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PYQ Question

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?

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?
  1. A. Only Conclusion-1 follows from the Statement.
  2. B. Only Conclusion-2 follows from the Statement.
  3. C. Both Conclusion-1 and Conclusion-2 follow from the Statement.
  4. D. Neither Conclusion-1 nor Conclusion-2 follows from the Statement.

Answer: B

Explanation

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 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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