Directions: Study the following information carefully and answer the questions…

2023

Directions: Study the following information carefully and answer the questions given below:

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

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

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

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

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

Statements : J # K, K @ P, P δ R

Conclusions :

I. J # R

II. R δ J

  1. A.

    if only conclusion I is true

  2. B.

    if only conclusion II is true

  3. C.

    if either conclusion I or II is true

  4. D.

    if neither conclusion I nor II is true

Show answer & explanation

Correct answer: D

Concept: In coded-inequality questions, first translate every symbol into its standard relation (>, <, =, ≥, ≤), then combine the statements into one chain. A conclusion is valid only if it can be derived directly from that chain. If the chain reverses direction (goes from > to <, or vice-versa) with only an equality bridging the two sides, the relation between the two end terms cannot be fixed — any conclusion claiming a direct relation between them is indeterminate.

Application:

  1. 'J # K' means J is neither smaller than nor equal to K, so J > K.

  2. 'K @ P' means K is neither greater than nor smaller than P, so K = P.

  3. 'P δ R' means P is neither greater than nor equal to R, so P < R.

  4. Combining all three: J > K = P < R.

This chain moves from '>' down to K = P and then to '<' — the direction reverses with only an equality in the middle, so there is no unbroken directional link carrying from J all the way to R.

Checking the conclusions:

  1. Conclusion I ('J # R' → J > R): this needs a direct, fixed relation between J and R, but the chain breaks direction at K = P, so J > R cannot be derived.

  2. Conclusion II ('R δ J' → R < J, which is the same statement as J > R): it faces the identical break in the chain, so it cannot be derived either.

Cross-check: Try value assignments consistent with J > K = P < R. With J = 10, K = P = 5, R = 8, J > R holds. With J = 6, K = P = 5, R = 8, J < R instead. Both assignments satisfy every statement, yet they give opposite relations between J and R — confirming no single relation between J and R can be fixed from the given information.

Since both conclusions reduce to the same unprovable claim (J > R), neither Conclusion I nor Conclusion II is true.

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