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Difficulty: MediumPercentages vs. Numbers Flaws

Software Executive: Over the past three years, the percentage of our company's total revenue generated by mobile applications has steadily declined. In contrast, the percentage of our total revenue generated by enterprise software has grown. Therefore, it is clear that our mobile applications are bringing in less money than they did three years ago.

Which one of the following most accurately describes a flaw in the software executive's reasoning?

  1. draws a conclusion about a decrease in an absolute quantity based solely on evidence regarding a decreasing share of a totalAnswer
  2. B
    presumes, without providing justification, that the growth of the enterprise software sector caused the decline in the mobile applications sector
  3. C
    inappropriately infers that a trend observed within specific divisions of the company must also apply to the company's total revenue
  4. D
    treats a revenue trend that applies to some of the company's products as though it applies to all of the company's products
  5. E
    relies on the unstated premise that mobile applications were previously the primary source of the company's overall revenue

Answer

The correct answer identifies that the argument draws a conclusion about an absolute quantity (actual money brought in) based entirely on a percentage (share of total revenue).
The correct answer accurately describes the logical vulnerability in the executive's reasoning. A percentage is a relative value. A smaller percentage of a much larger total pie can equate to a larger absolute slice than a bigger percentage of a smaller pie. By concluding that the mobile apps are bringing in 'less money' (an absolute quantity) based solely on the fact that their 'percentage' of total revenue dropped, the author commits a fundamental numbers-versus-percentages fallacy.

Step-by-Step Solution

1
Identify the premise of the argument.
The premise is that the percentage of total revenue from mobile applications has declined, while the percentage from enterprise software has grown.
Understanding the exact nature of the evidence (proportions vs. absolute numbers) is required to evaluate the logic.
2
Identify the conclusion drawn by the executive.
The conclusion is that mobile applications are bringing in less money (an absolute amount) than they did three years ago.
Isolating the conclusion allows us to spot the logical leap from the premise.
3
Analyze the relationship between the premise and the conclusion.
The argument assumes that a smaller percentage of a whole guarantees a smaller absolute number, failing to consider that the total size of the whole (overall revenue) may have increased.
This reveals the classic 'Percentages vs. Numbers' flaw, which is the exact vulnerability asked for in the question stem.

Key Concept

Percentages vs. Numbers Flaws
Estimated Time:1m 15s
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Topics

Percentages vs. Numbers Flaws

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