MAT - DICE PROBLEMS - MCQs -11

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🎲 Dice Reasoning – NMMS & Talent Exam MCQ Quiz

10 mathematically valid questions • Large SVG dice diagrams • Answer + step-by-step explanation

1. In the two positions of the same die, faces 1 and 2 are common. Which number is opposite to 3?

Position A

Position B

2 4 5 6

Correct Answer: Option B — 4

Step 1: The two views have the same adjacent pair, 1 and 2.

Step 2: In Position A, 3 touches the edge formed by 1 and 2.

Step 3: In Position B, 4 touches the same edge formed by 1 and 2.

Step 4: The two faces occupying the opposite sides of the same edge are opposite faces.

Shortcut: Same common edge + two different third faces → those third faces are opposite.

2. In the two valid positions below, faces 1 and 5 are common. Which face is opposite to 4?

Position A

Position B

1 3 2 6

Correct Answer: Option C — 2

Step 1: Faces 1 and 5 form the same common edge in both positions.

Step 2: Face 4 is shown beside that common edge in Position A.

Step 3: Face 2 is shown beside the same common edge in Position B.

Step 4: Therefore, 4 and 2 are opposite faces.

Shortcut: Two views with the same two faces on the same edge reveal the third faces as an opposite pair.

3. Faces 1 and 5 are common in the two positions. Which number is opposite to 3?

Position A

Position B

1 5 2 4

Correct Answer: Option D — 4

Step 1: The common edge is formed by faces 1 and 5.

Step 2: Face 3 occupies one side of this edge in Position A.

Step 3: Face 4 occupies the other side in Position B.

Step 4: Hence, 3 and 4 are opposite faces.

Shortcut: Common edge method is faster than trying to imagine every rotation.

4. A standard die has faces numbered 1 to 6. Which number is directly opposite to 6?

Standard Die

1 2 3 5

Correct Answer: Option A — 1

Step 1: For a standard die, opposite faces are paired as 1–6, 2–5 and 3–4.

Step 2: Therefore, the face opposite 6 is 1.

Shortcut: Standard die rule → opposite faces always add to 7.

5. How many faces are directly adjacent to any one face of a cube?

Cube Geometry

2 3 5 4

Correct Answer: Option D — 4

Step 1: A cube has 6 faces.

Step 2: One face is directly opposite the selected face.

Step 3: The remaining 4 faces share an edge with the selected face.

Step 4: Therefore, every face has exactly 4 adjacent faces.

Shortcut: Cube → 1 opposite + 4 adjacent = 5 other faces.

6. What is the sum of the numbers on a pair of opposite faces of a standard die?

Opposite-Pair Rule

6 7 8 9

Correct Answer: Option B — 7

Step 1: Standard opposite pairs are 1–6, 2–5 and 3–4.

Step 2: Each pair gives 7.

Step 3: Thus the sum of any opposite pair is 7.

Shortcut: Opposite faces of a standard die → 7.

7. In the displayed standard-die position, what is the sum of the three visible faces?

Top = 1, Front = 2, Right = 3

5 7 6 9

Correct Answer: Option C — 6

Step 1: Read the three visible faces: top = 1, front = 2, right = 3.

Step 2: Add them: 1 + 2 + 3 = 6.

Shortcut: Read only the three visible faces; do not include hidden faces.

8. A die is shown with 1 on top and 2 at the front. If the die is rolled forward once, which number comes to the top? (The front face moves downward.)

Before Rolling

Roll Forward ↓

1 2 3 5

Correct Answer: Option D — 5

Step 1: In the initial position, top = 1 and front = 2.

Step 2: Rolling forward makes the front face (2) move to the bottom.

Step 3: The back face moves to the top.

Step 4: In a standard die, the face opposite 2 is 5.

Therefore, 5 comes to the top.

Shortcut: Forward roll → back becomes top; front becomes bottom.

9. A standard die is shown with 2 on top, 6 at the front and 3 on the right. Which number is on the bottom?

Given Position

1 3 5 4

Correct Answer: Option C — 5

Step 1: The top face is 2.

Step 2: The bottom face is directly opposite the top face.

Step 3: For a standard die, 2 is opposite 5.

Therefore, the bottom face is 5.

Shortcut: Top ↔ Bottom are opposite faces.

10. A standard die has 1 on top, 2 at the front and 3 on the right. Which pair gives the three pairs of opposite faces?

Standard Die

(1,6), (2,5), (3,4) (1,5), (2,6), (3,4) (1,4), (2,5), (3,6) (1,2), (3,4), (5,6)

Correct Answer: Option A — (1,6), (2,5), (3,4)

Step 1: A standard die has opposite pairs whose sums are 7.

Step 2: 1 + 6 = 7.

Step 3: 2 + 5 = 7.

Step 4: 3 + 4 = 7.

Hence these are the three opposite pairs.

Shortcut: Pair every number n with 7 − n.