Directions for Questions: In the following questions the symbols +, ×, ?, @…

2025

Directions for Questions: In the following questions the symbols +, ×, ?, @ and $ are used with the following meanings:

P + Q means P is neither smaller nor greater than Q.

P × Q means P is neither equal to nor smaller than Q.

P ? Q means P is neither greater than nor equal to Q.

P @ Q means P is either greater than or equal to Q.

P $ Q means P is not equal to Q.

Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true.

Statements : A + B, B $ C, C ? A

Conclusions :

I. C $ A

II. B + C

  1. A.

    if only conclusion I is true;

  2. B.

    if only conclusion II is true;

  3. C.

    if either I or II is true;

  4. D.

    if neither I nor II is true; and

  5. E.

    if both I and II are true.

Show answer & explanation

Correct answer: A

Concept: In statement-and-conclusion puzzles built from coded relational symbols, a conclusion is definitely true only if it is logically entailed by the decoded statements — including a weaker relation entailed by a stronger one (a strict '<' or '>' always entails '≠', though '≠' alone does not entail either strict inequality).

Application:

  1. Decode the symbols used here: '+' = equal to (=); '×' = greater than (>); '?' = less than (<); '@' = greater than or equal to (≥); '$' = not equal to (≠).

  2. Decode the three statements: A + B → A = B; B $ C → B ≠ C; C ? A → C < A.

  3. Test Conclusion I (C $ A, i.e. C ≠ A): statement (iii) already gives C < A. A strict inequality always makes the two terms unequal, so C ≠ A is guaranteed — Conclusion I is definitely true.

  4. Test Conclusion II (B + C, i.e. B = C): statement (ii) directly gives B ≠ C — the exact opposite of what Conclusion II claims — so Conclusion II is definitely false.

Cross-check: Substituting A = B (statement i) into C < A (statement iii) gives C < B, which is fully consistent with B ≠ C (statement ii) — no contradiction arises, confirming the decoding holds together.

Result: Only Conclusion I follows definitely from the statements.

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