ATDH Perceptual Ability: Cube Counting — Questions and Answers

Question 1: In ATDH cube-counting items, a stack of identical cubes is painted on every exposed surface. Which surface is never counted as painted?

The bottom faces resting on the surface the stack sits on (Correct answer)
The top faces of the highest cubes
The faces visible from the front
The faces visible from the back

Correct answer: The bottom faces resting on the surface the stack sits on

Every exposed surface is painted except the bottom of the stack, which rests on the table. Faces covered by a neighbouring cube are also unpainted, but hidden back faces are still painted if nothing touches them.

Question 2: Three cubes sit side by side in a single straight row on a table (1 cube high, 1 cube deep, 3 cubes long). How many cubes have exactly 4 painted sides?

1
2 (Correct answer)
3
0

Correct answer: 2

Each end cube has its top, front, back and outer end painted, which is 4 sides. Its bottom and the side touching the middle cube are not painted. The middle cube has only 3 painted sides (top, front, back). So 2 cubes have exactly 4.

Question 3: Four cubes form a 2×2 square in a single layer on a table. How many cubes have exactly 3 painted sides?

0
2
4 (Correct answer)
3

Correct answer: 4

Every cube is a corner cube. Each has its top and two outer side faces painted, which is 3. Its bottom rests on the table and its two inner faces touch neighbours. All 4 cubes have exactly 3 painted sides.

Question 4: Eight cubes form a 2×2×2 block resting on a table. How many cubes have exactly 2 painted sides?

8
4 (Correct answer)
0
2

Correct answer: 4

Each top-layer cube has 3 painted sides: its top and two outer sides. Each bottom-layer cube has only its two outer sides painted, because its bottom is on the table and its top is covered. That makes 4 cubes with exactly 2.

Question 5: Under ATDH cube-counting rules, what is the maximum number of painted sides any single cube can have?

6
5 (Correct answer)
4
3

Correct answer: 5

A cube always rests on something, either the table or another cube, so at least its bottom face is unpainted. An isolated cube on the table has 5 painted sides, which is the maximum.

Question 6: Three cubes are stacked vertically into a single tower on a table. How many cubes have exactly 4 painted sides?

1
3
2 (Correct answer)
0

Correct answer: 2

The top cube has 5 painted sides: its top plus 4 sides. The middle cube has 4, since its top and bottom touch other cubes. The bottom cube has 4, since its top is covered and its bottom rests on the table. So 2 cubes have exactly 4.

ATDH Perceptual Ability: Cube Counting

In ATDH cube-counting items, a stack of identical cubes is painted on every exposed surface.
Which surface is never counted as painted?

What Practice Test Geeks adds beyond an AI chat for ATDH

An AI chatbot can quiz you, but it can't reproduce the exam conditions or keep your record. Here you get:

A timed, full-length ATDH mock exam — 240 questions in 230 minutes with a 50% pass mark, modeled on the official exam's question count and time limit, followed by a score report broken down by exam domain.
A fixed ATDH question bank: the same test every attempt, so your score is comparable from one try to the next instead of changing with every regenerated quiz.
Progress saved on your device: completed tests, scores and missed questions stay in My Progress, so you can retake only what you got wrong.
A printable ATDH cheat sheet you can print or save as a PDF.
ATDH flashcards built from the same question bank.

Start the Timed ATDH Mock Exam →

These practice questions were written with AI tools. They are not real exam questions. Exam facts are checked against the official sources listed below. Not reviewed by a subject-matter expert. Editorial policy

Sources & references

Exam facts on this page (fees, format, dates, passing scores) are checked against these official sources; the date is our last check. Editorial policy

ada.org — Test delivery, eligibility, fees, exam format, passing score, retake policy, score release, test dates, time limit · verified Sep 2026