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Difficulty: EasyPercentages vs. Numbers Flaws

University Administrator: Ten years ago, 15 percent of the enrolled students at our university were majoring in the humanities. This year, only 10 percent of our enrolled students are majoring in the humanities. Therefore, the actual number of humanities majors on campus today must be lower than it was ten years ago.

Which one of the following most accurately describes the flaw in the administrator's reasoning?

  1. A
    fails to establish a causal connection between the passage of time and the decline in humanities enrollment
  2. B
    relies on an unstated assumption regarding the academic preferences of students at comparable universities
  3. presumes, without providing justification, that a decrease in a proportion necessarily indicates a decrease in a total quantityAnswer
  4. D
    fails to distinguish the primary conclusion about current student numbers from a subsidiary premise about past enrollment percentages
  5. E
    inappropriately treats evidence about a specific percentage of students as if it provided information about the majority of the student body

Answer

The correct answer identifies that the argument mistakenly assumes a drop in percentage guarantees a drop in the absolute number of students.
The argument commits a classic percentages-versus-numbers fallacy. It uses evidence about a declining percentage (from 15 percent to 10 percent) to draw a conclusion about a declining absolute number. This reasoning is flawed because it fails to account for the total size of the university's student body. If the total number of enrolled students has increased substantially over the last ten years, the actual number of humanities majors could have increased even as their proportional share of the student body decreased.

Step-by-Step Solution

1
Identify the premises of the argument.
Ten years ago, humanities majors made up 15 percent of the student body. Today, they make up 10 percent.
Understanding the evidence provided is the first step in evaluating an argument's validity.
2
Identify the main conclusion.
The actual number of humanities majors today is lower than it was ten years ago.
Isolating the conclusion shows what the author is trying to prove.
3
Compare the evidence to the conclusion to find the gap.
The evidence is entirely in percentages (proportions), but the conclusion makes a claim about actual numbers (absolute quantities).
This mismatch between the type of evidence and the type of conclusion is the core of the logical flaw.
4
Evaluate why the gap makes the argument vulnerable.
To calculate the actual number of humanities majors, one needs both the percentage AND the total number of enrolled students. If the total university enrollment grew drastically over ten years, 10 percent of today's large student body could be a greater actual number than 15 percent of the smaller student body from ten years ago.
This proves that the conclusion does not logically follow from the premises.

Key Concept

Percentages vs. Numbers Flaws
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Topics

Percentages vs. Numbers Flaws

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