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Difficulty: HardPercentages vs. Numbers Flaws

Transportation Safety Board Director: A decade ago, mechanical failures accounted for 12%12\% of all commuter train cancellations nationwide. Last year, mechanical failures were responsible for 38%38\% of all commuter train cancellations. Because the standards for classifying a cancellation as due to a 'mechanical failure' have remained entirely unchanged throughout this ten-year period, it is clear that the actual number of commuter trains canceled because of mechanical issues has increased significantly.

The director's reasoning is most vulnerable to criticism on the grounds that it...

  1. draws a conclusion about a change in an absolute quantity based solely on evidence concerning a change in proportions, without providing information about the overall total.Answer
  2. B
    ignores the possibility that the criteria used by the board to define what constitutes a mechanical failure might have been quietly modified during the decade in question.
  3. C
    mistakenly assumes that because mechanical issues are strongly associated with commuter train cancellations, they must be the primary cause of those cancellations.
  4. D
    takes for granted that what is true of most commuter train cancellations over the past decade is also true of all commuter train cancellations.
  5. E
    fails to consider the possibility that the total number of scheduled commuter trains operating nationwide has expanded significantly over the past ten years.

Answer

The argument is flawed because it draws a conclusion about a change in an absolute quantity based solely on evidence concerning a change in proportions, without providing information about the overall total.
The argument concludes that the absolute number of mechanical cancellations went up simply because its share of total cancellations went up (from 12% to 38%). This reasoning is invalid because it assumes the total number of all cancellations remained roughly the same or increased. If the total number of cancellations dropped drastically over the decade, 38% of that new, smaller total could be a smaller absolute number than 12% of the original, larger total. The correct answer accurately identifies this unwarranted leap from percentages to absolute quantities.

Step-by-Step Solution

1
Identify the premises.
Premise 1: 10 years ago, mechanical failures = 12% of total cancellations. Premise 2: Last year, mechanical failures = 38% of total cancellations. Premise 3: Classification standards have not changed.
Understanding the exact evidence provided is required to evaluate the argument's structure.
2
Identify the main conclusion.
The actual number of commuter trains canceled because of mechanical issues has increased significantly.
Locating the conclusion allows you to see the gap between the evidence and the author's claim.
3
Analyze the logical gap (the flaw).
The premises provide percentages of a whole (total cancellations), but the conclusion makes a claim about an absolute number (the number of mechanical cancellations).
A percentage can only tell you about an absolute number if you know the size of the total baseline.
4
Test the reasoning with hypothetical numbers.
If there were 10,000 total cancellations a decade ago, 12% is 1,200. If improvements in scheduling and weather prediction dropped last year's total cancellations to 1,000, 38% is only 380. The absolute number would have decreased, not increased.
Testing with extreme numbers definitively proves the vulnerability in proportional reasoning.

Key Concept

Percentages vs. Numbers Flaws
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Topics

Percentages vs. Numbers Flaws

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