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Question

Difficulty: HardQuantifier Logic (Some, Most, All)

Most urban planners employed by the city hold degrees in architecture. Furthermore, most urban planners employed by the city have worked in the public sector for at least five years. According to municipal guidelines, all individuals who have worked in the public sector for at least five years are eligible for the municipal leadership grant.

Which one of the following statements must be true based on the information above?

  1. A
    Anyone employed as an urban planner by the city is eligible for the municipal leadership grant.
  2. B
    Any individual who is eligible for the municipal leadership grant has worked in the public sector for at least five years.
  3. At least one person holding a degree in architecture is eligible for the municipal leadership grant.Answer
  4. D
    Most of the city's urban planners who hold degrees in architecture are eligible for the municipal leadership grant.
  5. E
    Most of the individuals who are eligible for the municipal leadership grant are employed as urban planners by the city.

Answer

At least one person holding a degree in architecture is eligible for the municipal leadership grant.
The correct answer properly identifies the guaranteed overlap between two 'most' statements applied to the same group. Since most urban planners have architecture degrees and most have five years of public sector experience, at least one person must have both. Furthermore, because the stimulus states that ALL individuals with five years of public sector experience are eligible for the grant, that specific overlapping person (who is an architect) must be eligible for the grant.

Step-by-Step Solution

1
Analyze the first two premises regarding 'most' relationships within a single group.
Identify that 'most' urban planners are architects, and 'most' urban planners have five years of public sector experience.
When two 'most' statements apply to the exact same population (urban planners), the two subgroups must logically overlap by at least one member.
2
Form a deduction from the overlapping 'most' statements.
Conclude that there is at least one urban planner who is BOTH an architect AND has five years of public sector experience.
If group A is >50% of the total and group B is >50% of the total, their combined sum exceeds 100%, meaning they must share at least one individual.
3
Apply the conditional 'all' rule to the deduced overlap.
Because the overlapping individual has five years of public sector experience, and ALL such individuals are eligible for the grant, this individual must be eligible.
Applying a universal rule ('all') to a specific subject confirms a property of that subject.
4
Synthesize the final deduction.
Since the overlapping individual is an architect and is eligible for the grant, it must be true that at least one person holding an architecture degree is eligible for the grant.
This directly matches the logically proven facts.

Key Concept

Deducing overlap from two 'most' statements about the same subject group, and chaining that overlap with an 'all' statement.
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Topics

Quantifier Logic (Some, Most, All)

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