Ordered relations: Q = Z, C ≥ G, G ≥ Q, Q ≥ R. Which conclusions follow? I) G ≥ Z; II) C ≥ R.
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:We combine equalities and inequalities to deduce new ones.
Given Data / Assumptions:
- Q = Z
- C ≥ G
- G ≥ Q
- Q ≥ R
Concept / Approach:Use substitution and transitivity: if G ≥ Q and Q = Z, then G ≥ Z; if C ≥ G and G ≥ R (from G ≥ Q ≥ R), then C ≥ R.
Step-by-Step Solution: G ≥ Q and Q = Z ⇒ G ≥ Z (I true). Q ≥ R and G ≥ Q ⇒ G ≥ R; C ≥ G ⇒ C ≥ R (II true).
Verification / Alternative check:Pick numbers satisfying the premises (e.g., C=5, G=4, Q=3, Z=3, R=2). Both conclusions hold.
Why Other Options Are Wrong:Not “only I” or “only II”; both follow.
Common Pitfalls:Missing the intermediate step G ≥ R before concluding C ≥ R.
Final Answer:If both conclusions I and II follow