Given signs signify something and on that basis, assume the given statements…

2024

Given signs signify something and on that basis, assume the given statements to be true and find which of the two conclusions I and II is/are definitely true.

A+B means A is greater than B

A-B means A is less than B

A=B means A is greater than or equal to B

A*B means A is not equal to B

A/B means A is equal to B

Statement:- P/Q, Q+R, R=S

Conclusions:-

I. P/R

II. P=Q

  1. A.

    Only conclusion I is true.

  2. B.

    Only conclusion II is true.

  3. C.

    Neither conclusion I nor conclusion II is true.

  4. D.

    Both conclusions I and II are true.

Show answer & explanation

Correct answer: B

Concept: In coded-inequality reasoning, each symbol stands for a fixed relation. Decode every statement into its real mathematical relation first, chain the relations that share a common term, and only then test whether each conclusion's own coded relation is FORCED to hold in every case consistent with that chain - not merely possible in some case.

  1. Decode the three coded relations: P/Q means P is exactly equal to Q; Q+R means Q is strictly greater than R; R=S means R is greater than or equal to S.

  2. Combine the first two: since P equals Q exactly and Q is strictly greater than R, P must also be strictly greater than R in every valid case - this is a forced, non-equal relation.

  3. Test conclusion I (P/R, which claims P is exactly equal to R): the chained relation shows P is always strictly greater than R, so an exact equality between them can never hold - conclusion I is not definitely true.

  4. Test conclusion II (P=Q, which claims P is greater than or equal to Q): the statements already establish P equals Q exactly, and an exact equality always satisfies a 'greater than or equal to' test on the same pair - so conclusion II is definitely true.

Cross-check: Check with concrete numbers consistent with the statements, e.g. Q = 5, so P = 5 (from P/Q); pick R = 3, so Q > R holds; pick S = 3 (R is greater than or equal to S holds). Here does P equal R? 5 vs 3 - no, confirming conclusion I fails. Does P is greater than or equal to Q hold? 5 is greater than or equal to 5 - yes, confirming conclusion II holds. Any other valid choice of R less than Q and S less than or equal to R gives the same outcome, since the chain forces it every time.

Only conclusion II is definitely true.

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