UPSC Prelims 2010 Q118: Science & Technology – Logical Reasoning & Puzzles
In a meeting, the map of a village was placed in such a manner that south - east becomes
north, north - east becomes west and so on. What will south become?
- (a) North
- (b) North - east
- (c) North - west
- (d) West
Answer: (b) North - east
Explanation
A rotated-direction map puzzle
The map's directions are systematically relabeled: South-East becomes North, North-East becomes West — we need to find what South becomes.
| Step | Reasoning |
|---|---|
| Assign compass angles | South-East = 135°, North = 0°/360°; North-East = 45°, West = 270° |
| Find the rotation applied | From SE(135°) to N(360°): a shift of +225° (clockwise); checking NE(45°) to W(270°): also +225° — consistent |
| Apply the same +225° shift to South | South = 180°; 180° + 225° = 405°, which mod 360° = 45° |
| 45° corresponds to | North-East |
Verifying the consistent rotation:
| Original direction | New direction (after +225°) |
|---|---|
| South-East (135°) | North (360°/0°) |
| North-East (45°) | West (270°) |
| South (180°) | North-East (45°) |
Answer: (b) North-East.
Why each option is right or wrong
- (a) Incorrect. North is where South-East maps to, not South.
- (b) CORRECT. Applying the same consistent +225° rotation to South (180°) gives 45° = North-East.
- (c) Incorrect. North-West does not match the verified +225° rotation applied to South.
- (d) Incorrect. West is where North-East maps to, not South.
Key point
Working out the consistent rotation from the two given direction swaps (SE→N, NE→W) reveals a +225° shift — applying this to South (180°) gives 45°, which is North-East.
Remember
Direction puzzle: with SE→N and NE→W (a +225° rotation), South becomes North-East.
Common mistakes
- Guessing the new direction without first establishing the exact, consistent rotation angle from the given examples.
- Making an arithmetic error in the modular (mod 360°) angle calculation.
- Confusing clockwise and counter-clockwise rotation directions.
Exam tip
For rotated-direction puzzles, convert directions to compass degrees, find the consistent rotation from the given examples, then apply it to the target direction.
Sources
- R. S. Aggarwal — A Modern Approach to Verbal and Non-Verbal Reasoning (Direction Sense Test)
- Arun Sharma — How to Prepare for Logical Reasoning for the CAT (direction and distance problems)