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Difficulty: EasyMulti-Statement Boolean Evaluation

The table below provides financial performance metrics for five corporate divisions of Vertex Global:

DivisionRevenue ($M)Operating Cost ($M)Profit Margin (%)Employees
Alpha1209025.0%450
Beta20017015.0%800
Gamma805037.5%250
Delta15010530.0%500
Epsilon30027010.0%1,200

Evaluate the following statement as True or False based on the provided table:

Statement: For more than half of the divisions listed, the Revenue per employee strictly exceeds $250,000.

Answer: Answer

Answer

True. Exactly 3 out of the 5 divisions (Alpha, Gamma, and Delta) have a Revenue per employee greater than $250,000, which satisfies the condition of being more than half.
The correct evaluation is True because calculating the ratio of Revenue to Employees for each of the five divisions shows that Alpha (266,667),Gamma(266,667), Gamma ( 320,000), and Delta (300,000)allhaveaRevenueperemployeeabove300,000) all have a Revenue per employee above 250,000. Three out of five divisions represents 60% of the divisions, which is more than half.

Step-by-Step Solution

1
Understand the condition and metric required
Need to calculate Revenue per employee (Revenue in dollars divided by number of employees) for each division and check if it is strictly greater than $250,000.
The statement specifies 'strictly exceeds $250,000' and applies to 'more than half' (at least 3 out of 5) of the divisions.
2
Compute Revenue per employee for each division
Alpha: 120M/450=120M / 450 = 266,667; Beta: 200M/800=200M / 800 = 250,000; Gamma: 80M/250=80M / 250 = 320,000; Delta: 150M/500=150M / 500 = 300,000; Epsilon: 300M/1,200=300M / 1,200 = 250,000.
Performing explicit division allows precise comparison against the threshold value of $250,000.
3
Evaluate the threshold condition across all divisions
Divisions exceeding 250,000:Alpha,Gamma,Delta(Total=3divisions).Divisionsequalto250,000: Alpha, Gamma, Delta (Total = 3 divisions). Divisions equal to 250,000: Beta, Epsilon (Total = 2 divisions).
Values exactly equal to $250,000 do not satisfy 'strictly exceeds'.
4
Determine overall Boolean truth value
3 out of 5 divisions is 60%, which is more than half (50%). Thus, the statement evaluates to True.
Comparing the count of meeting divisions (3) against half of the dataset size (2.5).

Key Concept

Table Analysis & Boolean Statement Evaluation
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Topics

Multi-Statement Boolean Evaluation

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