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Reasoning — Cube and Dice
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Reasoning — Cube and Dice

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7 mins
Time
❓
9
Questions
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1
Per Q

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Reasoning — Cube and Dice — Questions with Answers Open after you finish the quiz — all 9 questions, with answers and explanations.
Q1. Two positions of a single dice are given. In the first position, the faces visible are 1, 2, and 3. In the second position, the faces visible are 2, 4, and 5. Which number is opposite to 6?
  1. 1
  2. 2
  3. 3
  4. 4
Show answer
Answer: B. 2
In the given positions, '2' is the common face. Rotating clockwise from '2' in both positions: Position 1: 2 -> 3 -> 1 Position 2: 2 -> 5 -> 4 This implies that 3 is opposite to 5, and 1 is opposite to 4. The remaining two numbers are 2 and 6, so 2 must be opposite to 6.
Q2. A dice has numbers 1 to 6 on its faces. If the sum of the numbers on any pair of adjacent faces is never 7, then what is the number opposite to 4?
  1. 1
  2. 2
  3. 3
  4. 5
Show answer
Answer: C. 3
The condition "sum of the numbers on any pair of adjacent faces is never 7" implies that the sum of numbers on opposite faces must be 7. This is the definition of a Standard Dice. In a standard dice, the number opposite to 4 will be 7 - 4 = 3.
Q3. An open dice pattern is described as follows: Face 'A' is at the top. Below 'A' are four faces in a row: 'B', 'C', 'D', 'E'. Below 'D' is face 'F'. Which face is opposite to 'C'?
  1. A
  2. B
  3. D
  4. F
Show answer
Answer: D. F
In an open dice pattern, alternate faces in a straight line are opposite to each other. The pattern can be visualized as: A B C D E F In this arrangement, A is opposite to D, B is opposite to E, and C is opposite to F. Therefore, C is opposite to F.
Q4. An open dice pattern is described as follows: Face '1' is at the top. Below '1' are three faces in a row: '2', '3', '4'. Below '3' is face '5'. Below '5' is face '6'. Which of the following is a pair of opposite faces?
  1. (1,2)
  2. (2,3)
  3. (3,6)
  4. (4,5)
Show answer
Answer: C. (3,6)
Let's visualize the pattern: 1 2 3 4 5 6 In an open dice, alternate faces in a straight line are opposite to each other. From the horizontal row (2-3-4): 2 is opposite to 4. From the vertical line (1-3-5-6): 1 is opposite to 5 (skipping 3). 3 is opposite to 6 (skipping 5). So, the pairs of opposite faces are (1,5), (2,4), and (3,6). The option (3,6) matches one of these pairs.
Q5. A large cube of side 6 cm is painted green on all its faces. It is then cut into smaller cubes of side 1 cm. How many smaller cubes have exactly two faces painted?
  1. 8
  2. 12
  3. 24
  4. 48
Show answer
Answer: D. 48
The side of the large cube (L) = 6 cm. The side of the smaller cubes (l) = 1 cm. Number of divisions along one edge (N) = L/l = 6/1 = 6. Cubes with exactly two faces painted are located on the edges of the large cube, excluding the corner cubes. The formula for cubes with exactly two faces painted is 12 * (N - 2). Number of cubes = 12 * (6 - 2) = 12 * 4 = 48.
Q6. Two positions of a single dice are given. In the first position, the faces visible are P, Q, R. In the second position, the faces visible are Q, R, S. Which face is opposite to P?
  1. Q
  2. R
  3. S
  4. T
Show answer
Answer: C. S
When two positions of a dice have two common faces, the remaining uncommon faces are opposite to each other. In Position 1: P, Q, R In Position 2: Q, R, S The common faces are Q and R. The remaining uncommon faces are P and S. Therefore, P is opposite to S.
Q7. A large cube of side 7 cm is painted yellow on all its faces. It is then cut into smaller cubes of side 1 cm. How many smaller cubes have exactly one face painted?
  1. 96
  2. 125
  3. 150
  4. 216
Show answer
Answer: C. 150
The side of the large cube (L) = 7 cm. The side of the smaller cubes (l) = 1 cm. Number of divisions along one edge (N) = L/l = 7/1 = 7. Cubes with exactly one face painted are located on the faces of the large cube, excluding the edges and corners. The formula for cubes with exactly one face painted is 6 * (N - 2)^2. Number of cubes = 6 * (7 - 2)^2 = 6 * (5)^2 = 6 * 25 = 150.
Q8. An open dice pattern is described as follows: Face 'A' is at the top. Below 'A' are three faces in a row: 'B', 'C', 'D'. Below 'C' is face 'E'. Below 'E' is face 'F'. Which of the following combinations of faces CANNOT be seen together on a cube formed by folding this pattern?
  1. (A, B, C)
  2. (B, E, F)
  3. (A, E, D)
  4. (C, D, A)
Show answer
Answer: C. (A, E, D)
Let's visualize the pattern: A B C D E F In an open dice, alternate faces in a straight line are opposite to each other. From the horizontal row (B-C-D): B is opposite to D. From the vertical line (A-C-E-F): A is opposite to E (skipping C). C is opposite to F (skipping E). So, the pairs of opposite faces are (A,E), (B,D), and (C,F). A cube cannot show two opposite faces simultaneously. We need to find an option that contains an opposite pair. 1. (A, B, C): No opposite pairs. Can be seen. 2. (B, E, F): No opposite pairs. Can be seen. 3. (A, E, D): A and E are opposite faces. Therefore, they cannot be seen together. 4. (C, D, A): No opposite pairs. Can be seen. Thus, the combination (A, E, D) cannot be seen together.
Q9. Four positions of a single dice are shown. Position 1: Visible faces are 1, 2, 3. Position 2: Visible faces are 2, 4, 5. Position 3: Visible faces are 3, 5, 6. Position 4: Visible faces are 1, 3, 6. Which number is opposite to 5?
  1. 1
  2. 2
  3. 3
  4. 4
Show answer
Answer: A. 1
To find the face opposite to 5, we list the faces adjacent to 5 from the given positions. From Position 2 (2, 4, 5): 5 is adjacent to 2 and 4. From Position 3 (3, 5, 6): 5 is adjacent to 3 and 6. So, the faces adjacent to 5 are 2, 4, 3, and 6. The numbers on a dice are 1, 2, 3, 4, 5, 6. Since 5 is adjacent to 2, 3, 4, 6, the only remaining number that cannot be adjacent to 5 is its opposite. The remaining number is 1. Therefore, 5 is opposite to 1.
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