UPSC Prelims 2007 Q141: Science & Technology – Logical Reasoning & Puzzles
Six faces of a cube are numbered from 1 to 6, each face carrying one different number.
Further,
1. The face 2 is opposite to the face 6.
2. The face 1 is opposite to the face 5.
3. The face 3 is between the face 1 and face 5.
4. The face 4 is adjacent to the face 2.
Which one of the following is correct?
- (a) The face 2 is adjacent to the face 3
- (b) The face 6 is between the face 2 and the face 4
- (c) The face 1 is between the face 5 and the face 6
- (d) None of the above
Answer: (a) The face 2 is adjacent to the face 3
Explanation
Cube face puzzle
Opposite pairs from the clues:
| Clue | Opposite pair |
|---|---|
| Face 2 is opposite face 6 | 2 ↔ 6 |
| Face 1 is opposite face 5 | 1 ↔ 5 |
| Only 3 and 4 remain | 3 ↔ 4 |
On a cube, every face touches all faces except its opposite.
So face 3 touches 1, 2, 5, 6.
Check the options:
| Option | Claim | True? |
|---|---|---|
| (a) | Face 2 is adjacent to face 3 | Yes — 3 is opposite only 4 |
| (b) | Face 6 is between face 2 and face 4 | No — 6 is opposite 2, so it cannot lie between 2 and anything |
| (c) | Face 1 is between face 5 and face 6 | No — 1 is opposite 5 |
Answer: (a) The face 2 is adjacent to the face 3.
Why each option is right or wrong
- (a) CORRECT. Face 3 is opposite only face 4, so it is adjacent to face 2.
- (b) Incorrect. Face 6 is opposite face 2, so it cannot sit between face 2 and face 4.
- (c) Incorrect. Face 1 is opposite face 5, so it cannot be between face 5 and face 6.
- (d) Incorrect. Option (a) is correct.
Key point
Opposite pairs: 2-6, 1-5, 3-4. Every face is adjacent to the 4 faces that are not its opposite.
Remember
On a cube, a face touches every face except its opposite.
Common mistakes
- Not working out the third opposite pair (3-4) by elimination.
- Thinking a face can be 'between' its own opposite face and another face.
- Drawing a net when simple opposite-pair logic is enough.
Exam tip
Cube rule: find the 3 opposite pairs first. Everything else is adjacent.
Sources
- NCERT Class VIII — Mathematics, Visualising Solid Shapes
- R. S. Aggarwal — A Modern Approach to Verbal and Non-Verbal Reasoning (Cubes and Dice)