In this question, the relationship between different elements is shown in the…
2025
In this question, the relationship between different elements is shown in the statements. The statements are followed by two conclusions. Study the conclusions based on the given statements and select the appropriate answer:
Statements: P ≥ M = O < D; R > O = T; R < H
Conclusions:
I. H > M
II. P ≥ T
Answer: D. If both conclusions I and II are true — In statement-and-conclusion inequality puzzles, combine the given relations using two rules: substitute equal terms freely (if A = B, replace A with B…
- A.
If only conclusion I is true
- B.
If only conclusion II is true
- C.
If either conclusion I or II is true
- D.
If both conclusions I and II are true
- E.
If neither conclusion I nor II is true
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Correct answer: D
In statement-and-conclusion inequality puzzles, combine the given relations using two rules: substitute equal terms freely (if A = B, replace A with B anywhere), and chain inequalities transitively only across an unbroken run of the same or compatible direction (A > B and B > C give A > C; A ≥ B and B = C give A ≥ C). A conclusion is definitely true only when it can be derived this way from the full statement set.
The statements give M = O and O = T, so M = O = T — these three quantities are chained by equality.
The statements also give R > O and R < H (that is, H > R), so H > R > O. Since M = O, this chain gives H > M, so Conclusion I (H > M) is definitely true.
The statements give P ≥ M. Since M = T (from step 1), substituting gives P ≥ T, so Conclusion II (P ≥ T) is definitely true.
Statement O < D involves D, but neither conclusion mentions D — Conclusion I compares H and M, and Conclusion II compares P and T — so this statement plays no role in evaluating either conclusion, even though D is chained above O (and hence above M and T) by the O < D inequality.
As a confirming check on the symbolic derivation above, assign values satisfying every statement: O = T = M = 5, D = 10, R = 6, H = 7, P = 6. Verify: P ≥ M (6 ≥ 5), M = O (5 = 5), O < D (5 < 10), R > O (6 > 5), O = T (5 = 5), R < H (6 < 7) — all hold. Then H > M (7 > 5) and P ≥ T (6 ≥ 5) both hold in this assignment, consistent with the derivation.
Both conclusions I and II are true.