Direction: In the following questions, the symbols #, %, @, & and © are used…

2024

Direction: In the following questions, the symbols #, %, @, & and © are used with the following meaning as illustrated below:

'X # Y' means 'X is neither greater than nor equal to Y'.

'X © Y' means 'X is neither smaller than nor greater than Y'.

'X & Y' means 'X is not greater than Y'.

'X % Y' means 'X is greater than Y'.

'X @ Y' means 'X is either greater than or equal to Y'.

Now in each of the following questions assuming the given statements to be True, find which of the conclusion/s given below them is/are definitely True?

Statements:

A © C, Z % Y & B, D # X, X # Z, B @ A

Conclusions:

I. X & B

II. B @ C

III. X © C

  1. A.

    Only Conclusion II is True.

  2. B.

    Both Conclusions I and II are True.

  3. C.

    Either Conclusion II or III is True.

  4. D.

    Neither Conclusion I nor III is True.

Show answer & explanation

Correct answer: A

Concept: Coded-inequality items replace <, >, ≤, ≥ and = with symbols. Decode every symbol into its operator, chain the statements through shared variables into one composite inequality, and then check each conclusion against that chain: a conclusion is definitely True only when the chain fixes a direct order between its two terms. If two terms are linked only through a common 'peak' (a value exceeding both) or through two independent branches, their mutual order stays indeterminate — such a conclusion is not definitely True.

  1. Decode the definitions: '#' is <, '©' is =, '&' is ≤, '%' is >, and '@' is ≥.

  2. Decode each statement: A © C → A = C; Z % Y & B → Z > Y and Y ≤ B; D # X → D < X; X # Z → X < Z; B @ A → B ≥ A.

  3. Chain the decoded relations through their shared variables: D < X < Z > Y ≤ B ≥ A = C.

  4. Check Conclusion I (X & B → X ≤ B): X reaches B only via Z, a term greater than both X and Y — a shared peak never fixes how the two terms below it compare, so this relation is indeterminate.

  5. Check Conclusion II (B @ C → B ≥ C): B ≥ A and A = C combine directly (same-direction, transitive) to give B ≥ C — this is fixed by the chain.

  6. Check Conclusion III (X © C → X = C): X is separated from C by the peak at Z and by the B ≥ A = C branch, so no fixed relation between X and C can be read off the chain — indeterminate.

Cross-check: Only Conclusion II is pinned down by a direct transitive link (B ≥ A = C); Conclusions I and III each require crossing the peak at Z, which the chain never resolves, and they do not form a complementary either/or pair (II is already independently decided). Hence only Conclusion II follows.

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