In the following questions, the symbols @, #, $, % and © are used with…

2025

In the following questions, the symbols @, #, $, % and © are used with different meanings as explained below:

‘A @ B’ means ‘A is neither smaller than nor equal to B’.

‘A # B’ means ‘A is not greater than B’.

‘A $ B’ means ‘A is neither greater than nor equal to B’.

‘A % B’ means ‘A is neither greater than nor smaller than B’.

‘A © B’ means ‘A is not smaller than B’.

Assuming the above statements to be true, you have to decide which of the conclusions is/are definitely true and then mark your answer accordingly.

Statement: F @ J, J # R, R % L, L © M

Conclusions:

I. F $ R

II. M # R

III. M © J

  1. A.

    None is true

  2. B.

    Only I is true

  3. C.

    Only II is true

  4. D.

    Only either II or III is true

Show answer & explanation

Correct answer: C

CONCEPT: In coded-symbol inequality problems, each symbol stands for one relational operator (>, <, =, <=, or >=). To decide whether a conclusion is definitely true, decode every symbol in the statements into its real operator, then chain the resulting relations using transitivity - a conclusion follows only when an unbroken chain of >=/<=/= links its two terms in one fixed direction; if no such chain exists, the conclusion cannot be determined.

Decoding the symbols used here:

  • @ means 'greater than' (>)

  • # means 'less than or equal to' (<=)

  • $ means 'less than' (<)

  • % means 'equal to' (=)

  • © means 'greater than or equal to' (>=)

Applying these to the statement gives the following steps:

  1. F @ J -> F > J

  2. J # R -> J <= R

  3. R % L -> R = L

  4. L © M -> L >= M

  5. Combining all four: F > J <= R = L >= M

  6. Conclusion I (F < R): F > J and J <= R do not chain into any fixed relation between F and R, so Conclusion I is not determined.

  7. Conclusion II (M <= R): since R = L and L >= M, substituting R for L gives R >= M, i.e. M <= R - this matches Conclusion II exactly, so it is definitely true.

  8. Conclusion III (M >= J): the chain only shows J <= R and M <= R; there is no direct link between J and M, so Conclusion III is not determined.

CROSS-CHECK: Since Conclusion II is independently provable, the 'either/or' pattern (which requires that neither conclusion be provable alone) does not apply here, so the answer is not 'either II or III' but exactly 'Only II'.

Hence, only Conclusion II is definitely true — 'Only II is true' is the correct choice.

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