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Difficulty: HardIdentifying Sufficient Assumptions

Urban planner: A public transit initiative successfully reduces citywide traffic congestion only if its total end-to-end commute time is strictly less than the equivalent journey by private automobile. The proposed underground maglev system will feature longer passenger wait times at terminals than the city's current express bus network. Consequently, the proposed maglev system will fail to alleviate citywide traffic congestion.

Which one of the following, if assumed, enables the conclusion to be properly drawn?

  1. Any transit system with longer terminal wait times than the city's express bus network has a total end-to-end commute time that is at least as long as an equivalent journey by private automobile.Answer
  2. B
    If a public transit initiative's total end-to-end commute time is strictly less than an equivalent journey by private automobile, it will successfully reduce citywide traffic congestion.
  3. C
    Any transit system whose total end-to-end commute time is at least as long as an equivalent journey by private automobile features longer terminal wait times than the express bus network.
  4. D
    Most transit systems with longer terminal wait times than the city's express bus network have a total end-to-end commute time that exceeds an equivalent journey by private automobile.
  5. E
    The proposed underground maglev system will have a total end-to-end commute time that is significantly longer than that of the city's current express bus network.

Answer

The assumption that any transit system with longer terminal wait times than the express bus network has a commute time at least as long as an automobile journey.
To prove the maglev will fail to alleviate congestion, we must show it fails the necessary condition provided in the first sentence (meaning its commute time must NOT be strictly less than an automobile journey). Since the only evidence given about the maglev is that its wait times are longer than the express bus network, the correct assumption must mathematically link this specific evidence to the failure of the necessary condition. The correct choice does exactly this: Wait time > Bus -> Commute Time >= Automobile. This triggers the contrapositive and guarantees the conclusion.

Step-by-Step Solution

1
Deconstruct the first premise into formal conditional logic.
Reduce Congestion -> Commute Time < Automobile.
Identifying the 'only if' condition establishes the necessary requirement for success.
2
Determine the contrapositive of the first premise, which is what the conclusion relies upon.
If Commute Time is NOT < Automobile (i.e., it is >= Automobile) -> WILL NOT Reduce Congestion.
The argument concludes that the maglev will fail to reduce congestion, so we must trigger this contrapositive.
3
Identify the remaining premise and the logical gap.
Premise given: Maglev Wait Time > Bus Wait Time. Gap: We must logically link 'Maglev Wait Time > Bus Wait Time' to 'Commute Time >= Automobile'.
A sufficient assumption must perfectly bridge the new evidence in the premises to the required trigger for the conclusion.
4
Evaluate the options to find the one that explicitly provides this conditional bridge.
The correct option states: Wait Time > Bus Wait Time -> Commute Time >= Automobile.
This provides 100% logical closure, forcing the conclusion to be true.

Key Concept

Identifying Sufficient Assumptions (Contrapositive Bridging)
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Identifying Sufficient Assumptions

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