Logical Reasoning

PT111 · S4 · Q4 Last year a large firm

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Last year a large firm set a goal of decreasing its workforce by 25 percent.

Given that ...

Three divisions, totaling 25% of the workforce at the time, were eliminated and no new people were hired.

How can it be that ...

The workforce has decreased by only 15 %?

Evaluate / Goal

This paradox is mathematical in nature. While we don't normally try to predict answers on Paradox, the exception to that is mathematical paradoxes. For those, there usually is only one way to make the math work. We might need to consider some numbers.

Let's say our company has 100 people. We need to decrease that by 25%, so we need to get rid of 25 workers. We decide to get rid of these three divisions: Division X: 6 workers Division Y: 14 workers Division Z: 5 workers

One year later ... we got rid of those three divisions and we didn't hire any new people to join the firm. But we only decreased our workforce by 15 workers. We still have 85 workers. How could this be?

It seems like the only possible explanation is that 10 of these workers didn't actually get fired from the firm. They just got reassigned to a different division (one that didn't get eliminated).

So let's look for an answer saying that some of the employees from the divisions that got eliminated were reassigned to other divisions within the firm.

4.

Which one of the following, if true, contributes most to an explanation of the difference in the planned versus the actual reduction in the workforce?

  1. The three divisions that were

    Unrelated to Goal

    This doesn't give us any way of explaining how we got rid of three divisions that accounted for 25% of the workforce and yet we only eliminated 15% of the workforce.

    0% picked this

  2. Normal attrition in the retained

    Deepens Paradox

    This answer would help explain how the workforce could have decreased by more than 25%. It's saying, "in addition to the workers fired when we eliminated those three divisions, we also have other workers quitting from the remaining divisions." We need to explain how the workforce decreased by less than 25%, so this answer goes in the opposite direction.

    2% picked this

  3. Some of the employees in

    No Impact

    This is saying that at least one employee in Division X, Y, or Z said, "Oh, the division is getting eliminated at the end of the year and so I'll be laid off or reassigned? Hmm, I'll just retire early, I think." Since this answer is talking about people who left the company, it doesn't help us explain our mystery. We have retained more employees than we should have. We thought we were only retaining 75% of the workforce, but we retained 85% of it. The correct answer needs to tell us about people who stayed working for the firm, even though their division was eliminated.

    4% picked this

  4. Correct

    As the divisions were being

    Why this is right

    This is what we were predicting. In order for the math to work, some of the employees who worked in the divisions we eliminated need to still be working for the firm. If we're told that some of the employees from those eliminated divisions were assigned to other divisions, then that helps us explain how they could still be working for the firm. We had a workforce of 100 people. We eliminated three divisions that employed 25 of those people, but 10 of those 25 got assigned to divisions that weren't being eliminated. Thus, 15 people lost their jobs, 10 people changed their job within the firm. And so the firm's workforce only decreased by 15 people (15%).

    Skill tested: Paradox · how this choice captures the argument's function is the move to repeat next time.

    91% picked this

  5. Employees in the retained divisions

    Unrelated to Goal

    This doesn't give us any way of explaining how we got rid of three divisions that accounted for 25% of the workforce and yet we only eliminated 15% of the workforce. This answer would allow us to explain a riddle of how we could eliminate 25% of the workforce but only decrease productivity by 15%.

    2% picked this

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