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SBI PO Cube & Dice

Study Material — 9 PYQs (2024–2024) · Concept Notes · Shortcuts

SBI PO Cube & Dice is a frequently tested subtopic — 9 previous year questions from 2024–2024 papers are included below with concept notes, key rules and shortcut tricks.

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Previous Year Questions

SBI PO Cube & Dice — Past Exam Questions

9 questions from actual SBI PO papers · all shown free · click option to reveal solution

Exam Q 12024Previous Year Pattern

A standard cube has faces numbered 1 to 6. If face 1 is opposite to face 6, and face 2 is opposite to face 5, then which face is opposite to face 3?

Exam Q 22024Previous Year Pattern

A cube has six faces. Three faces meeting at one corner are colored red, blue, and green respectively. How many faces are NOT colored?

Exam Q 32024Previous Year Pattern

A cube is unfolded into a net. One face shows a star (★), and an adjacent face shows a circle (●). If the star face is opposite to a blank face, which of the following cannot be opposite to the circle?

Exam Q 42024Previous Year Pattern

A standard die is placed on a table. The face showing 6 is on top, and the face showing 3 is facing you. Which face is on the bottom of the die?

Exam Q 52024Previous Year Pattern

A die shows faces with 1, 2, 3, 4, 5, and 6 dots. When face 1 is on top and face 2 faces you, which face is on the bottom?

Exam Q 62024Previous Year Pattern

A cube has six faces with different symbols: ★, ●, ■, ▲, ◆, and ○. The following are known: ★ is opposite ●, ■ is opposite ▲, and ◆ is opposite ○. The cube is positioned with ★ on top and ■ facing you. The cube is then tilted 90° forward (away from you). After tilting, which symbol is now facing you?

Exam Q 72024Previous Year Pattern

A cube has faces labeled 1 through 6. It is known that: 1 is opposite 2, 3 is opposite 4, and 5 is opposite 6. The cube is placed with face 1 facing north and face 3 facing up. The cube is then rotated 90° clockwise (when viewed from above) around the vertical axis. After this rotation, which face is now facing north?

Exam Q 82024Previous Year Pattern

A standard die is rolled and lands with face value 3 on top. The die is then rolled again and lands with face value 5 on top. Before the first roll, the die was positioned such that faces 1 and 6 were on the left and right respectively. After the first roll (showing 3 on top), which face is now on the bottom?

Exam Q 92024Previous Year Pattern

A cube has six faces. On one face, the number 1 is written. On the face opposite to it, the number 6 is written. On another face, the number 2 is written. On the face opposite to it, the number 5 is written. The remaining two faces have numbers 3 and 4 written on them, and they are also opposite to each other. When the cube is placed such that face 1 is on top and face 2 is facing you, which number is on the bottom face?

Concept Notes

Cube & Dice— Rules & Concept

Core ConceptRead this first — the foundation of the topic

A cube is a three-dimensional object with 6 faces, 12 edges, and 8 vertices. Each face is a square. In SSC CGL exams, cube and dice questions test your ability to visualize how a flat pattern folds into a 3D shape or how a cube looks when rotated. Key Rules for Cubes:

1. Opposite faces never touch each other when the cube is folded 2. Adjacent faces share a common edge

3. When a cube is cut, count the pieces formed 4. In dice problems, opposite faces always add up to 7 (1-6, 2-5, 3-4)

Main Question Types: - Net to Cube: Given a flat pattern, identify which cube it forms

- Cube Views: Different views of the same cube from various angles - Dice Problems: Find opposite faces or adjacent faces

- Cube Cutting: Calculate pieces when cube is cut by planes Shortcut for Net Problems:

Use the 'Corner Method' - pick any corner in the net and trace which three faces meet at that corner. In the answer choices, the same three faces must meet at one corner. This eliminates wrong options quickly.

Worked ExampleSolve this step-by-step before moving on
1
Step 1

Identify which faces are opposite to each other in the net.

2
Step 2

Faces that are separated by exactly one face in between are opposite.

3
Step 3

In the net A-B-C-D, face A is opposite to face C (one face B in between).

4
Step 4

Face E is above B, so E is opposite to F (which is below C).

5
Step 5

Face B is opposite to face D.

6
Step 6

Since A is at bottom, its opposite face C will be at top. Answer: Face C For Dice Problems: Remember the standard dice pattern: 1 opposite 6, 2 opposite 5, 3 opposite 4. If you see faces 1, 2, 3 meeting at a corner, you know 6, 5, 4 meet at the opposite corner. Cube Cutting Formula: If a cube is cut by n planes parallel to faces: Total pieces = (n₁ + 1) × (n₂ + 1) × (n₃ + 1), where n₁, n₂, n₃ are cuts along length, breadth, and height.

Exam TrapsCommon mistakes students make — avoid these

Students often confuse adjacent faces with opposite faces. Remember - opposite faces never appear together in any single view of a cube. If two faces are visible together in a view, they cannot be opposite faces.

Key Points to Remember

  • A cube has 6 faces, 12 edges, and 8 vertices with each face being a perfect square
  • Opposite faces in a cube never share an edge or vertex with each other
  • In standard dice, opposite faces always sum to 7: (1,6), (2,5), (3,4)
  • Net to cube problems: faces separated by one face in between are opposite
  • Corner method: three faces meeting at any corner must be consistent in all views
  • Cube cutting formula: pieces = (cuts+1) along each dimension multiplied together
  • Adjacent faces share a common edge and can be seen together in cube views
  • If two faces appear together in any view, they cannot be opposite faces

Exam-Specific Tips

  • Standard dice opposite pairs sum to 7: 1-6, 2-5, 3-4
  • A cube has exactly 6 faces, 12 edges, and 8 vertices
  • Each vertex of a cube is formed by exactly 3 faces meeting together
  • Maximum 3 faces of a cube can be visible from any single viewpoint
  • In net problems, faces separated by exactly one face are opposite
  • Cube cutting by n parallel planes creates (n+1) pieces in that direction
  • Each face of a cube is adjacent to exactly 4 other faces
  • Each edge of a cube is shared by exactly 2 faces

60-Second Revision — Cube & Dice

  • Remember: Opposite faces never appear together in any cube view
  • Formula: Dice opposite pairs always sum to 7 (1-6, 2-5, 3-4)
  • Trick: Use corner method - trace three faces meeting at any corner
  • Pattern: In nets, faces with one face gap between them are opposite
  • Cutting: Total pieces = (cuts+1) multiplied for each dimension
  • Trap: Don't confuse adjacent faces with opposite faces
  • Quick check: Maximum 3 faces visible from any single angle
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