CSAT Solved Papers/ 2023/Q70

2023 CSAT — Q70

Quant Statement validity 2.5 marks Hard

Consider the following:

I. A+BA + B means AA is neither smaller nor equal to BB.

II. ABA - B means AA is not greater than BB.

III. A×BA \times B means AA is not smaller than BB.

IV. A÷BA \div B means AA is neither greater nor equal to BB.

V. A±BA \pm B means AA is neither smaller nor greater than BB.

Statement: P×Q, PT, T÷R, R±SP \times Q,\ P - T,\ T \div R,\ R \pm S

Conclusion-1: Q±TQ \pm T

Conclusion-2: S+QS + 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. Answer
  3. C Both Conclusion-1 and Conclusion-2 follow from the Statement.
  4. D Neither Conclusion-1 nor Conclusion-2 follows from the Statement.

Worked rationale

Decode the coded operators into plain inequalities first:

  • A+BA + B: AA neither smaller nor equal A>B\Rightarrow A > B
  • ABA - B: AA not greater AB\Rightarrow A \le B
  • A×BA \times B: AA not smaller AB\Rightarrow A \ge B
  • A÷BA \div B: AA neither greater nor equal A<B\Rightarrow A < B
  • A±BA \pm B: AA neither smaller nor greater A=B\Rightarrow A = B

Now translate the Statement:

P×Q: PQ,PT: PT,T÷R: T<R,R±S: R=S.P\times Q:\ P \ge Q,\quad P - T:\ P \le T,\quad T \div R:\ T < R,\quad R \pm S:\ R = S.

Chain them: QPT<R=SQ \le P \le T < R = S, i.e.

QPT<R=S.Q \le P \le T < R = S.

Conclusion-1 (Q±TQ \pm T, i.e. Q=TQ = T): we only have QPTQ \le P \le T, so QTQ \le T but possibly Q<TQ < T. Equality is not forced. Does not follow.

Conclusion-2 (S+QS + Q, i.e. S>QS > Q): S=R>TPQS = R > T \ge P \ge Q, so S>QS > Q strictly. Follows.

Answer: (b) Only Conclusion-2 follows from the Statement.

Why the other options miss

  • A
    upgrades \le to ==: reads QTQ \le T as Q=TQ = T, forcing an equality the chain never guarantees.
  • C
    correctly derives S>QS > Q but also wrongly accepts Q=TQ = T, not testing whether Q<TQ < T is possible.
  • D
    mis-decodes an operator (e.g. reads "÷\div" as \le or "±\pm" as \ne), breaking the chain so even S>QS > Q is rejected.

Specialist insight

The discipline is decode every operator into an ordering symbol before reasoning — the words “neither smaller nor equal,” “not greater,” etc. each map to exactly one of >,,,<,=>, \le, \ge, <, =. Then assemble the single chain QPT<R=SQ \le P \le T < R = S. A “follows” conclusion must hold in every model: S>QS > Q always holds (strict, via T<RT < R), but Q=TQ = T can fail (when Q<TQ < T). Distinguishing a forced strict inequality from a merely-possible equality is the whole item.

The trap, in one line

Decode to QPT<R=SQ\le P\le T < R = S: S>QS>Q is forced (Concl-2 ✓) but Q=TQ=T is not (only QTQ\le T) \Rightarrow (b).

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