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Difficulty: Very hardPercentages vs. Numbers Flaws

Financial Columnist: In 2015, traditional brick-and-mortar retailers accounted for 80 percent of all retail corporate bankruptcies, while online-only retailers accounted for the remaining 20 percent. Since then, the total number of online-only retailers operating in the market has quadrupled. Last year, traditional brick-and-mortar retailers accounted for only 55 percent of all retail corporate bankruptcies, whereas online-only retailers accounted for 45 percent. It is clear from these figures that the financial stability of traditional brick-and-mortar retailers has improved since 2015, as they are now experiencing fewer bankruptcies annually than they did previously.

Which of the following most accurately describes a flaw in the financial columnist's reasoning?

  1. It infers a decline in an absolute quantity based solely on a decline in the proportion of a whole, without establishing whether the total pool has remained stable.Answer
  2. B
    It derives a conclusion regarding a shift in the percentage of a total based solely on evidence that the absolute size of one group within that total has increased.
  3. C
    It takes for granted that an increase in the absolute number of online-only retailers guarantees an increase in the overall number of retail bankruptcies across the market.
  4. D
    It fails to account for the possibility that the 2015 statistics regarding corporate bankruptcies were incomplete or based on a mathematically flawed sampling method.
  5. E
    It treats the introduction of new competitors into a market as the primary cause of shifting bankruptcy proportions, without ruling out alternative economic factors.

Answer

The correct answer is the option stating that the argument infers a decline in an absolute quantity based solely on a decline in the proportion of a whole, without establishing whether the total pool has remained stable.
The correct answer perfectly diagnoses the mathematical vulnerability in the columnist's reasoning. The author observes that brick-and-mortar stores represent a smaller slice of the bankruptcy 'pie' (55% down from 80%). From this, they conclude that the actual amount of brick-and-mortar bankruptcies has decreased. This logic only works if the total size of the pie remained the same or shrank. If the total number of corporate bankruptcies across all sectors skyrocketed over those years, 55% of the new total could easily represent a much larger absolute number of failed businesses than 80% of the old total. The author fails to establish whether the total pool remained stable, making the conclusion invalid.

Step-by-Step Solution

1
Identify the premises.
Premise 1: In 2015, brick-and-mortar = 80% of bankruptcies. Premise 2: Last year, brick-and-mortar = 55% of bankruptcies. Premise 3: The number of online retailers has quadrupled.
Deconstructing the argument structure is required to isolate what evidence the author is relying upon.
2
Identify the main conclusion.
Brick-and-mortar retailers are now experiencing fewer absolute bankruptcies annually than they did in 2015.
Locating the conclusion reveals the exact claim that needs to be scrutinized for logical leaps.
3
Analyze the relationship between the premises and the conclusion.
The author takes a decrease in a percentage (from 80% to 55%) and assumes it equates to a decrease in an absolute number (fewer bankruptcies overall).
This exposes the core mechanism of the author's reasoning.
4
Determine why this reasoning is flawed.
A percentage only has absolute meaning relative to its total. If the total number of retail bankruptcies grew massively between 2015 and last year, 55% of the new, massive total could be a much larger number than 80% of the small 2015 total.
This uncovers the specific vulnerability in the argument: the failure to establish a stable baseline total.
5
Match the identified flaw to the answer choices.
The correct option accurately describes concluding an absolute decline from a proportional decline without considering the total.
Selecting the answer choice that perfectly matches our structural abstraction.

Key Concept

Percentages vs. Numbers Flaws
Estimated Time:2m 0s
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Topics

Percentages vs. Numbers Flaws

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