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Difficulty: Very hardAvoiding Out-of-Scope and 'Could Be True' Inference Traps

In a recent study evaluating corporate restructuring in high-tech manufacturing firms from 2018 to 2024, researchers observed that every firm that reduced its middle-management workforce by more than 20% simultaneously increased its expenditure on automated workflow software by at least 30%. Furthermore, none of the firms that increased their software expenditure by at least 30% experienced a drop in quarterly operating margins during the study period. However, more than half of all manufacturing firms in the study that retained their entire middle-management workforce reported a decrease in annual R&D allocation.

If the statements above are all true, which of the following must also be true based on them?

  1. No high-tech manufacturing firm in the study that reduced its middle-management workforce by more than 20% experienced a drop in quarterly operating margins during the study period.Answer
  2. B
    Any high-tech manufacturing firm in the study that increased its expenditure on automated workflow software by at least 30% reduced its middle-management workforce by more than 20%.
  3. C
    Firms in the study that increased their software expenditure by at least 30% did so primarily to prevent a drop in quarterly operating margins.
  4. D
    High-tech manufacturing firms that retained their entire middle-management workforce suffered lower overall net profits than those that reduced middle management by more than 20%.
  5. E
    Firms in the study that did not reduce their middle-management workforce by more than 20% experienced a drop in quarterly operating margins during the study period.

Answer

No high-tech manufacturing firm in the study that reduced its middle-management workforce by more than 20% experienced a drop in quarterly operating margins during the study period.
The passage establishes two formal statements: (1) Every firm reducing middle management by >20% increased software expenditure by ≥30%, and (2) None of the firms increasing software expenditure by ≥30% had a drop in quarterly operating margins. Combining these statements transitively proves that any firm reducing middle management by >20% necessarily avoided a drop in quarterly operating margins. Thus, the statement asserting that no such firm experienced a drop in operating margins must be true.

Step-by-Step Solution

1
Identify and symbolize the explicit conditional premises from the text
Premise 1: Reduced middle management >20% → Increased software expenditure ≥30%. Premise 2: Increased software expenditure ≥30% → NO drop in quarterly operating margins.
Mapping the conditional logic allows clear evaluation of valid chain deductions versus invalid reversals or inverses.
2
Synthesize the premises via hypothetical syllogism (transitive property)
Reduced middle management >20% → NO drop in quarterly operating margins.
Since the necessary condition of Premise 1 matches the sufficient condition of Premise 2, a direct link between the initial condition and final result is logically guaranteed.
3
Evaluate the answer choices to identify the strictly necessary deduction and eliminate 'could be true' or out-of-scope traps
The statement asserting that no firm reducing middle management by >20% experienced a drop in quarterly operating margins is logically mandatory.
GMAT Critical Reasoning inference items require a statement that MUST be true without outside assumptions or formal logical fallacies.

Key Concept

Combining Conditional Logic Premises and Avoiding 'Could Be True' / Out-of-Scope Traps
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Topics

Avoiding Out-of-Scope and 'Could Be True' Inference Traps

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