B. Using Reasoning to Solve Problems

Reasoning can be used to solve a wide variety of problems. As long as your premises are true and your reasoning is correct, you should be able to draw valid conclusions. Most problems that require reasoning are not straightforward. You may need to combine various strategies and conclusions to fully solve a problem. Often it is useful to approach the problem multiple ways and to try to keep any information you have organized.

Example 1

Anna, Barak, Caden, and Dale are friends. One of them is a police officer, one is a carpenter, one is a firefighter, and one is a paramedic. Use the following clues to determine who does each job.

  • The firefighter is a fireman not a firewoman.
  • Barak and Dale regularly exercise with the police officer.
  • Anna regularly helps people in distress.
  • Barak doesn't regularly visit the hospital.
  • The firefighter's name contains the letter 'n'.

This problem contains a lot of information so keeping your thoughts organized is important. Using a table can help.

Each time you learn that a relationship must occur or cannot occur, mark it on the table. For example, the firefighter is not a woman, so Anna cannot be the firefighter.

Barak and Dale exercise with the police officer so neither of them can be the police officer.

Anna helps people in distress, so she is probably not a carpenter.

Barak doesn't regularly visit the hospital, so he isn't a paramedic.

The firefighter's name contains the letter 'n', so it cannot be Barak or Dale.

All of the information from the clues has been used (sometimes you will need to read the clues more than once). Now use your table determine each person's job.

Caden must be the firefighter because no other person can be. Now Caden cannot have the other jobs.


Barak cannot be a police officer, firefigher, or paramedic, so he must be a carpenter. This means nobody else is the carpenter.
From here you can see that Dale must be the paramedic and Anna is the police officer.

Part of the strategy shown in Example 1 was to eliminate possibilities you knew could not occur until only one possibility remained. This strategy is used again in Example 2.