Logical Reasoning Questions for CLAT | QB Set 108 [Dice Rotation]

A standard six-faced die has the numbers 1, 2, 3, 4, 5 and 6 written on its six faces, with each number appearing exactly once. The die is placed on a table and rotated several times without changing the relative positions of the numbers on its faces. Three different views of the same die are observed.

In the first position, the number 1 is on the top, 2 is on the front, and 3 is on the right. The die is then rotated to obtain a second position, where 1 remains on the top, while 3 is on the front and 5 is on the right. In a third position, the die is rotated again so that 2 is on the top, 6 is on the front, and 3 is on the right.

While analysing the die, it must be remembered that faces sharing an edge are adjacent, while two faces that never appear together around the same corner may be opposite. The relative arrangement of all six faces remains unchanged during every rotation.

Questions

1. Which number is on the face opposite to 2?

A. 3
B. 4
C. 5
D. 6

2. Which number is on the face opposite to 1?

A. 6
B. 4
C. 5
D. 2

3. Which number is on the face opposite to 3?

A. 2
B. 4
C. 5
D. 6

4. If the face numbered 1 is placed on the top, which number must be on the bottom?

A. 5
B. 6
C. 3
D. 2

5. Which of the following pairs of faces cannot be adjacent to each other?

A. 1 and 3
B. 2 and 3
C. 3 and 5
D. 2 and 5

Answers and Detailed Explanations

1. Correct Answer: C. 5

Compare the first and second positions:

• First position: 1, 2 and 3 are visible.
• Second position: 1, 3 and 5 are visible.

The numbers 1 and 3 are common in both positions. When two faces remain common in two views of the same die, the other two faces—here 2 and 5—are opposite to each other.

Therefore:

2 ↔ 5

Hence, the number opposite to 2 is 5.

2. Correct Answer: A. 6

Compare the first and third positions:

• First position: 1, 2 and 3
• Third position: 2, 6 and 3

The common faces are 2 and 3. The remaining faces are 1 and 6.

Therefore, these two faces are opposite:

1 ↔ 6

Hence, if 1 is on one face, 6 must be on the opposite face.

Correct answer: 6.

3. Correct Answer: B. 4

From the previous observations, two pairs of opposite faces have already been identified:

• 1 ↔ 6
• 2 ↔ 5

A die has exactly three pairs of opposite faces. The only numbers remaining are 3 and 4.

Therefore:

3 ↔ 4

Hence, the face opposite to 3 is 4.

4. Correct Answer: B. 6

From the comparison of the first and third positions, it has already been established that:

1 and 6 are opposite faces.

Opposite faces always remain opposite regardless of how the die is rotated.

Therefore, whenever 1 is on the top, its opposite face, 6, must automatically be on the bottom.

Hence, the correct answer is 6.

5. Correct Answer: D. 2 and 5

From the first two positions:

• First: 1, 2, 3
• Second: 1, 3, 5

Since 1 and 3 are common, the remaining faces 2 and 5 are opposite.

Opposite faces of a die can never share an edge. Therefore, they can never be adjacent to each other.

The other given pairs can be adjacent:

• 1 and 3 are visible together.
• 2 and 3 are visible together.
• 3 and 5 are visible together.

Therefore, the pair that cannot be adjacent is:

2 and 5.