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Home › Non-Verbal Reasoning › Non-Verbal Reasoning - Cube Cutting into Sub-Cubes

Non-Verbal Reasoning - Cube Cutting into Sub-Cubes — Non-Verbal Reasoning Questions & Practice

Practise 1,288 Non-Verbal Reasoning - Cube Cutting into Sub-Cubes questions from Non-Verbal Reasoning for competitive exams such as UPSC, Banking, SSC and Railway. Read the worked questions below, check every answer with an explanation, and track what you get wrong.

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Practice questions on Non-Verbal Reasoning - Cube Cutting into Sub-Cubes — with answers

Try each question first, then open the answer. Explanations are included.

1. A cube of side 4 units is painted on all six faces and then cut into smaller cubes, each of side 2 units. How many smaller cubes have exactly 3 faces painted?

  1. A8
  2. B9
  3. C10
  4. D7
Show answer

Answer: A

With side 4 cut into pieces of side 2, there are 2 pieces per edge. Exactly 3 faces painted occurs only at the 8 corners, regardless of 2.

2. A cube of side 4 units is painted on all six faces and then cut into smaller cubes, each of side 2 units. How many smaller cubes have exactly 2 faces painted?

  1. A0
  2. B1
  3. C2
  4. D3
Show answer

Answer: A

With 2 pieces per edge, cubes with exactly 2 faces painted lie along the edges (excluding corners): 12 x (2-2) = 0.

3. A cube of side 4 units is painted on all six faces and then cut into smaller cubes, each of side 2 units. How many smaller cubes have exactly 1 face painted?

  1. A0
  2. B1
  3. C2
  4. D3
Show answer

Answer: A

With 2 pieces per edge, cubes with exactly 1 face painted lie at face centres (excluding edges): 6 x (2-2)^2 = 0.

4. A cube of side 4 units is painted on all six faces and then cut into smaller cubes, each of side 2 units. How many smaller cubes have no face painted at all?

  1. A0
  2. B1
  3. C2
  4. D3
Show answer

Answer: A

With 2 pieces per edge, completely unpainted cubes are internal: (2-2)^3 = 0.

5. A cube of side 6 units is painted on all six faces and then cut into smaller cubes, each of side 2 units. How many smaller cubes have exactly 3 faces painted?

  1. A8
  2. B9
  3. C10
  4. D7
Show answer

Answer: A

With side 6 cut into pieces of side 2, there are 3 pieces per edge. Exactly 3 faces painted occurs only at the 8 corners, regardless of 3.

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