Consider the following statements in respect of five candidates P, Q, R, S and T. Two statements are true and one statement is false.
True Statement: One of P and Q was selected for the job.
False Statement: At least one of R and S was selected for the job.
True Statement: At most two of R, S and T were selected for the job.
Which of the following conclusions can be drawn?
- 1.At least four were selected for the job.
- 2.S was selected for the job.
Select the correct answer using the code given below:
Answer & explanation
Answer: (d) Neither 1 nor 2
Since 'at least one of R and S was selected' is false, neither R nor S was selected. That leaves only P, Q and T as possible selections — at most three people — so neither conclusion can be drawn.
- The false statement means neither R nor S was selected.
- So only P, Q and T could have been selected: at most three candidates.
- Conclusion 1 (at least four selected) is impossible.
- Conclusion 2 (S selected) contradicts the false statement.
- Check: the third statement (at most two of R, S, T) holds, since only T can be among them.
- ✗ 1. With R and S both out, at most P, Q and T can be selected — never four.
- ✗ 2. The false statement tells us S was not selected.
Remember · The negation of 'at least one of X and Y' is 'neither X nor Y'. Negate the false statement first; it usually settles the case.
Question and answer: UPSC's official GS Paper II (2023, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·