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Difficulty: HardPercentages vs. Numbers Flaws

Industry Analyst: In 20242024, software engineers accounted for 45%45\% of all new hires at major tech firms, while product managers accounted for 25%25\%. In 20252025, software engineers accounted for 55%55\% of all new hires at these same firms, and product managers accounted for 15%15\%. Clearly, these firms hired a greater total number of software engineers and a smaller total number of product managers in 20252025 than they did in 20242024.

The analyst's conclusion depends on assuming which of the following? Select all that apply.

  1. The total number of new employees hired by major tech firms in 20252025 was not significantly smaller than the total number hired in 20242024.Answer
  2. The overall volume of new hires at major tech firms did not increase dramatically between 20242024 and 20252025.Answer
  3. C
    The shifts in the hiring proportions between 20242024 and 20252025 were not the direct result of an industry-wide budget reduction.
  4. D
    Most individual major tech firms saw an increase in the percentage of software engineers they hired and a decrease in the percentage of product managers they hired.
  5. E
    Major tech firms did not terminate significantly more product managers than software engineers during the 20242024 to 20252025 period.

Answer

The argument requires assuming BOTH that the total number of hires was not significantly smaller (which protects the software engineer claim) AND that the total number of hires did not increase dramatically (which protects the product manager claim).
The argument attempts to draw two specific conclusions about absolute numbers based on percentage changes moving in opposite directions. To guarantee that a rising percentage (45% to 55%) yields a rising absolute number, the baseline total cannot shrink too much. Conversely, to guarantee that a falling percentage (25% to 15%) yields a falling absolute number, the baseline total cannot grow too much. Therefore, the argument implicitly assumes bounds on how much the total hiring pool could have fluctuated in either direction.

Step-by-Step Solution

1
Identify the core logical flaw.
The argument conflates percentages (proportions) with absolute numbers (counts).
An increase or decrease in a percentage only guarantees a corresponding increase or decrease in the absolute number if the baseline total remains relatively constant.
2
Analyze the first half of the conclusion: 'greater total number of software engineers'.
The percentage rose from 45% to 55%. For the actual number to rise, the total pool of hires could not have shrunk drastically. If total hires went from 1,000 down to 100, software engineers would drop from 450 to 55.
This reveals the first required assumption: the overall hiring volume must not have been significantly smaller in 2025.
3
Analyze the second half of the conclusion: 'smaller total number of product managers'.
The percentage fell from 25% to 15%. For the actual number to fall, the total pool of hires could not have exploded in size. If total hires went from 1,000 up to 10,000, product managers would increase from 250 to 1,500.
This reveals the second required assumption: the overall hiring volume must not have increased dramatically in 2025.

Key Concept

Percentages vs. Numbers Flaws
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Topics

Percentages vs. Numbers Flaws

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