UPSC Prelims 2006 Q77: Science & Technology – Logical Reasoning & Puzzles
Each of the six faces of a cube is numbered by one of the six digits from 1 to 6. This cube is
shown in its four different positions in the figures I, II, III and IV.
Consider the following statements:
1. Figures II and III are sufficient to know as to which face is opposite to the face numbered 6.
2. Figures II and III are sufficient to know as to which face is opposite to the face numbered 4.
3. Figures I and IV are sufficient to know as to which face is opposite to the face numbered 4.
Which of the statements given above are correct?
- (a) 1 and 3, only
- (b) 1 and 2, only
- (c) 2 and 3, only
- (d) 1, 2 and 3
Answer: (d) 1, 2 and 3
Explanation
Cube with faces numbered 1 to 6 (figure-based)
This question depends on four printed positions of the cube (figures I to IV), which are not reproduced in this dataset. The reasoning method for 'which face is opposite' is as follows.
| Step | Rule |
|---|---|
| Faces sharing an edge in any figure | Two numbers visible together are adjacent, never opposite |
| A face is opposite to a number | Only if it never appears adjacent to it and elimination leaves one candidate |
| Check each statement | Use only the figures named (II and III, or I and IV) and test whether they pin down the opposite face |
The stored key marks all three statements as correct.
Answer: (d) 1, 2 and 3.
Why each option is right or wrong
- (a) Incorrect. This accepts statements 1 and 3 but rejects statement 2, which the key accepts.
- (b) Incorrect. This accepts statements 1 and 2 but rejects statement 3, which the key accepts.
- (c) Incorrect. This accepts statements 2 and 3 but rejects statement 1, which the key accepts.
- (d) CORRECT. The stored key accepts all three statements as sufficient to find the opposite faces.
Key point
Faces seen together are adjacent, so elimination across the named figures fixes the opposite face; the stored key accepts all three statements.
Remember
Cube puzzle: adjacent faces appear together; stored key accepts statements 1, 2 and 3.
Common mistakes
- Treating faces seen together as opposite.
- Using a figure not named in the statement.
- Stopping before eliminating all adjacent numbers.
Exam tip
Faces visible together are adjacent; the opposite face is the one never seen alongside it.
Sources
- R. S. Aggarwal — A Modern Approach to Verbal and Non-Verbal Reasoning (Cubes and Dice)
- Arun Sharma — How to Prepare for Logical Reasoning for the CAT (cubes and dice puzzles)