Dice and Cube – Logical Reasoning – MBA CUET PG – Notes & Practice Questions

Dice

Dice is a cube. In cube there are 6 faces.

1. There are 6 faces in the cube – ABCG, GCDE, DEFH, BCDH, AGEF and ABHF
2. Always four faces are adjacent to one face.
3. CDEG is the upper face of the cube.
4. ABHF is the bottom face of the cube.

Types of Dice

1. Simple Dice: In simple dice, sum of the opposite sides are not seven. It means sum of any two adjacent sides is equal to seven.

Here, 3 + 4 = 7, Sp it is simple dice

2. Standard Dice: In standard dice, the sum of two opposite sides is seven. In other words the sum of any two adjacent is not seven.

From the Figure;

1+2 = 3, 2+3 = 5, 3+1 = 4 does not have total seven. So, we can say that the opposite sides no. must be equal to be seven.

In Standard dice:

• 1 will be opposite to 6
• 2 will be opposite to 5
• 3 will be opposite to 4

Some Rules are:

1. When two different position of dice have different number then they are opposite to each other.

• 3 will be opposite to 4
• 1 will be opposite to 6
• 5 will be opposite to 2

2. If one side of given two dice is common in the same position then remaining are opposite to each other.

• 1 will be opposite to 3
• 5 will be opposite to 2
• 6 will be opposite to 4

If common sides are not in same position, then we rotate it clockwise or anti-clockwise to bring it into the same position.

Here, common side is 2, but not in the same position, so we rotate (b) in clockwise direction.

Now,

• 2 will be opposite to 1
• 4 will be opposite to 5
• 3 will be opposite to 6
• 3. If two sides of a given dice are common in the same position, then remaining is opposite to each other.

• 1 will be opposite to 2.

Expanded form of Dice:

• 6 will be opposite to 4
• 1 will be opposite to 3
• 2 will be opposite to 5

Cube

Cubes are 3-dimensional objects, they also follow same property as dice rather than numbering. Cube have all side same and cuboid have different length, height and breadth. They also have 8 vertex, 6 faces and 12 edges. In exam, these topics contain cutting of both cube and cuboid and counting the number of small cubes and cuboid.

If a cube is painted on all of its surfaces and divided into smaller cubes of equal size, then after separation number of smaller cubes so obtained will be calculated as:

\(n=\;\lbrack\frac{Side\;of\;larger\;Cube}{Side\;of\;smaller\;cube}\rbrack\)

(n number of smaller cubes along each edge)

• Total number of smaller cubes = n³
• 3 faces coloured = 8
• 2 faces coloured = 12 (n-2)
• 1 face coloured = 6(n – 2)²
• No face colured = (n – 2)³
• Total number of coloured cube = n³-(n-2)³
• Number of cubes with atleast 2 face coloured = 12(n – 2) + 8

Practice Questions

1. On the basis of two figures of dice. You have to tell what number will be there on the opposite side of number 2?

(a) 3

(b) 6 or 5

(c) 1

(d) Cannot be determined

2. On the basis of two figures of dice you have to tell what number will be there on the opposite side of number 1?

(a) 3

(b) 4

(c) 6

(d) 5

Direction (3-5): On the basis of two figures of dice. Answer the following questions.

3. Which number is at the opposite of number 2?

(a) 1

(b) 2

(c) 3

(d) 5

4. Which number is at the opposite of number 4?

(a) 1

(b) 6

(c) 3

(d) 4

5. Which number is at the opposite of number 5?

(a) 2

(b) 4

(c) 3

(d) 6