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UPSC Prelims 2023CSATLogical Reasoning & Analytical AbilityInequality and Logic

Q60. 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.✓ Correct
C. Both Conclusion-1 and Conclusion-2 follow from the Statement.
D. Neither Conclusion-1 nor Conclusion-2 follows from the Statement.

Detailed Solution

✓ Correct Answer: Option B

First, let's decode the symbols into standard inequalities: I. A + B means A > B II. A – B means A ≤ B III. A × B means A ≥ B IV. A ÷ B means A < B V. A ± B means A = B Now, translate the given statement: - P × Q means P ≥ Q - P – T means P ≤ T - T ÷ R means T < R - R ± S means R = S Combining these, we get the chain of inequalities: S = R > T ≥ P ≥ Q.

Now, let's evaluate the conclusions: Conclusion 1: Q ± T means Q = T. From the combined inequality, T ≥ P ≥ Q. This implies T can be equal to Q, or T can be greater than Q. We cannot definitively conclude Q = T.

So, Conclusion 1 does not follow. Conclusion 2: S + Q means S > Q. From the combined inequality, S = R > T ≥ P ≥ Q. Since S is equal to R, and R is strictly greater than T, and T is greater than or equal to P, and P is greater than or equal to Q, it logically follows that S is strictly greater than Q.

So, Conclusion 2 follows. Therefore, only Conclusion 2 follows from the statement. This question tests logical reasoning, specifically decoding symbols and deriving conclusions from a chain of inequalities, a common topic in CSAT.

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