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Difficulty: HardMulti-Statement Boolean Evaluation

The table below presents operational and usage metrics for eight branch locations within a regional public library network during 2025:

Branch CodeTotal Volumes (thousands)Active Cardholders (thousands)Annual Circulations (thousands)Operating Expenses ($ thousands)Digital Resource Accesses (thousands)
CEN450609003,600300
NOR120253001,000150
EAS801616064080
WES15020240960120
SOU200405001,500250
RIV901822572090
HAR11022220880110
UPL160324801,440160

Consider the following three statements regarding the data:

I. The median number of Annual Circulations among the branches with more than 20,000 Active Cardholders is greater than 350,000.
II. For Eastgate (EAS), the ratio of Annual Circulations per Total Volume is higher than that for West End (WES).
III. Exactly three branches satisfy both of the following conditions: Operating Expenses per Circulation are strictly less than $4.00, AND Digital Resource Accesses exceed 140,000.

Which of the following correctly identifies the truth values (True or False) of Statements I, II, and III, respectively?

  1. Statement I: True; Statement II: True; Statement III: TrueAnswer
  2. B
    Statement I: False; Statement II: True; Statement III: True
  3. C
    Statement I: True; Statement II: False; Statement III: True
  4. D
    Statement I: True; Statement II: True; Statement III: False
  5. E
    Statement I: False; Statement II: False; Statement III: True

Answer

Statement I: True; Statement II: True; Statement III: True
The correct option is the one identifying all three statements as True. Statement I is True because the median circulation of the 5 filtered branches is 480,000, which exceeds 350,000. Statement II is True because EAS has a circulation-to-volume ratio of 2.0 compared to 1.6 for WES. Statement III is True because NOR, SOU, and UPL are the exactly three branches that satisfy both expenses per circulation < $4.00 and digital accesses > 140,000.

Step-by-Step Solution

1
Evaluate Statement I by filtering and sorting.
Branches with Active Cardholders > 20 (in thousands) are CEN (60), NOR (25), SOU (40), HAR (22), and UPL (32), total 5 branches. Their Annual Circulations (in thousands) are 900, 300, 500, 220, and 480. Sorting these values yields 220, 300, 480, 500, 900. The median (3rd value) is 480 thousand (480,000). Since 480,000 > 350,000, Statement I is True.
Filtering required strict application of the cardholder threshold before ordering the circulation data.
2
Evaluate Statement II by calculating row ratios.
For EAS, Circulations / Volumes = 160 / 80 = 2.0. For WES, Circulations / Volumes = 240 / 150 = 1.6. Since 2.0 > 1.6, Statement II is True.
Ratio comparison requires placing Circulations in the numerator and Volumes in the denominator.
3
Evaluate Statement III using dual-condition logical filtering.
Calculate Operating Expenses (thousands)/AnnualCirculations(thousands)toget thousands) / Annual Circulations (thousands) to get per circulation: CEN (3,600 / 900 = 4.00),NOR(1,000/300=4.00), NOR (1,000 / 300 = 3.33), EAS (640 / 160 = 4.00),WES(960/240=4.00), WES (960 / 240 = 4.00), SOU (1,500 / 500 = 3.00),RIV(720/225=3.00), RIV (720 / 225 = 3.20), HAR (880 / 220 = 4.00),UPL(1,440/480=4.00), UPL (1,440 / 480 = 3.00). Branches with expense per circulation strictly less than $4.00 are NOR, SOU, RIV, and UPL. Among these, Digital Resource Accesses (> 140 thousand) are NOR (150), SOU (250), and UPL (160). RIV has only 90. Exactly 3 branches meet both conditions. Statement III is True.
Strict inequality rules out branches with expenses per circulation equal to $4.00.

Key Concept

Multi-Statement Boolean Evaluation on Tabular Data
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Topics

Multi-Statement Boolean Evaluation

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