Ordered relations: A > B, B ≥ C = D < E. Which conclusions follow? I) C < A; II) D ≤ B.
Verbal Reasoning
Mathematical Operations
Difficulty: Easy
Choose an option
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AIf only conclusion I follows
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BIf only conclusion II follows
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CIf both conclusions I and II follow
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DIf neither conclusion I nor II follows
Answer
Correct Answer: If both conclusions I and II follow
Explanation
Introduction / Context:Use the given equalities and inequalities to compare C with A and D with B.
Given Data / Assumptions:
- A > B
- B ≥ C = D
- D < E
Concept / Approach:From B ≥ C and A > B, it follows A > C, so C < A (I true). Also B ≥ D by B ≥ C = D, hence D ≤ B (II true).
Step-by-Step Solution: C = D ≤ B < A ⇒ C < A and D ≤ B.
Verification / Alternative check:Choose values: C=D=3, B=3 or 4, A=5. Both statements hold.
Why Other Options Are Wrong:Both conclusions follow; not “only” or “neither”.
Common Pitfalls:Missing that “≥” permits equality; the conclusion about ≤ is thus appropriate.
Final Answer:If both conclusions I and II follow