Dice and Cube Aptitude MCQ Questions with Answers Set 02

Multiple Choice Questions (MCQs) for General Aptitude Arithmetic Ability: Dice and Cube

Access targeted multiple-choice questions for Dice and Cube designed to align with the latest Aptitude academic syllabus for General Aptitude Arithmetic Ability. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

Practice Dice and Cube MCQs for General Aptitude Arithmetic Ability

Access the complete set of multiple-choice questions for Dice and Cube below. This focused format allows students to isolate specific topics for thorough review and uninterrupted practice alongside official Aptitude textbooks.

Multiple Choice Questions

Question 1: Directions: A cube of 10" dimensions is coloured yellow, brown, and orange on the three sets of opposite faces. The cube is then cut into smaller cubes of 2" dimensions.
How many smaller cubes are painted only on two of their faces, one with brown and the other with orange?
(a) 12
(b) 16
(c) 18
(d) 30
Show Answer & Explanation

Answer: (a) 12

Explanation:
1. Brown and orange meet along 4 edges.
2. On each edge, leave out the 2 corner cubes (they have three colours): 5 - 2 = 3.
3. 4 x 3 = 12.

Teacher's Note:
1. For an n x n x n painted cube: 3 faces = 8 corners, 2 faces = 12(n - 2), 1 face = 6(n - 2)2, none = (n - 2)3.
2. When only some faces are painted, count layer by layer instead of using the standard formulas.

Question 2: Directions: A solid cube is painted red on two adjacent faces, green on the faces opposite to the faces painted red, and black on the remaining faces. The cube is then cut into two parts through the centre without touching the black face. One part is cut into 32 smaller identical cubes and the other part is cut into four smaller cubes of equal size. Answer the question by considering the smaller cubes of both the sizes.
How many smaller cubes have black colour face(s)?
(a) 10
(b) 12
(c) 20
(d) 32
Show Answer & Explanation

Answer: (c) 20

Explanation:
1. Each half is a slab with one black face. Part A: 32 cubes = 4 x 4 x 2 (two layers). Part B: 4 cubes = 2 x 2 x 1 (one layer).
2. In Part A only the layer touching the black face is black: 16 cubes.
3. In Part B all 4 cubes touch the black face. Total = 16 + 4 = 20.

Teacher's Note:
1. For an n x n x n painted cube: 3 faces = 8 corners, 2 faces = 12(n - 2), 1 face = 6(n - 2)2, none = (n - 2)3.
2. When only some faces are painted, count layer by layer instead of using the standard formulas.

Question 3: Directions: A solid cube is painted red on two adjacent faces, green on the faces opposite to the faces painted red, and black on the remaining faces. The cube is then cut into two parts through the centre without touching the black face. One part is cut into 32 smaller identical cubes and the other part is cut into four smaller cubes of equal size. Answer the question by considering the smaller cubes of both the sizes.
How many smaller cubes have only red colour face(s)?
(a) 6
(b) 12
(c) 8
(d) 5
Show Answer & Explanation

Answer: (d) 5

Explanation:
1. Each half is a slab with one black face. Part A: 32 cubes = 4 x 4 x 2 (two layers). Part B: 4 cubes = 2 x 2 x 1 (one layer).
2. Only the Part A layer next to the cut has no black. In that 4 x 4 layer, cubes on the two red sides but not on a green side: 3 along one red side + 2 more along the other = 5.
3. All Part B cubes have black, so the answer is 5.

Teacher's Note:
1. For an n x n x n painted cube: 3 faces = 8 corners, 2 faces = 12(n - 2), 1 face = 6(n - 2)2, none = (n - 2)3.
2. When only some faces are painted, count layer by layer instead of using the standard formulas.

Question 4: Directions: A solid cube is painted red on two adjacent faces, green on the faces opposite to the faces painted red, and black on the remaining faces. The cube is then cut into two parts through the centre without touching the black face. One part is cut into 32 smaller identical cubes and the other part is cut into four smaller cubes of equal size. Answer the question by considering the smaller cubes of both the sizes.
How many smaller cubes have none of their faces painted?
(a) 2
(b) 8
(c) 6
(d) 4
Show Answer & Explanation

Answer: (d) 4

Explanation:
1. Each half is a slab with one black face. Part A: 32 cubes = 4 x 4 x 2 (two layers). Part B: 4 cubes = 2 x 2 x 1 (one layer).
2. Unpainted cubes are in the Part A layer next to the cut and away from all four side faces: the inner 2 x 2 = 4.
3. Every Part B cube has a black face. Answer 4.

Teacher's Note:
1. For an n x n x n painted cube: 3 faces = 8 corners, 2 faces = 12(n - 2), 1 face = 6(n - 2)2, none = (n - 2)3.
2. When only some faces are painted, count layer by layer instead of using the standard formulas.

Question 5: Directions: A solid cube is painted red on two adjacent faces, green on the faces opposite to the faces painted red, and black on the remaining faces. The cube is then cut into two parts through the centre without touching the black face. One part is cut into 32 smaller identical cubes and the other part is cut into four smaller cubes of equal size. Answer the question by considering the smaller cubes of both the sizes.
How many smaller cubes have only two of their faces painted?
(a) 8
(b) 12
(c) 24
(d) 16
Show Answer & Explanation

Answer: (b) 12

Explanation:
1. Each half is a slab with one black face. Part A: 32 cubes = 4 x 4 x 2 (two layers). Part B: 4 cubes = 2 x 2 x 1 (one layer).
2. Part A black layer: non-corner edge cubes have black + one side colour: 4 sides x 2 = 8. Part A cut layer: 4 corner cubes have two side colours = 4.
3. Part B cubes each have black plus two side faces (3 faces), so none. Total = 8 + 4 = 12.

Teacher's Note:
1. For an n x n x n painted cube: 3 faces = 8 corners, 2 faces = 12(n - 2), 1 face = 6(n - 2)2, none = (n - 2)3.
2. When only some faces are painted, count layer by layer instead of using the standard formulas.

Question 6: Directions: A cube of dimensions 10" is painted red, blue, and green, respectively, on the three sets of opposite faces. The cube is then cut into 104 smaller cubes, some with 4" dimensions and some with 2" dimensions. Two of the cubes of dimensions 4" have only one of their faces painted red. The remaining cubes of dimensions 4" have only one of their faces painted green. The question is based on the smaller cubes of dimensions 4" and 2".
How many smaller cubes have three of their faces painted red, blue, and green?
(a) 4
(b) 6
(c) 10
(d) 8
Show Answer & Explanation

Answer: (d) 8

Explanation:
1. If x cubes are 4" and the rest 2": 64x + 8(104 - x) = 1000, so x = 3. So 3 cubes of 4" and 101 cubes of 2".
2. Each 4" cube has only one painted face, so all 8 corners are 2" cubes.
3. Three-coloured cubes = 8 corners.

Teacher's Note:
1. When a cube is cut into cubes of different sizes, equate total volumes first.
2. Check that the pieces can actually fit: larger cubes must occupy whole blocks of the original cube.

Question 7: Directions: A cube of dimensions 10" is painted red, blue, and green, respectively, on the three sets of opposite faces. The cube is then cut into 104 smaller cubes, some with 4" dimensions and some with 2" dimensions. Two of the cubes of dimensions 4" have only one of their faces painted red. The remaining cubes of dimensions 4" have only one of their faces painted green. The question is based on the smaller cubes of dimensions 4" and 2".
How many smaller cubes of 4" dimensions have two of their faces coloured red and blue?
(a) 1
(b) 0
(c) 4
(d) 3
Show Answer & Explanation

Answer: (b) 0

Explanation:
1. If x cubes are 4" and the rest 2": 64x + 8(104 - x) = 1000, so x = 3. So 3 cubes of 4" and 101 cubes of 2".
2. Every 4" cube has exactly one painted face (two red, one green).
3. So none has red and blue together: 0.

Teacher's Note:
1. When a cube is cut into cubes of different sizes, equate total volumes first.
2. Check that the pieces can actually fit: larger cubes must occupy whole blocks of the original cube.

Question 8: Directions: A cube of dimensions 10" is painted red, blue, and green, respectively, on the three sets of opposite faces. The cube is then cut into 104 smaller cubes, some with 4" dimensions and some with 2" dimensions. Two of the cubes of dimensions 4" have only one of their faces painted red. The remaining cubes of dimensions 4" have only one of their faces painted green. The question is based on the smaller cubes of dimensions 4" and 2".
How many smaller cubes have at least two of their faces coloured?
(a) 24
(b) 36
(c) 44
(d) 32
Show Answer & Explanation

Answer: (c) 44

Explanation:
1. If x cubes are 4" and the rest 2": 64x + 8(104 - x) = 1000, so x = 3. So 3 cubes of 4" and 101 cubes of 2".
2. Cubes with two or more coloured faces lie along the 12 edges; the 4" cubes are not on edges.
3. Along an edge there are 10/2 = 5 cubes: 12 x 3 middle cubes + 8 corners = 36 + 8 = 44.

Teacher's Note:
1. For an n x n x n painted cube: 3 faces = 8 corners, 2 faces = 12(n - 2), 1 face = 6(n - 2)2, none = (n - 2)3.
2. When only some faces are painted, count layer by layer instead of using the standard formulas.

Question 9: Directions: A cube of dimensions 10" is painted red, blue, and green, respectively, on the three sets of opposite faces. The cube is then cut into 104 smaller cubes, some with 4" dimensions and some with 2" dimensions. Two of the cubes of dimensions 4" have only one of their faces painted red. The remaining cubes of dimensions 4" have only one of their faces painted green. The question is based on the smaller cubes of dimensions 4" and 2".
How many smaller cubes have at least one of their faces painted blue?
(a) 36
(b) 48
(c) 42
(d) 50
Show Answer & Explanation

Answer: (d) 50

Explanation:
1. If x cubes are 4" and the rest 2": 64x + 8(104 - x) = 1000, so x = 3. So 3 cubes of 4" and 101 cubes of 2".
2. No 4" cube touches a blue face, so each blue face is covered by 5 x 5 = 25 small cubes.
3. The two blue faces are opposite: 25 + 25 = 50.

Teacher's Note:
1. For an n x n x n painted cube: 3 faces = 8 corners, 2 faces = 12(n - 2), 1 face = 6(n - 2)2, none = (n - 2)3.
2. When only some faces are painted, count layer by layer instead of using the standard formulas.

Question 10: Directions: A cube of dimensions 10" is painted red, blue, and green, respectively, on the three sets of opposite faces. The cube is then cut into 104 smaller cubes, some with 4" dimensions and some with 2" dimensions. Two of the cubes of dimensions 4" have only one of their faces painted red. The remaining cubes of dimensions 4" have only one of their faces painted green. The question is based on the smaller cubes of dimensions 4" and 2".
How many smaller cubes have none of their faces coloured?
(a) 27
(b) 15
(c) 18
(d) 12
Show Answer & Explanation

Answer: (b) 15

Explanation:
1. If x cubes are 4" and the rest 2": 64x + 8(104 - x) = 1000, so x = 3. So 3 cubes of 4" and 101 cubes of 2".
2. Without the 4" cubes, the hidden core would be 3 x 3 x 3 = 27 small cubes.
3. Each 4" cube sits on a face and takes up 2 x 2 x 1 = 4 of those core positions: 27 - 3 x 4 = 15.

Teacher's Note:
1. When a cube is cut into cubes of different sizes, equate total volumes first.
2. Check that the pieces can actually fit: larger cubes must occupy whole blocks of the original cube.

Question 11: Directions: A solid cube of size 4" is cut into smaller cubes of ½", 1", and 2" dimensions. The question is based on the smaller cubes.
If 1" and 2" cubes are one each in number, what will be the total number of ½" cubes?
(a) 510
(b) 440
(c) 424
(d) 460
Show Answer & Explanation

Answer: (b) 440

Explanation:
1. Volumes: big cube 64, a 2" cube 8, a 1" cube 1, a ½" cube 1/8 cubic inch.
2. Volume left = 64 - 8 - 1 = 55.
3. Number of ½" cubes = 55 x 8 = 440.

Teacher's Note:
1. When a cube is cut into cubes of different sizes, equate total volumes first.
2. Check that the pieces can actually fit: larger cubes must occupy whole blocks of the original cube.

Question 12: Directions: A solid cube of size 4" is cut into smaller cubes of ½", 1", and 2" dimensions. The question is based on the smaller cubes.
If the numbers of 1" and 2" cubes are multiples of 7, what will be the total number of smaller cubes (of all sizes together)?
(a) 21
(b) 8
(c) 20
(d) 22
Show Answer & Explanation

Answer: (d) 22

Explanation:
1. Volumes: big cube 64, a 2" cube 8, a 1" cube 1, a ½" cube 1/8 cubic inch.
2. Only 7 cubes of 2" (56) and 7 cubes of 1" (7) fit: 56 + 7 = 63.
3. Volume left = 1, giving 8 cubes of ½". Total = 7 + 7 + 8 = 22.

Teacher's Note:
1. When a cube is cut into cubes of different sizes, equate total volumes first.
2. Check that the pieces can actually fit: larger cubes must occupy whole blocks of the original cube.

Question 13: Directions: A solid cube of size 4" is cut into smaller cubes of ½", 1", and 2" dimensions. The question is based on the smaller cubes.
If we get maximum possible number of 2" cubes, then how many ½" cubes will be obtained (along with the maximum number of 2" cubes)?
(a) 0
(b) 2
(c) 4
(d) 8
Show Answer & Explanation

Answer: (a) 0

Explanation:
1. Volumes: big cube 64, a 2" cube 8, a 1" cube 1, a ½" cube 1/8 cubic inch.
2. The maximum number of 2" cubes is 64/8 = 8, which uses the whole cube.
3. Nothing is left for ½" cubes: 0.

Teacher's Note:
1. When a cube is cut into cubes of different sizes, equate total volumes first.
2. Check that the pieces can actually fit: larger cubes must occupy whole blocks of the original cube.

Question 14: Directions: A solid cube of size 4" is cut into smaller cubes of ½", 1", and 2" dimensions. The question is based on the smaller cubes.
If the numbers of 1" and 2" cubes are multiples of 5, how many ½" cubes can be obtained?
(a) 36
(b) 80
(c) 112
(d) 120
Show Answer & Explanation

Answer: (c) 112

Explanation:
1. Volumes: big cube 64, a 2" cube 8, a 1" cube 1, a ½" cube 1/8 cubic inch.
2. 2" cubes can only be 5 (10 would need 80 > 64), using 40; 24 cubic inches remain.
3. With 10 cubes of 1", 14 cubic inches remain = 14 x 8 = 112 ½" cubes (5 or 15 cubes of 1" give 152 or 72, which are not offered).

Teacher's Note:
1. When a cube is cut into cubes of different sizes, equate total volumes first.
2. Check that the pieces can actually fit: larger cubes must occupy whole blocks of the original cube.

Question 15: Directions: The six faces of a cube are painted in such a manner that no two adjacent faces have the same colour. The three colours used are red, white, and black. The cube is then cut into 36 smaller cubes in such a manner that 32 cubes are of one size and the rest are of bigger size, and each of the bigger cubes has no red-coloured face. Answer the question by considering the smaller cubes of both the sizes.
How many smaller cubes have two or more of their faces painted?
(a) 32
(b) 36
(c) 28
(d) 16
Show Answer & Explanation

Answer: (c) 28

Explanation:
1. Opposite faces share a colour. Volume: 32 x 1 + 4 x 8 = 64, so the cube is 4 x 4 x 4 with four 2 x 2 x 2 cubes.
2. The big cubes avoid both red faces, so they fill the middle 2-unit slab between the red faces; the 32 small cubes form the two 4 x 4 layers on the red faces.
3. Each red layer: 4 corners (3 faces) + 8 edge cubes (2 faces) = 12, so 24 in both. Each big cube touches 2 faces (white, black): 4. Total 28.

Teacher's Note:
1. For an n x n x n painted cube: 3 faces = 8 corners, 2 faces = 12(n - 2), 1 face = 6(n - 2)2, none = (n - 2)3.
2. When only some faces are painted, count layer by layer instead of using the standard formulas.

Question 16: Directions: The six faces of a cube are painted in such a manner that no two adjacent faces have the same colour. The three colours used are red, white, and black. The cube is then cut into 36 smaller cubes in such a manner that 32 cubes are of one size and the rest are of bigger size, and each of the bigger cubes has no red-coloured face. Answer the question by considering the smaller cubes of both the sizes.
How many smaller cubes have a red-coloured face?
(a) 20
(b) 32
(c) 16
(d) 0
Show Answer & Explanation

Answer: (b) 32

Explanation:
1. Opposite faces share a colour. Volume: 32 x 1 + 4 x 8 = 64, so the cube is 4 x 4 x 4 with four 2 x 2 x 2 cubes.
2. The big cubes avoid both red faces, so they fill the middle 2-unit slab between the red faces; the 32 small cubes form the two 4 x 4 layers on the red faces.
3. Every small cube lies in a red layer, and no big cube is red: 32.

Teacher's Note:
1. For an n x n x n painted cube: 3 faces = 8 corners, 2 faces = 12(n - 2), 1 face = 6(n - 2)2, none = (n - 2)3.
2. When only some faces are painted, count layer by layer instead of using the standard formulas.

Question 17: Directions: The six faces of a cube are painted in such a manner that no two adjacent faces have the same colour. The three colours used are red, white, and black. The cube is then cut into 36 smaller cubes in such a manner that 32 cubes are of one size and the rest are of bigger size, and each of the bigger cubes has no red-coloured face. Answer the question by considering the smaller cubes of both the sizes.
How many smaller cubes have three of their faces painted?
(a) 16
(b) 32
(c) 20
(d) 8
Show Answer & Explanation

Answer: (d) 8

Explanation:
1. Opposite faces share a colour. Volume: 32 x 1 + 4 x 8 = 64, so the cube is 4 x 4 x 4 with four 2 x 2 x 2 cubes.
2. The big cubes avoid both red faces, so they fill the middle 2-unit slab between the red faces; the 32 small cubes form the two 4 x 4 layers on the red faces.
3. Only the 8 corners of the big cube have three painted faces, and they are all small cubes.

Teacher's Note:
1. For an n x n x n painted cube: 3 faces = 8 corners, 2 faces = 12(n - 2), 1 face = 6(n - 2)2, none = (n - 2)3.
2. When only some faces are painted, count layer by layer instead of using the standard formulas.

Question 18: Observe the dots on the dice (one to six dots) in the following figures. How many dots are contained on the face opposite to the face containing four dots?

(a) 2
(b) 3
(c) 5
(d) 6
Show Answer & Explanation

Answer: (a) 2

Explanation:
1. Both positions show 5 on the right side, so the die has only been rolled about the 5-axis.
2. First position: top 2, front 1. Second position: top 1, front 4. The die rolled so the front (1) came to the top.
3. In that roll the old top (2) goes to the back and the old bottom comes to the front, so 4 was the bottom - opposite 2.

Teacher's Note:
1. When a face stays in the same place in two positions, the die has only been turned about that face's axis.
2. Write the four faces around a common face in cyclic order; faces two steps apart in that ring are opposite.

Question 19: Two positions of a dice are shown below. How many points will be on the top when 2 points are at the bottom?

(a) 6
(b) 5
(c) 4
(d) 1
Show Answer & Explanation

Answer: (d) 1

Explanation:
1. 3 is on the right in both positions, so the die has only been turned about the 3-axis.
2. First: top 2, front 6. Second: top 1, front 5. With 2 and 6 both gone from view, a half turn has taken place: 1 is opposite 2 and 5 is opposite 6.
3. So when 2 is at the bottom, 1 is on top.

Teacher's Note:
1. When a face stays in the same place in two positions, the die has only been turned about that face's axis.
2. Write the four faces around a common face in cyclic order; faces two steps apart in that ring are opposite.

Question 20: How many points will be on the face opposite to the face which contains 2 points?

(a) 1
(b) 5
(c) 4
(d) 6
Show Answer & Explanation

Answer: (d) 6

Explanation:
1. Dice 1 and 3 both have 2 on top; round 2 the faces run 1, 3, 5 in order, so 1 is opposite 5.
2. Dice 3 and 4 both have 1 in front; the ring round 1 must hold 2, 3, 4, 6 (5 is opposite 1). Dice 3 gives 2 then 3; dice 4 gives 6 then 4.
3. The only cyclic order fitting both is 2, 3, 6, 4, so 2 is opposite 6 (and 3 is opposite 4).

Teacher's Note:
1. When a face stays in the same place in two positions, the die has only been turned about that face's axis.
2. Write the four faces around a common face in cyclic order; faces two steps apart in that ring are opposite.

Question 21: Directions: Four positions of the same dice have been shown. You have to see these figures and select the number opposite to the number as asked.
Which number is on the opposite surface of number 3?
563133246116(i)(ii)(iii)(iv)
(a) 4
(b) 6
(c) 5
(d) 1
Show Answer & Explanation

Answer: (a) 4

Explanation:
1. Numbers seen with 3: 5, 6 (i); 6, 1 (ii); 2, 1 (iii).
2. So 1, 2, 5 and 6 are adjacent to 3; the remaining 4 is opposite 3.

Teacher's Note:
1. Two faces that appear together in any single position can never be opposite each other.
2. Collect every number seen next to the asked face; the one number never seen with it is its opposite.

Question 22: Directions: Four positions of the same dice have been shown. You have to see these figures and select the number opposite to the number as asked.
Which number is opposite to number 1?
415525165264(i)(ii)(iii)(iv)
(a) 4
(b) 6
(c) 2
(d) 3
Show Answer & Explanation

Answer: (a) 4

Explanation:
1. 5 is the front face in both (iii) and (iv), so the die has only been turned about the 5-axis.
2. Going round 5 from top to right: (iii) gives 1 then 6, (iv) gives 6 then 4. So the ring round 5 is 1, 6, 4, ...
3. In that ring 1 and 4 are two steps apart, so 4 is opposite 1.

Teacher's Note:
1. When a face stays in the same place in two positions, the die has only been turned about that face's axis.
2. Write the four faces around a common face in cyclic order; faces two steps apart in that ring are opposite.

Question 23: Directions: Four positions of the same dice have been shown. You have to see these figures and select the number opposite to the number as asked.
Which number is opposite to number 5?
562532564143(i)(ii)(iii)(iv)
(a) 6
(b) 5
(c) 1
(d) 3
Show Answer & Explanation

Answer: (c) 1

Explanation:
1. Numbers seen with 5: 3, 4 (i); 2, 4 (iii); 6, 3 (iv).
2. So 2, 3, 4 and 6 are adjacent to 5; the remaining 1 is opposite 5.

Teacher's Note:
1. Two faces that appear together in any single position can never be opposite each other.
2. Collect every number seen next to the asked face; the one number never seen with it is its opposite.

Question 24: Directions: Four positions of the same dice have been shown. You have to see these figures and select the number opposite to the number as asked.
Which number is opposite to number 5?
143426513122(i)(ii)(iii)(iv)
(a) 4
(b) 6
(c) 1
(d) 3
Show Answer & Explanation

Answer: (c) 1

Explanation:
1. Numbers seen with 1: 2, 3 (i); 6, 4 (ii); 4, 2 (iv). So 2, 3, 4 and 6 are adjacent to 1.
2. Hence 5 is opposite 1, i.e. the number opposite 5 is 1.
3. 3 cannot be the answer because 3 and 5 appear together in (iii).

Teacher's Note:
1. Two faces that appear together in any single position can never be opposite each other.
2. Collect every number seen next to the asked face; the one number never seen with it is its opposite.

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Multiple Choice Questions (MCQs) for General Aptitude Arithmetic Ability Dice and Cube

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