Dice and Cube Aptitude MCQ Questions with Answers Set 01

Download Aptitude MCQs for General Aptitude Arithmetic Ability: Dice and Cube

Explore reliable objective questions for Dice and Cube tailored for General Aptitude learners. Utilizing these Arithmetic Ability multiple-choice formats ensures thorough preparation and strengthens problem-solving speed for upcoming school assessments.

Chapter-wise Objective Questions: Dice and Cube

View or download the dedicated Dice and Cube MCQ resource below. Practicing these 50 objective questions regularly builds familiarity with standard exam patterns and helps secure higher marks in final Arithmetic Ability evaluations.

Multiple Choice Questions

Question 1: A dice has been thrown four times and produces the following results. Which number will appear opposite to the number 3?
325365321416(i)(ii)(iii)(iv)
(a) 4
(b) 5
(c) 6
(d) 1
Show Answer & Explanation

Answer: (a) 4

Explanation:
1. Faces seen with 3: 6 and 1 in (i), 5 and 1 in (iii), 2 and 6 in (iv).
2. So 1, 2, 5 and 6 are all adjacent to 3 and cannot be opposite it.
3. The only number left is 4, so 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 2: The figures given below show two different positions of a dice. Which number will appear opposite to number 2?
344526(i)(ii)
(a) 3
(b) 4
(c) 5
(d) 6
Show Answer & Explanation

Answer: (c) 5

Explanation:
1. 4 is common to both positions, so put 4 in the centre of an unfolded net.
2. From (i), going anticlockwise round 4: 3 then 2. From (ii): 6 then 5. Number 1 takes the last square.
3. Folding this net gives the pairs 3-6, 2-5 and 4-1, so 5 is 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 3: From the following figures of a dice, find which number will come in place of '?'.
21645132?(i)(ii)(iii)
(a) 4
(b) 5
(c) 2
(d) 3
Show Answer & Explanation

Answer: (d) 3

Explanation:
1. 2 is seen with 4, 3 (in i) and with 5, 1 (in ii), so 2 is opposite 6; also 1 is opposite 4 and 3 is opposite 5.
2. Start from (ii): top 5, front 1, right 2. Roll it forward so 1 comes to the top; the front becomes 3 (opposite of 5) and the right stays 2, so 6 is on the left.
3. Now turn the die so 6 comes to the front: the old front 3 moves to the right. So '?' = 3.

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 4: A die is thrown four times and its four different positions are given below. Find the number on the face opposite the face showing 2.
(i)(ii)(iii)(iv)
(a) 3
(b) 4
(c) 5
(d) 6
Show Answer & Explanation

Answer: (c) 5

Explanation:
1. 2 appears in (i), (ii) and (iv).
2. Numbers seen with 2: 3 and 4 in (i), 1 and 3 in (ii), 6 and 4 in (iv), i.e. 1, 3, 4 and 6.
3. The only number never adjacent to 2 is 5, so 5 is opposite 2.

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 5: Shown below are four different positions of the same dice. Find the number on the face opposite the face showing 6.
(i)(ii)(iii)(iv)
(a) 1
(b) 2
(c) 4
(d) 5
Show Answer & Explanation

Answer: (c) 4

Explanation:
1. 6 is seen with 5, 3 and 1, so its opposite is 2 or 4.
2. 3 appears in (i), (ii) and (iii) next to 5, 6, 1 and 4, so 2 is opposite 3.
3. Since 2 is opposite 3, it cannot be opposite 6; hence 4 is opposite 6.

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 6: A wooden cube is painted black on four adjoining faces and green on two opposite faces, that is, top and bottom. It is then cut into 27 smaller, identical cubes.
How many smaller cubes have only one of their faces painted black?

(a) 1
(b) 2
(c) 3
(d) 4
Show Answer & Explanation

Answer: (d) 4

Explanation:
1. Look at the three horizontal layers. Top and bottom layer cubes all touch a green face.
2. In the middle layer, the four edge-middle cubes have exactly one face painted (black); the corners have two black faces and the centre has none.
3. So 4 cubes have only one face painted, and it is black.

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 7: A wooden cube is painted black on four adjoining faces and green on two opposite faces, that is, top and bottom. It is then cut into 27 smaller, identical cubes.
How many smaller cubes have only one of their faces painted green?

(a) 1
(b) 2
(c) 3
(d) 4
Show Answer & Explanation

Answer: (b) 2

Explanation:
1. A cube with only a green face must be in the top or bottom layer and must not touch any side face.
2. Only the centre cube of the top layer and the centre cube of the bottom layer qualify.
3. So the answer is 2.

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 8: A wooden cube is painted black on four adjoining faces and green on two opposite faces, that is, top and bottom. It is then cut into 27 smaller, identical cubes.
How many smaller cubes have only two of their faces painted black?

(a) 2
(b) 4
(c) 6
(d) 8
Show Answer & Explanation

Answer: (b) 4

Explanation:
1. Two black faces only means a vertical corner edge, but not touching top or bottom.
2. Each of the 4 vertical edges has 3 cubes; only the middle one avoids the green faces.
3. So 4 cubes have exactly two black faces.

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: A wooden cube is painted black on four adjoining faces and green on two opposite faces, that is, top and bottom. It is then cut into 27 smaller, identical cubes.
How many smaller cubes have at least three of their faces painted?

(a) 8
(b) 6
(c) 3
(d) 2
Show Answer & Explanation

Answer: (a) 8

Explanation:
1. All six faces of the big cube are painted (black or green).
2. A small cube can have at most 3 painted faces, and only the corner cubes do.
3. A cube has 8 corners, so 8 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 10: A wooden cube is painted black on four adjoining faces and green on two opposite faces, that is, top and bottom. It is then cut into 27 smaller, identical cubes.
How many smaller cubes have none of their faces painted at all?

(a) 1
(b) 2
(c) 3
(d) 4
Show Answer & Explanation

Answer: (a) 1

Explanation:
1. An unpainted cube must not touch any outer face.
2. In a 3 x 3 x 3 cube only the central cube is hidden: (3 - 2)3 = 1.

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 11: A solid cube is painted on only three adjacent faces and then cut into 64 smaller cubes of equal size.
How many smaller cubes have three of their faces coloured?
(a) 0
(b) 1
(c) 2
(d) 4
Show Answer & Explanation

Answer: (b) 1

Explanation:
1. 64 = 4 x 4 x 4, so each edge has 4 small cubes.
2. Three adjacent faces meet at only one corner of the big cube.
3. So only 1 small cube has three coloured faces.

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 12: A solid cube is painted on only three adjacent faces and then cut into 64 smaller cubes of equal size.
How many smaller cubes have only two of their faces coloured?
(a) 6
(b) 8
(c) 9
(d) 16
Show Answer & Explanation

Answer: (c) 9

Explanation:
1. Each pair of the three painted faces meets along one edge, so there are 3 such edges.
2. Each edge has 4 cubes; the cube at the common corner has three painted faces, leaving 3 cubes per edge with exactly two.
3. Total = 3 x 3 = 9.

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 13: A solid cube is painted on only three adjacent faces and then cut into 64 smaller cubes of equal size.
How many smaller cubes have only one of their faces coloured?
(a) 36
(b) 27
(c) 16
(d) 9
Show Answer & Explanation

Answer: (b) 27

Explanation:
1. On each painted 4 x 4 face, remove the row and column lying along the other two painted faces.
2. That leaves 3 x 3 = 9 cubes per face with only one coloured face.
3. Total = 9 x 3 = 27.

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 14: Each of the faces of a cube is painted with different colours. The face painted red is opposite to the one painted green. The face painted blue is between the red and green coloured faces. The face painted yellow is adjacent to the one painted pink. The face painted white is adjacent to the yellow coloured one, and the green face is facing down.
What is the colour of the face at the top?
(a) Blue
(b) White
(c) Red
(d) Yellow
Show Answer & Explanation

Answer: (c) Red

Explanation:
1. Green is at the bottom, so red (opposite green) is at the top.
2. So the top face is red.

Teacher's Note:
1. Fix the top and bottom first, then arrange the remaining four colours in a ring around the sides.
2. In the side ring, each face is adjacent to its two neighbours and to the top and bottom, and opposite the face two places away.

Question 15: Each of the faces of a cube is painted with different colours. The face painted red is opposite to the one painted green. The face painted blue is between the red and green coloured faces. The face painted yellow is adjacent to the one painted pink. The face painted white is adjacent to the yellow coloured one, and the green face is facing down.
What is the colour of the face which is opposite to the one coloured pink?
(a) White
(b) Green
(c) Blue
(d) Yellow
Show Answer & Explanation

Answer: (a) White

Explanation:
1. Green is at the bottom, so red (opposite green) is at the top.
2. The four side faces are blue, yellow, pink and white. Yellow touches both pink and white, so pink and white sit on either side of yellow and blue is opposite yellow.
3. Then pink and white are opposite each other.

Teacher's Note:
1. Fix the top and bottom first, then arrange the remaining four colours in a ring around the sides.
2. In the side ring, each face is adjacent to its two neighbours and to the top and bottom, and opposite the face two places away.

Question 16: Each of the faces of a cube is painted with different colours. The face painted red is opposite to the one painted green. The face painted blue is between the red and green coloured faces. The face painted yellow is adjacent to the one painted pink. The face painted white is adjacent to the yellow coloured one, and the green face is facing down.
What is the colour of the face which is opposite to the one coloured blue?
(a) Red
(b) Yellow
(c) White
(d) Pink
Show Answer & Explanation

Answer: (b) Yellow

Explanation:
1. Green is at the bottom, so red (opposite green) is at the top.
2. The four side faces are blue, yellow, pink and white. Yellow touches both pink and white, so pink and white sit on either side of yellow and blue is opposite yellow.
3. So yellow is opposite blue.

Teacher's Note:
1. Fix the top and bottom first, then arrange the remaining four colours in a ring around the sides.
2. In the side ring, each face is adjacent to its two neighbours and to the top and bottom, and opposite the face two places away.

Question 17: Each of the faces of a cube is painted with different colours. The face painted red is opposite to the one painted green. The face painted blue is between the red and green coloured faces. The face painted yellow is adjacent to the one painted pink. The face painted white is adjacent to the yellow coloured one, and the green face is facing down.
Which are the four colours on the faces adjacent to yellow coloured face?
(a) Red, white, blue, pink
(b) Green, white, blue, pink
(c) White, pink, red, green
(d) Blue, pink, red, green
Show Answer & Explanation

Answer: (c) White, pink, red, green

Explanation:
1. Green is at the bottom, so red (opposite green) is at the top.
2. The four side faces are blue, yellow, pink and white. Yellow touches both pink and white, so pink and white sit on either side of yellow and blue is opposite yellow.
3. Yellow touches every face except blue: white, pink, red (top) and green (bottom).

Teacher's Note:
1. Fix the top and bottom first, then arrange the remaining four colours in a ring around the sides.
2. In the side ring, each face is adjacent to its two neighbours and to the top and bottom, and opposite the face two places away.

Question 18: A cube of 3 cm edge is painted red on all its faces. It is then cut at equal distances, at right angles, into 27 smaller cubes of 1 cm edge, as shown in the figure, where the lines represent the cuts made. Study the diagram and answer the following question.
How many smaller cubes have three of their faces painted red?
a1b3a2b9c2b8a5b4a6b1c1b2a3b5a4b6c3a7b7
(a) 64
(b) 4
(c) 12
(d) 8
Show Answer & Explanation

Answer: (d) 8

Explanation:
1. Here n = 3 cubes along each edge.
2. Only the corner cubes have three painted faces, and a cube has 8 corners.

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 19: A cube of 3 cm edge is painted red on all its faces. It is then cut at equal distances, at right angles, into 27 smaller cubes of 1 cm edge, as shown in the figure, where the lines represent the cuts made. Study the diagram and answer the following question.
How many cubes have two of their faces painted?
a1b3a2b9c2b8a5b4a6b1c1b2a3b5a4b6c3a7b7
(a) 4
(b) 8
(c) 12
(d) 6
Show Answer & Explanation

Answer: (c) 12

Explanation:
1. Two painted faces = edge cubes other than corners: (n - 2) per edge.
2. (3 - 2) x 12 edges = 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 20: A cube of 3 cm edge is painted red on all its faces. It is then cut at equal distances, at right angles, into 27 smaller cubes of 1 cm edge, as shown in the figure, where the lines represent the cuts made. Study the diagram and answer the following question.
How many cubes have only one of their sides painted red?
a1b3a2b9c2b8a5b4a6b1c1b2a3b5a4b6c3a7b7
(a) 9
(b) 6
(c) 1
(d) 4
Show Answer & Explanation

Answer: (b) 6

Explanation:
1. One painted face = centre cubes of each face: (n - 2)2 per face.
2. (3 - 2)2 x 6 = 6.

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 21: A cube of 3 cm edge is painted red on all its faces. It is then cut at equal distances, at right angles, into 27 smaller cubes of 1 cm edge, as shown in the figure, where the lines represent the cuts made. Study the diagram and answer the following question.
How many cubes have none of their sides painted?
a1b3a2b9c2b8a5b4a6b1c1b2a3b5a4b6c3a7b7
(a) 1
(b) 4
(c) 0
(d) 4
Show Answer & Explanation

Answer: (a) 1

Explanation:
1. Unpainted cubes lie fully inside: (n - 2)3.
2. (3 - 2)3 = 1.

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 22: 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 yellow and brown on two adjacent faces?
(a) 12
(b) 24
(c) 20
(d) 8
Show Answer & Explanation

Answer: (c) 20

Explanation:
1. 10/2 = 5 cubes along each edge, so 125 small cubes.
2. Yellow and brown faces meet along 4 edges; each edge holds 5 cubes, all of which have a yellow face and a brown face next to each other.
3. 4 x 5 = 20 (12 middle-edge cubes with only these two colours plus the 8 corner 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 23: 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 one of their faces?
(a) 18
(b) 54
(c) 36
(d) 42
Show Answer & Explanation

Answer: (b) 54

Explanation:
1. n = 5, so each face has (5 - 2)2 = 9 cubes with one painted face.
2. 6 x 9 = 54.

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 24: 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 yellow on one face and brown on the opposite face?
(a) 0
(b) 4
(c) 8
(d) None of these
Show Answer & Explanation

Answer: (a) 0

Explanation:
1. Yellow and brown are on adjacent faces of the big cube, never on opposite ones.
2. A small cube cannot touch two faces of the big cube that are 10" apart, since it is only 2" wide.
3. So no such cube exists: 0.

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 25: 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 brown at least on one of their faces?
(a) 18
(b) 20
(c) 30
(d) 50
Show Answer & Explanation

Answer: (d) 50

Explanation:
1. Each brown face is a 5 x 5 layer of 25 cubes.
2. The two brown faces are opposite, so their layers do not overlap: 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.

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Dice and Cube Objective Questions & Solutions for General Aptitude Arithmetic Ability

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