Question

33Steve would like to determine the relative salaries of three co-workers using two facts. First, he knows that if Fred is not the highest paid of the three, then Janice is. Second, he knows that if Janice is not the lowest paid, then Maggie is paid the most. Is it possible to determine the relative salaries of Fred, Maggie, and Janice from what Steve knows? If so, who is paid the most and who the least? Explain your reasoning.

Short answer

Fred is paid the most, Maggie next, and Janice the least.

Step-by-step solution

Tips

There are three workers

We focus on how to find the salaries.

We compare the statement between three workers.

Fact one says that if Fred is not the highest paid then Janice is.

First assume that Fred is not the highest paid, therefore Janice is. If Janice is not the lowest paid, that means Steve is, and Maggie is the highest paid. This is a contradiction. Therefore Fred is the highest paid. Next assume that Janice is not the lowest paid. This would mean that Maggie is the highest paid. But that contradicts the fact that Fred is the highest paid. Therefore Janice is the lowest paid.

This means that Fred is paid the most, Maggie next, and Janice the least.