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Soru

Zorluk: OrtaDrawing Inferences and Valid Conclusions

From 2015 to 2023, all municipal transit authorities in Region M derived their annual operational funding exclusively from passenger fares and regional tax subsidies. In 2019, a regional ordinance mandated that any transit authority receiving more than 40 percent of its operational funding from passenger fares must provide discounted passes to senior citizens. Furthermore, under the ordinance, no transit authority could receive regional tax subsidies if passenger fares accounted for more than 50 percent of its operational funding.

If the statements above are true, which of the following must also be true about municipal transit authorities in Region M after the 2019 ordinance took effect?

  1. A
    Municipal transit authorities that provided discounted passes to senior citizens experienced a net decrease in total operational funding after 2019.
  2. B
    Any municipal transit authority that provided discounted passes to senior citizens derived at least 40 percent of its operational funding from passenger fares.
  3. Any municipal transit authority whose passenger fares accounted for more than 50 percent of its operational funding was required to provide discounted passes to senior citizens.Cevap
  4. D
    Most municipal transit authorities in Region M altered their fare structures after 2019 in order to remain eligible for regional tax subsidies.
  5. E
    A municipal transit authority that received regional tax subsidies was prohibited from offering discounted passes to senior citizens.

Cevap

Any municipal transit authority whose passenger fares accounted for more than 50 percent of its operational funding was required to provide discounted passes to senior citizens.
The correct response logically follows by synthesizing the rules given in the stem. If passenger fares exceeded 50 percent of operational funding, the authority could receive no regional tax subsidies. Because operational funding came exclusively from fares and subsidies, an authority receiving no subsidies derived 100 percent of its funding from fares. Because 100 percent is greater than 40 percent, the authority was required under the 2019 ordinance to provide discounted passes to senior citizens.

Adım Adım Çözüm

1
Identify the strict constraints provided in the premises.
Constraint 1: Total Funding = Passenger Fares + Tax Subsidies (exclusively).
Constraint 2: If Fares > 40%, Senior Discounts are mandatory.
Constraint 3: If Fares > 50%, Tax Subsidies = 0.
Establishing the exact formal logic parameters allows synthesizing multi-sentence premises.
2
Analyze the condition where Fares > 50%.
By Constraint 3, Tax Subsidies must equal 0%. Combined with Constraint 1, Fares must account for 100% of total operational funding.
Synthesizing the exclusive funding sources with the subsidy restriction reveals the precise percentage of funding coming from fares.
3
Apply Constraint 2 to the calculated result.
Since 100% is greater than 40%, the condition for mandatory senior discounts is satisfied.
Deducing that Fares = 100% guarantees that the > 40% threshold is met, making the requirement inescapable.

Anahtar Kavram

Drawing Deductive Inferences from Synthesized Constraints
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Konular

Drawing Inferences and Valid Conclusions

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