Statement — Many business offices are in buildings with two to eight floors. Rule — If a building has more than three floors, then that building has a lift (elevator). Question — Which conclusion is necessarily true?
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AAll floors in every such building can be reached by lifts.
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BOnly floors above the third floor have lift service.
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CAny building that has a fifth floor necessarily has a lift.
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DSecond-floor buildings never have lifts.
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ENone of the above.
Answer
Correct Answer: Any building that has a fifth floor necessarily has a lift.
Explanation
Introduction / Context:We must apply a conditional rule: floors > 3 → has lift. The task is to select the logically compelled consequence, not speculative statements about coverage of floors or buildings with ≤ 3 floors.
Given Data / Assumptions:
- Domain: office buildings with 2–8 floors.
- Conditional: If a building’s floor-count > 3, then the building has a lift.
- No promises are made for 2- or 3-floor buildings.
Concept / Approach:For any building to “have a fifth floor,” its floor-count is at least five, hence > 3. Therefore, by the rule, it must have a lift. Claims about “only above third” or “all floors reachable” exceed the given information.
Step-by-Step Solution:
Option A: Overreach; the rule states existence of a lift, not its reach.Option B: Adds a restriction (“only”) not present in the rule.Option C: Direct application of the conditional; compelled.Option D: Talks about 2 floors (≤ 3), which the rule leaves open.Option E: Incorrect since C follows.Verification / Alternative check:Any 5-, 6-, 7-, or 8-floor building must satisfy the antecedent and therefore has a lift.
Why Other Options Are Wrong:
A and B invent details; D asserts a negative beyond scope.Common Pitfalls:Confusing “has a lift” with operational details like which floors are served.
Final Answer:Any building that has a fifth floor necessarily has a lift.