UPSC Prelims 2010 Q106: Science & Technology – Logical Reasoning & Puzzles
- (a) PQRS, RSPQ
- (b) PRQS, RSPQ
- (c) PRQS, RSQP
- (d) PRSQ, RSPQ
Answer: (b) PRQS, RSPQ
Explanation
An age-and-richness ordering logic puzzle
Four men — P, Q, R, S — with clues about relative age and wealth.
| Clue | Deduction |
|---|---|
| P is oldest, not poorest | P = oldest; P is not the poorest (so at least one person is poorer than P) |
| R is richest, not oldest | R = richest; R is not the oldest (consistent, since P is oldest) |
| Q is older than S, but not older than P or R | Age order so far: P and R are both older than Q, and Q > S |
| P is richer than Q, but not richer than S | Richness: P > Q, and S > P (since P is 'not richer than S' means S is richer or equal, so S > P) |
Building the age order: P is oldest; R and Q are both below P, with R > Q (since Q is 'not older than R'); Q > S. So age (descending): P > R > Q > S.
Building the richness order: R is richest (given). S > P > Q (from the richness clues). Combining with R on top: R > S > P > Q.
Final orders:
| Type | Descending order |
|---|---|
| Age | P, R, Q, S |
| Richness | R, S, P, Q |
Answer: (b) PRQS, RSPQ.
Why each option is right or wrong
- (a) Incorrect. The age order 'PQRS' incorrectly places Q above R, contradicting the clue that Q is not older than R.
- (b) CORRECT. Working through all the age and richness clues gives exactly PRQS (age) and RSPQ (richness).
- (c) Incorrect. The richness order 'RSQP' incorrectly places Q above P, contradicting 'P is richer than Q'.
- (d) Incorrect. The age order 'PRSQ' incorrectly places S above Q, contradicting 'Q is older than S'.
Key point
Working through all the clues: age order (descending) = P, R, Q, S; richness order (descending) = R, S, P, Q.
Remember
Age-richness puzzle: age order PRQS, richness order RSPQ — derived by working through each comparative clue.
Common mistakes
- Misreading 'not older/richer than X' as a direct ranking statement rather than an upper-bound constraint.
- Mixing up the age and richness clues, applying one set's logic to the other attribute.
- Not working through each clue systematically before attempting to pick a final order.
Exam tip
For multi-attribute ranking puzzles, build each ranking (age, richness) separately and completely before cross-checking against the answer options.
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 and attribute-matching puzzles)