UPSC Prelims 2006 Q61: Science & Technology – Logical Reasoning & Puzzles
P, Q, R, S and T reside in a 5 - storeyed (Ground + 4) building, and each of them resides on a
separate floor. Further,
1. T does not reside on the topmost floor.
2. Q does not reside on the ground floor.
3. S resides on one storey above that of P and one storey below that of R.
To know as to which of the 5 persons resides on the ground floor
which of the above statements are sufficient / insufficient?
- (a) 1 and 3 are sufficient
- (b) 2 and 3 are sufficient
- (c) 1, 2 and 3 are sufficient
- (d) 1, 2 & 3 are insufficient
Answer: (d) 1, 2 & 3 are insufficient
Explanation
Who lives on the ground floor? (Ground + 4 floors, P, Q, R, S, T)
Statement 3 makes P, S, R occupy three consecutive floors in that order (P lowest, R highest). List the possible placements:
| P, S, R on floors | Remaining floors for Q and T | Fits statements 1 and 2? | Ground floor |
|---|---|---|---|
| 0, 1, 2 | 3 and 4 | T not on top, so T on 3 and Q on 4 | P |
| 1, 2, 3 | 0 and 4 | Q not on ground, so Q on 4, T on 0 | T |
| 2, 3, 4 | 0 and 1 | Q not on ground, so Q on 1, T on 0 | T |
The ground floor may belong to P or to T, so the statements together cannot identify one person.
Answer: (d) 1, 2 & 3 are insufficient.
Why each option is right or wrong
- (a) Incorrect. Statements 1 and 3 alone leave both P and T possible on the ground floor.
- (b) Incorrect. Statements 2 and 3 alone also leave more than one possibility.
- (c) Incorrect. Even all three statements leave P or T on the ground floor.
- (d) CORRECT. Two valid arrangements put different persons (P or T) on the ground floor, so the statements are insufficient.
Key point
With statement 3 fixing P, S, R as consecutive floors, valid arrangements place either P or T on the ground floor, so all three statements together are insufficient.
Remember
Ground floor could be P or T, so the data are insufficient.
Common mistakes
- Stopping at the first valid arrangement without checking the others.
- Forgetting that the floors are ground plus four, giving three placements for P-S-R.
- Treating 'one storey above' as adjacent in either direction.
Exam tip
List every placement of the fixed block, then apply the other conditions and see if one answer remains.
Sources
- R. S. Aggarwal — A Modern Approach to Verbal and Non-Verbal Reasoning (Puzzle Test)
- Arun Sharma — How to Prepare for Logical Reasoning for the CAT (arrangement puzzles and data sufficiency)