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Difficulty: MediumFlaw in the Reasoning

Retail Manager: We should shift our promotional focus from weekend afternoon events to weekday evening events. At our most recent weekday evening event, 40 percent of the attendees purchased a premium membership. By contrast, at our most recent weekend afternoon event, only 15 percent of the attendees purchased a premium membership. Clearly, the weekday evening event generated a greater total number of premium membership sales than the weekend afternoon event did.

The reasoning in the retail manager's argument is most vulnerable to criticism on the grounds that the argument:

  1. confuses a claim about the percentage of a group exhibiting a certain behavior with a claim about the absolute number of individuals exhibiting that behavior.Answer
  2. B
    takes a mere correlation between the timing of an event and the purchasing behavior of attendees as proof of a causal relationship.
  3. C
    treats a condition that is necessary for generating a high number of sales as a condition that is sufficient to do so.
  4. D
    relies on an ambiguous use of the phrase 'premium membership' throughout the argument.
  5. E
    mistakes a subsidiary conclusion about the number of memberships sold for the main conclusion of the argument.

Answer

The correct answer is the option stating that the argument confuses a percentage with an absolute number.
The argument commits a classic 'percentage versus number' fallacy. It draws a definitive conclusion about a total absolute quantity (the total number of sales) based purely on comparative percentages (40 percent vs. 15 percent). This reasoning is flawed because it fails to establish the total size of the two groups being compared. If 1,000 people attended the weekend event and only 50 attended the weekday event, 15 percent of the weekend crowd (150 sales) would vastly exceed 40 percent of the weekday crowd (20 sales).

Step-by-Step Solution

1
Identify the premises and the conclusion of the argument.
Premise 1: 40% of weekday event attendees bought a membership. Premise 2: 15% of weekend event attendees bought a membership. Conclusion: The weekday event resulted in a greater total number of sales.
Deconstructing the argument is necessary to evaluate the logical relationship between the evidence and the claim.
2
Analyze the logical gap between the premises and the conclusion.
The premises offer relative, proportional data (percentages), while the conclusion makes a definitive claim about an absolute quantity (total number of sales).
Recognizing the shift from proportional language to absolute language reveals the core vulnerability.
3
Formulate a description of the flaw.
The argument assumes that a higher percentage guarantees a higher total number, entirely ignoring the total size of the two groups (the number of attendees at each event).
To accurately answer the question, one must describe the error in abstract logical terms.

Key Concept

Flaw in the Reasoning: Percentages vs. Numbers
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Topics

Flaw in the Reasoning

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