A) 44

B) 32

C) 45

D) 53

**Answer:A**

**Explanation:**

x = Cube root of 125 = 5. More than one colour means two or more colours. So, total number of cubes whose two faces are varnished = (x - 2) × number of edges = (5 - 2) × 12 = 36. The three varnished cubes have the number of corners = 8. So total number of required cubes = 36 + 8 = 44. Hence option A is the answer.

A) 64

B) 20

C) 55

D) 53

**Answer:**B

**Explanation:**x = Cube root of 27 = 3. More than one colour means two or more colours. So total number of cubes whose two faces are varnished = (x - 2) × number of edges = (3 - 2) × 12 = 12. The three varnished cubes have the number of corners = 8. So total number of required cubes = 12 + 8 = 20. Hence option B is the answer.

A) 78

B) 32

C) 45

D) 56

**Answer:**D

**Explanation:**x = Cube root of 216 = 6. More than one colour means two or more colours. So total number of cubes whose two faces are varnished is = (x - 2) × number of edges = (6 - 2) × 12 = 48. The three varnished cubes have the number of corners = 8. So total number of required cubes = 48 + 8 = 56. Hence option D is the answer.

How many tiny cubes will be formed having all the three colours?

A) 7

B) 9

C) 10

D) 8

**Answer:**D

**Explanation:**The number of corners is 8 hence answer for tiny cubes which have all the three colours are related to 8 corners. Hence optoption D is correct.

A) 18

B) 20

C) 16

D) 24

**Answer:**B

**Explanation:**Green and white varnished faces are joined by 4 edges, so number of cubes having green and white varnished faces = (x - 2) × number of edges = (5 - 2) × 4 = 3 × 4 = 12. Here X = Cube root of 125 = 5. Number of cubes having three faces varnished will also have green and white colours = 8. So total cubes = 12 + 8 = 20.

A) 7

B) 9

C) 10

D) 8

**Answer:**D

**Explanation:**The number of corners is 8 hence answer for tiny cubes which have all the three colours are related to 8 corners. Hence option D.

A) 12

B) 20

C) 16

D) 24

**Answer:**A

**Explanation:**Black and yellow varnished faces are joined by 4 edges, so number of cubes having black and yellow varnished faces = (3 - 2) × no. of edges = (3 - 2) × 4 = 1 × 4 = 4. Here X = Cube root of 27 = 3. Number of cubes having three faces varnished will also have black and yellow colours = 8. So total cubes = 4 + 8 = 12

A) 1

B) 2

C) 3

D) 4

**Answer:**A

**Explanation:**Here x = 12/4 = 3. Such cubes can be found by following method. X – 2 = 3 - 2 = 1 and 1 × 1 × 1 = 1. So number of cubes will be formed such that each face of these cubes is surrounded by other cubes is only one.

A) 8

B) 19

C) 17

D) 32

**Answer:**A

**Explanation:**Here x = 24/6 = 4 cm. So x - 2 = 4 - 2 = 2. Finally: 2 × 2 × 2 = 8. Hence answer is option A.

A) 26

B) 25

C) 27

D) 40

**Answer:**C

**Explanation:**Here x = 20/4 = 5. Such cubes can be found by following method. X – 2 = 5 -2 = 3 and 3 × 3 × 3 = 27. So number of cubes will be formed such that each face of these cubes is surrounded by other cubes is 27.