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Difficulty: MediumMulti-Statement Boolean Evaluation

The table below displays Q2 2026 performance data for seven autonomous cargo drone fleets operated by a logistics provider:

Fleet IDTotal Flight HoursOn-Time Delivery Rate (%)Payload Capacity (kg)Operating Cost per Km ($)
Alpha-142094.5%15012.40
Beta-255091.0%20015.80
Gamma-331096.0%12010.50
Delta-460088.5%25018.20
Epsilon-548093.0%18014.10
Zeta-639097.5%14011.80
Eta-751089.0%22016.50

Consider the following three statements:

I. The median Operating Cost per Km among fleets with a Payload Capacity of at least 150 kg is greater than $15.00.
II. Among fleets with an On-Time Delivery Rate above 92.0%, the fleet with the lowest Total Flight Hours also has the lowest Operating Cost per Km.
III. The mean Total Flight Hours for fleets with a Payload Capacity under 180 kg is greater than 400 hours.

Which of the statements evaluate to True based on the table?

  1. A
    Only Statement I is true
  2. B
    Only Statement II is true
  3. Exactly Statements I and II are trueAnswer
  4. D
    Exactly Statements II and III are true
  5. E
    All three statements (I, II, and III) are true

Answer

Statements I and II are True, while Statement III is False.
Evaluating each statement systematically shows that Statement I is True because the sorted costs for eligible fleets are 12.40,12.40, 14.10, 15.80,15.80, 16.50, 18.20,givingamedianof18.20, giving a median of 15.80 (which exceeds 15.00).StatementIIisTruebecauseGamma−3meetsthedeliveryratethreshold(>92.015.00). Statement II is True because Gamma-3 meets the delivery rate threshold (> 92.0%) and holds both the minimum flight hours (310) and minimum operating cost ( 10.50) among those fleets. Statement III is False because the filtered fleets (Alpha-1, Gamma-3, Zeta-6) have a mean flight hour of 373.33 hours, which is less than 400 hours. Thus, exactly Statements I and II are true.

Step-by-Step Solution

1
Evaluate Statement I by filtering and sorting Operating Cost per Km for fleets with Payload Capacity ≥150 kg\ge 150\text{ kg}.
Fleets meeting the condition are Alpha-1 (150 kg), Beta-2 (200 kg), Delta-4 (250 kg), Epsilon-5 (180 kg), and Eta-7 (220 kg). Their operating costs sorted from lowest to highest are 12.40,12.40, 14.10, 15.80,15.80, 16.50, 18.20.Themedianofthese5valuesisthe3rdvalue,whichis18.20. The median of these 5 values is the 3rd value, which is 15.80. Since 15.80>15.80 > 15.00, Statement I is TRUE.
Finding the median of an odd number of items requires ordering the subset values and taking the middle element.
2
Evaluate Statement II by filtering fleets with On-Time Delivery Rate >92.0%> 92.0\%.
Fleets meeting the condition are Alpha-1 (94.5%), Gamma-3 (96.0%), Epsilon-5 (93.0%), and Zeta-6 (97.5%). Among these 4 fleets, Gamma-3 has the lowest Total Flight Hours (310 hours) and also the lowest Operating Cost per Km ($10.50). Therefore, Statement II is TRUE.
Cross-column multi-condition filtering verifies both the minimum flight hours and minimum operating cost within the subset.
3
Evaluate Statement III by calculating the mean Total Flight Hours for fleets with Payload Capacity <180 kg< 180\text{ kg}.
Fleets with Payload Capacity strictly less than 180 kg are Gamma-3 (120 kg), Zeta-6 (140 kg), and Alpha-1 (150 kg). (Epsilon-5 is excluded as its payload is exactly 180 kg). Their flight hours are 310, 390, and 420. Mean = 310+390+4203=11203≈373.33 hours\frac{310 + 390 + 420}{3} = \frac{1120}{3} \approx 373.33\text{ hours}. Since 373.33<400373.33 < 400, Statement III is FALSE.
Computing the arithmetic mean of the correctly filtered subset shows it is below the threshold of 400 hours.

Key Concept

Multi-Statement Boolean Evaluation on structured tables involving subset filtering, median calculation, and conditional verification.
Estimated Time:2m 0s
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Topics

Multi-Statement Boolean Evaluation

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