Question

Difficulty: MediumMulti-Statement Boolean Evaluation

The table below presents operational data for seven regional flight routes operated by an airline during Q1 2026:

Route CodeDistance (miles)Flights ScheduledOn-Time Arrival RateAverage Passenger Load FactorFuel Consumption (gallons/flight)
R-10145012088%82%1,400
R-1028209075%86%2,300
R-1031,2506092%78%3,600
R-10431015084%74%1,100
R-1059608080%90%2,850
R-1061,5004594%85%4,200
R-10768011085%88%1,950

Match each of the following statements to its corresponding truth value and evaluation justification based on the table.

  • Statement I: For all routes with a distance greater than 800 miles, the median On-Time Arrival Rate is greater than 85%.Evaluates to True because the median On-Time Arrival Rate for the four qualifying routes (75%, 80%, 92%, 94%) is 86%.
  • Statement II: The route with the highest Average Passenger Load Factor also has the fewest total number of scheduled flights.Evaluates to False because the route with the highest load factor (R-105 with 90%) scheduled 80 flights, whereas R-106 scheduled the fewest (45 flights).
  • Statement III: The ratio of Fuel Consumption per flight to Distance is strictly decreasing as Route Distance increases across all seven routes.Evaluates to False because the fuel-to-distance ratio increases from R-102 (approximately 2.80 gallons per mile) to R-105 (approximately 2.97 gallons per mile).

Answer

Statement I matches with the evaluation of True (median rate is 86%). Statement II matches with the evaluation of False (R-105 has 80 flights while minimum is 45). Statement III matches with the evaluation of False (the ratio increases from R-102 to R-105).
Each statement is evaluated against the quantitative data provided in the table. Statement I correctly identifies the four routes exceeding 800 miles and calculates their median as 86%. Statement II correctly identifies that R-105 has the highest load factor (90%) but 80 flights, whereas R-106 has the minimum flights (45). Statement III correctly identifies a counterexample where the fuel-to-distance ratio increases from R-102 to R-105.

Step-by-Step Solution

1
Filter and compute the median for Statement I.
Qualifying routes (>800 miles): R-102 (75%), R-105 (80%), R-103 (92%), R-106 (94%). Sorted rates: [75%, 80%, 92%, 94%]. Median = \(\frac{80\% + 92\%}{2} = 86\%\) > 85%.
Identify sub-population based on distance criterion and determine the median of an even-sized dataset.
2
Locate maximum load factor and compare scheduled flights for Statement II.
Max load factor = 90% (R-105, 80 flights). Fewest flights overall = 45 flights (R-106). Since 80 != 45, statement is False.
Identify row-level extrema across two independent columns (Load Factor and Flights Scheduled).
3
Calculate rates/ratios for Statement III across increasing distances.
R-102 (820 miles): \(\frac{2300}{820} \approx 2.805\) gal/mi. R-105 (960 miles): \(\frac{2850}{960} = 2.96875\) gal/mi. Ratio increases, so trend is not strictly decreasing.
Test monotonic trend hypothesis by evaluating specific calculated ratios across sorted distances.

Key Concept

Multi-statement boolean verification requiring subset filtering, descriptive statistics (median of even-sized set), cross-column extrema matching, and rate trend testing.
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