Consider the following : I. A + B means A is neither smaller nor equal to B. II. A - B means A is not greater than B. III. A × B means A is not smaller than B. IV. A ÷ B means A is neither greater nor equal to B. V. A ± B means A is neither smaller nor greater than B. Statement : P × Q, P - T, T ÷ R, R ± S Conclusion-1 : Q ± T Conclusion-2 : S + Q Which one of the following is correct in respect of the above Statement and the Conclusions ?
- (a) Only Conclusion-1 follows from the Statement.
- (b) Only Conclusion-2 follows from the Statement. ✓ UPSC's answer
- (c) Both Conclusion-1 and Conclusion-2 follow from the Statement.
- (d) Neither Conclusion-1 nor Conclusion-2 follows from the Statement.
Why the answer is (b)
• Translate the codes: '×' means ≥, '-' means ≤, '÷' means <, '±' means =, and '+' means >.
• The statement P × Q, P - T, T ÷ R, R ± S translates to P ≥ Q, P ≤ T, T < R, and R = S.
• Combining these gives the chain: Q ≤ P ≤ T < R = S, which simplifies to Q < S.
• Conclusion-1 states Q ± T (Q = T). Since Q ≤ P ≤ T and T < R, Q is strictly less than T (Q < T), so Q cannot equal T; thus, Conclusion-1 does not follow.
• Conclusion-2 states S + Q (S > Q). From the derived chain Q < S, this conclusion is true.
• Therefore, only Conclusion-2 follows, making option (b) the correct answer.
Why the other options are wrong
- (a) Only Conclusion-1 follows from the Statement.
- Conclusion-1 (Q = T) is false because the chain establishes Q < T, so it cannot be that only Conclusion-1 follows.
- (c) Both Conclusion-1 and Conclusion-2 follow from the Statement.
- Conclusion-1 (Q = T) is false because Q is strictly less than T, so it is incorrect to say both conclusions follow.
- (d) Neither Conclusion-1 nor Conclusion-2 follows from the Statement.
- Conclusion-2 (S > Q) is true based on the derived inequality Q < S, so it is incorrect to say neither conclusion follows.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2023, held on 28 May 2023. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.