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Difficulty: Very hardDistinguishing Inferences from Assumptions and Speculations

Consider the following passage:

A three-year financial analysis of mid-sized manufacturing firms in Sector K revealed that every firm that fully automated its inventory tracking system achieved a reduction in warehousing overhead costs within twelve months. Furthermore, during those three years, no mid-sized manufacturing firm in Sector K that retained a fully manual inventory system achieved any reduction in warehousing overhead costs. Throughout the period of the analysis, overall energy costs for manufacturing facilities across Sector K decreased substantially.

Statement: Based solely on the information provided in the passage, it must be true that any mid-sized manufacturing firm in Sector K that achieved a reduction in warehousing overhead costs during the three-year period had automated its inventory tracking system at least partially.

Answer: Answer

Answer

True
The evaluated statement is a mathematically valid deduction derived directly from the passage premises via contraposition. Because the passage asserts that no fully manual firm reduced overhead costs, any firm that did reduce overhead costs logically could not be fully manual. Therefore, such a firm must have implemented at least partial automation. This requires zero unstated assumptions or speculative leaps.

Step-by-Step Solution

1
Analyze the given premises and establish their formal logical structure.
Premise 1: Fully Automated Inventory System → Reduced Warehousing Overhead Costs.
Premise 2: Fully Manual Inventory System → NO Reduction in Warehousing Overhead Costs.
Premise 3: Energy costs across Sector K decreased substantially.
Deconstructing the passage into clear logical terms isolates facts from speculation.
2
Formulate the contrapositive of Premise 2.
The logical contrapositive of 'Fully Manual → NO Reduction' is 'Reduction → NOT Fully Manual'.
In formal logic, a conditional statement and its contrapositive are logically equivalent.
3
Evaluate the condition 'NOT Fully Manual'.
If an inventory tracking system is NOT fully manual, it must possess at least partial automation.
Binary categorization between fully manual and non-manual implies any non-manual system incorporates at least some degree of automation.
4
Compare the derived deduction with the evaluated statement.
The deduction confirms that any firm achieving a reduction in warehousing overhead costs MUST have automated its system at least partially. Thus, the statement is a valid logical inference ('Must Be True').
Valid inferences follow strictly from premises without requiring additional unstated assumptions.

Key Concept

Distinguishing Inferences from Assumptions and Speculations
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Distinguishing Inferences from Assumptions and Speculations

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