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Difficulty: HardNumerical, Proportion, and Statistical Inferences

In City Y, between 2018 and 2023, the proportion of all daily commuter trips taken via the municipal subway system increased from 20 percent to 30 percent. During this same five-year period, the total number of daily commuter trips taken across all modes of transportation in City Y decreased by 40 percent.

If the statements above are true, which of the following conclusions must also be true regarding daily commuter trips in City Y from 2018 to 2023?

  1. A
    The municipal subway system experienced an increase in the absolute volume of daily passengers carried between 2018 and 2023.
  2. B
    The total resident population of City Y declined significantly between 2018 and 2023.
  3. The total number of daily commuter trips taken via the municipal subway system was lower in 2023 than in 2018.Answer
  4. D
    The total number of daily commuter trips taken via non-subway modes of transportation remained unchanged over the five-year period.
  5. E
    More commuters in City Y chose subway transit over personal automobiles in 2023 than did so in 2018.

Answer

The total number of daily commuter trips taken via the municipal subway system was lower in 2023 than in 2018.
The correct option is derived directly through exact percentage calculations. By establishing total 2018 daily commuter trips as TT, subway trips accounted for 20%20\% of TT, or 0.20T0.20T. Because total trips across all modes dropped by 40%40\% by 2023, total trips in 2023 equaled 0.60T0.60T. In 2023, subway trips accounted for 30%30\% of this reduced total (0.30×0.60T=0.18T0.30 \times 0.60T = 0.18T). Comparing 0.18T0.18T to 0.20T0.20T demonstrates a logical and mathematically inescapable reduction in total subway trips.

Step-by-Step Solution

1
Define an initial baseline for total daily commuter trips.
Let the total number of daily commuter trips in 2018 be represented as TT.
Establishing a baseline variable allows quantitative comparisons across years.
2
Calculate the absolute number of subway trips in 2018.
Subway trips in 2018 = 0.20×T=0.20T0.20 \times T = 0.20T.
The passage states that 20 percent of all commuter trips were taken via subway in 2018.
3
Determine the total number of daily commuter trips in 2023 after the specified decrease.
Total trips in 2023 = T×(1−0.40)=0.60TT \times (1 - 0.40) = 0.60T.
The total number of daily commuter trips across all modes decreased by 40 percent.
4
Calculate the absolute number of subway trips in 2023 and compare with 2018.
Subway trips in 2023 = 0.30×0.60T=0.18T0.30 \times 0.60T = 0.18T. Since 0.18T<0.20T0.18T < 0.20T, absolute subway trips decreased.
Comparing 0.18T0.18T to 0.20T0.20T shows a net decrease in absolute subway trip volume.

Key Concept

Numerical and Statistical Inferences: Base Rate Fallacy and Percentage vs. Absolute Quantity
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Topics

Numerical, Proportion, and Statistical Inferences

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