A
  • B
  • C
  • D
  1. The punched stack, with one hole.

  2. Open the fold from drawing 3. Mirror each hole across the crease between columns 2 and 3: one hole becomes two.

  3. Open the fold from drawing 2. Mirror each hole across the crease between rows 2 and 3: two holes become four.

The answer is B. The four holes are in row 1, columns 1 and 4; row 4, columns 1 and 4. The paper folding guide has four more examples.

Example 5: cube counting (Cube counting, level 2)

This one is from Cube counting. In the DAT, the only hidden cubes are the ones that hold others up, and the practice here uses the same rule. The DAT then asks how many cubes have a given number of painted sides. The practice asks first for the total.

The question as the practice draws it.

How many cubes are there?

  • 8
  • 7
  • 5
  • 6
  1. Every stack stands on the ground with no gaps, so count stack by stack: 2, 2, 1, 1 and 1 cubes.
  2. That makes 7. One of them is out of sight under a cube you can see.

The answer is 7. Now count it the DAT way. Paint every outside face except the bottom, then count each cube's painted sides. One cube has two painted sides, three have three, one has four and two have five.

Example 6: spatial relations (Cube nets, level 3)

This one is from Cube nets. The DAT shows a flat pattern and asks which solid it folds into. In the Match the cube mode here, the pattern is always a cube net with six different marks.

The question as the practice draws it.

Which cube can this net make?

  • ACube A. Top: ring. Front, on the left: square. Right: four dots.
  • BCube B. Top: dot. Front, on the left: ring. Right: square.
  • CCube C. Top: ring. Front, on the left: four dots. Right: dot.
  • DCube D. Top: plus. Front, on the left: cross. Right: ring.
  1. Find the opposite pairs first. On this net they are four dots opposite plus, ring opposite dot and cross opposite square.
  2. Cubes B and C show ring and dot side by side. Opposite faces never touch, so they are out.
  3. Cube D shows no opposite pair, but the three marks go round the corner the wrong way. That is a mirror image, and no turn makes it.
  4. That leaves cube A.

The answer is A.

Common mistakes

Using one face of the solid. An opening must fit the outline of the whole solid. In example 1, no single row of columns gives it.

Mixing up the sides. On the top view here, the front is at the bottom. On the right view, the front is on the left. Check both before you compare.

Judging an angle by its arms. Long arms and the way an angle points change nothing. Only the opening counts, which is why the practice lines them up after you answer.

Counting only what you can see. A cube under another cube is there even when the drawing hides it. In the DAT count, the bottom is never painted, so no cube has six painted sides.

Accepting a mirror image. A cube can show three marks that each belong on the net and still be wrong, because they run the wrong way round the corner.

How to practise it here

Each practice has a lesson that teaches its method one step at a time.

Start without a clock and check each answer against the drawing the practice shows after you answer. The DAT gives about 40 seconds a question, so time yourself only once your answers come out right. The score is the number right. It describes that practice on that day, nothing wider.

Related guides

Questions people ask

What is on the DAT Perceptual Ability Test?

The Perceptual Ability Test is one of four sections of the Dental Admission Test, which the American Dental Association runs. It has 90 questions in 60 minutes, about 40 seconds a question. The questions come in six types: apertures, view recognition, angle discrimination, paper folding, cube counting, and spatial relations, also called 3D form development. The ADA publishes instructions and one sample question for each type.

How do you solve aperture questions?

Look along the arrow and find the outline of the whole solid. At each place across it, only the tallest column counts, in whichever row it stands. The right opening holds that whole outline. One face or one row of the solid is not enough: the opening must fit the whole outline. In the DAT you may turn the solid before it starts through the opening, but not once it is moving.

How do you rank angles from smallest to largest?

Sort them against a square corner first: sharper, close to square, or wider. Then compare the angles inside each group. Long arms and the way an angle points change nothing. Only the opening counts. In Angle ranking on this site, the gaps between angles shrink from 18 to 28 degrees at Easy to 5 to 9 at Challenge, and after you answer each angle is turned to start from the same line.

How do you count cubes in a DAT cube counting question?

Count stack by stack. In the DAT, the only hidden cubes are the ones that hold others up, so a cube under another cube is there even when the drawing hides it. The DAT then asks how many cubes have a given number of painted sides, with every outside face painted except the bottom. The bottom is never painted, so no cube has six painted sides.

How do you tell which cube a net folds into?

Find the opposite pairs on the net first. Opposite faces never touch, so a cube that shows both marks of a pair side by side is wrong. Then check the order of the three marks round the corner. A cube can show three marks that each belong on the net and still be wrong, because they run the wrong way round. That is a mirror image, and no turn makes it.

How should you practise for the Perceptual Ability Test?

Start without a clock and check each answer against the drawing the practice shows after you answer. The DAT gives about 40 seconds a question, so time yourself only once your answers come out right. The practices on this site cover all six question types, but they are original, not DAT questions, and some of their rules differ. The score describes that practice on that day, nothing wider.

Sources