Examkin

Question

Difficulty: Very hardIdentifying Necessary Assumptions

Urban planner: Over the last decade, the percentage of City M's residents who commute by bicycle has tripled. During this exact same timeframe, the total number of traffic accidents involving bicycles in the city has only doubled. Therefore, the comprehensive network of protected bicycle lanes installed a decade ago has successfully achieved its goal of making bicycle commuting safer per rider.

Which one of the following is an assumption on which the urban planner's argument depends?

  1. A
    The absolute number of bicycle commuters in City M has increased by a factor of at least three over the last decade.
  2. B
    The implementation of the protected bicycle lanes was the primary reason that the percentage of residents commuting by bicycle tripled.
  3. City M has not experienced a population decline over the last decade severe enough to prevent the absolute number of bicycle commuters from doubling.Answer
  4. D
    The criteria used by City M to classify an incident as a bicycle-related traffic accident have remained exactly the same over the last decade.
  5. E
    The total number of traffic accidents in City M, including those not involving bicycles, has decreased over the last decade.

Answer

The argument depends on the assumption that the city's overall population did not drop so drastically that a tripled percentage failed to double the absolute number of riders.
The conclusion claims that bicycling is 'safer per rider' (meaning a lower ratio of accidents to riders). We know the absolute number of accidents doubled. Therefore, for the ratio to decrease, the absolute number of riders must have more than doubled. The premise only tells us that the *percentage* of the population that rides has tripled. If the city's total population had plummeted by more than 33% over the decade, a tripled percentage would yield an absolute number of riders that grew by less than a factor of two. If riders grew by less than 2x but accidents grew by 2x, the danger per rider would actually increase. Thus, the argument absolutely requires that the population did not decline this severely.

Step-by-Step Solution

1
Identify the core structure of the urban planner's argument, separating premises from the main conclusion.
Premises: The percentage of residents biking tripled; the total number of bike accidents doubled. Conclusion: Bicycle commuting has become safer per rider.
Understanding the logical gap requires isolating the exact evidence provided and the specific causal claim being made.
2
Analyze the mathematical relationship required to prove the conclusion 'safer per rider'.
For biking to be 'safer per rider', the ratio of accidents to total riders must have decreased. Since accidents doubled (increased by a factor of 2), the absolute number of riders must have more than doubled.
The conclusion relies on a rate (accidents per rider), but the premises provide a percentage of a population and an absolute number of accidents.
3
Identify the logical gap between the premises and the required mathematical relationship.
The premise states the *percentage* of residents biking tripled, but we need the *absolute number* of bikers to have at least doubled. This connects the population size to the absolute number of riders.
If the total population of the city decreased drastically, a tripled percentage might still result in fewer than twice as many absolute riders.
4
Apply the Negation Technique to the correct option to verify it is a necessary assumption.
Negating the correct option yields: 'City M HAS experienced a population decline severe enough to prevent the absolute number of riders from doubling.' If riders increased by less than 2x, but accidents increased by exactly 2x, the accident rate per rider went UP, destroying the conclusion.
A statement is a necessary assumption if and only if its logical negation causes the argument to collapse.

Key Concept

Identifying Necessary Assumptions involving Proportions vs. Absolute Numbers
Rate this question

Topics

Identifying Necessary Assumptions

More questions from this topic