Q70·CSAT · Prelims 2023

Coded inequality statements and conclusions

ReasoningInequalitiesInequality logic● Medium

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?

Options

Only Conclusion-1 follows from the Statement.

Only Conclusion-2 follows from the Statement.

Answer

Both Conclusion-1 and Conclusion-2 follow from the Statement.

Neither Conclusion-1 nor Conclusion-2 follows from the Statement.

Explanation

Decode the operational symbols into standard mathematical inequalities first:

`+` means neither smaller nor equal \rightarrow >

`-` means not greater than \rightarrow \le

`×` means not smaller than \rightarrow \ge

`÷` means neither greater nor equal \rightarrow <

`±` means neither smaller nor greater \rightarrow =

Translate the given statement chain: P \ge Q, P \le T, T < R, R = S.

Link the chain together starting from Q: Q \le P \le T < R = S \implies Q \le T < S.

Evaluate the conclusions based on this unified chain:

Conclusion 1: Q ± T \implies Q = T. The chain indicates Q \le T, meaning Q could be strictly less than T. It does not definitely follow.

Conclusion 2: S + Q \implies S > Q. Looking at our chain, Q \le T < S, which simplifies directly to Q < S (or S > Q). This is absolutely certain.

For coded inequalities, decode the expressions into clean linear chains lined up in a single direction (e.g., all `<` and `\le`) to read relationships instantly.

Answer: (b).

Question details

Year

2023

Paper

CSAT

Question

Q70

Section

Logical & Analytical Reasoning

Sub-topic

Inequalities

Type

Inequality logic

Difficulty

Medium

Source hint

Logical deduction

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