‘A$B’ means ‘A is smaller than B’ ‘A#B’ means ‘A is neither greater than nor…

2025

‘A$B’ means ‘A is smaller than B’

‘A#B’ means ‘A is neither greater than nor smaller than B’

‘A%B’ means ‘A is greater than B’

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: P $ Q, Q # R, R % S

Conclusions: I. R $ P II. Q % S

  1. A.

    if only Conclusion I is true

  2. B.

    if only Conclusion II is true

  3. C.

    if neither Conclusion I nor II is true

  4. D.

    if both Conclusions I and II are true

Show answer & explanation

Correct answer: B

Concept: Coded-inequality ‘Statements and Conclusions’ questions replace the ordinary signs <, =, > with made-up symbols. Solving them always follows the same three moves — translate every statement into its real mathematical relation, chain the individual relations into one single ordered relation wherever the terms link up, and then read each conclusion directly off that combined chain. A conclusion is ‘definitely true’ only when the chain forces it, never merely because it seems plausible.

  1. Translate the first statement: ‘P $ Q’ means P is smaller than Q, i.e. P < Q.

  2. Translate the second statement: ‘Q # R’ means Q is neither greater nor smaller than R, i.e. Q = R.

  3. Translate the third statement: ‘R % S’ means R is greater than S, i.e. R > S.

  4. Chain all three relations into one ordered relation, since Q is common to the first two and R is common to the last two: P < Q = R > S.

  5. Check Conclusion I (‘R $ P’, i.e. R < P): the chain gives P < Q = R, so P is smaller than R — that is, R is greater than P, the opposite of what Conclusion I claims. Conclusion I is not definitely true.

  6. Check Conclusion II (‘Q % S’, i.e. Q > S): the chain gives Q = R and R > S; since Q equals R, the same ‘greater than S’ relation carries over to Q, giving Q > S. Conclusion II is definitely true.

Cross-check with concrete numbers consistent with the chain, e.g. P = 1, Q = R = 3, S = 0 (this satisfies P < Q, Q = R, and R > S). Directly comparing: R (3) is not smaller than P (1), so Conclusion I fails; Q (3) is greater than S (0), so Conclusion II holds — matching the chain-based result.

Result: only Conclusion II is definitely true, so the correct choice is the option stating that only Conclusion II holds.

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