Logical Reasoning and Problem Solving Help (page 2)
Introduction to Logical Reasoning and Problem Solving
—Norman Vincent Peale, Protestant preacher and author and creator of the theory of "positive thinking" (1898–1993)
Logic problems and puzzles can be fun, but they can also help determine the direction of your career if you ever have to take an exam that tests your logic and reasoning skills. This lesson will show you what types of questions you'll typically find on such an exam and how to tackle those kinds of questions.
Strong critical thinking and reasoning skills will help you make better decisions and solve problems more effectively on a day-to-day basis. But they'll also help you in special situations, such as when you are being tested on your logic and reasoning skills. For example, you may be taking a critical thinking class, applying for a promotion, or hoping to be a police officer or fireman—or maybe you just like to solve logic problems and puzzles for fun. Whatever the case, if you find yourself facing logic problems, you'll see they generally come in the form of questions that test your:
- Common sense
- Ability to distinguish good evidence from bad evidence
- Ability to draw logical conclusions from evidence
You've been learning a lot about critical thinking and deductive and inductive reasoning, so you should already have the skills to tackle these kinds of questions. This lesson aims to familiarize you with the format of these kinds of test questions and to provide you with strategies for getting to the correct answer quickly.
Questions that test your common sense often present you with decision-making scenarios. Though the situation may be foreign to you and the questions may seem complicated, you can find the answer by remembering how to break a problem down into its parts and by thinking logically about the situation.
Read the following question:
A police officer arrives at the scene of a two-car accident. In what order should the officer do the following?
- Interview witnesses.
- Determine if anyone needs immediate medical attention.
- Move the vehicles off of the roadway.
- Interview the drivers to find out what happened.
- II, IV, III, I
- II, IV, I, III
- II, III, I, IV
- IV, II, III, I
The best answer is b, II, IV, I, III. Your common sense should tell you that no matter what, the first priority is the safety of the people involved in the crash. That's why II has to come first on the list—and that means you can automatically eliminate answer d. Now, again using your common sense, what should come next? While statements from witnesses are important, it's more important to speak directly to the people involved in the accident, so IV should follow II—and that eliminates answer c. Now you're down to a and b. Now why should you wait to move the vehicles out of the roadway? The main reason this doesn't come earlier is because you need to see the evidence—exactly where and how the cars ended up—as you listen to driver and witness testimony. Once you have their statements and have recorded the scene, then you can safely move the vehicles.
Common sense is a trait that it is important to develop. It is often the gut instinct you have to a situation, the answer that pops into your head first. It's your conscience that reminds you what is right and wrong. Learn to listen to it.
Logic tests often measure deductive as well as inductive reasoning skills. That's why some questions may ask you to evaluate evidence. Remember, strong evidence for a deductive argument is both credible and reasonable.
You'll need to keep these criteria in mind and use your common sense to work your way through problems like the following:
Karen has complained to her supervisor that the company provides the math department with more technological amenities than it does the English department. Which of the following would provide the strongest support for her claim?
- All the people in the English department agree with Karen.
- The 30 people in the English department have only one printer and one fax machine, whereas the 35 people in the math department have three printers, three fax machines, and a scanner.
- There are 8 percent more people in the math department than in the English department.
- The English department prints more documents than the math department does.
You should have selected b as the answer. Why? Because b provides the most specific and relevant support for the argument. Though there is strength in numbers and it helps that all the people in the English department support Karen's claim (choice a), Karen is more likely to convince the management by citing concrete statistics. It's clear from the numbers provided in choice b that the math department does indeed have more technological amenities than the English department does. Choice c isn't the strongest piece of evidence because it merely states that there is a small percentage difference between the amount of employees in the math and English departments, without relating this fact to the issue at hand—the technological amenities. Choice d, while it could be used to support Karen's claim, is not as strong as b, because it also doesn't directly address the amenities.
Now it's your turn.
Drawing Conclusions from Evidence
Many questions you face when you're being tested on your reasoning skills will ask you to draw conclusions from evidence. You've completed several lessons on inductive reasoning, so you should be quite good at these questions, even if their format is different from what you're used to.
As in the other types of questions, you can help ensure a correct response by using the process of elimination. Given the evidence the question provides, you should automatically be able to eliminate some of the possible answers.
For example, read the following question:
A jeep has driven off the road and hit a tree. There are skid marks along the road for several yards leading up to a dead fawn. The marks then swerve to the right and off the road, stopping where the jeep is. The impact with the tree is head-on, but the damage is not severe. Based on the evidence, which of the following is most likely what happened?
- The driver was aiming for the fawn and lost control of the jeep.
- The driver fell asleep at the wheel and was awakened when he hit the fawn.
- The driver tried to avoid the fawn and lost control of the jeep.
- The driver was drunk and out of control.
You have most likely been using the process of elimination for years. It comes in quite handy on most tests, especially on multiple-choice questions. You look at your choices and then eliminate the ones you immediately recognize as wrong.
Given the facts—especially the key fact that there are skid marks—you can automatically eliminate choices a and b. If the driver were aiming for the fawn, he probably wouldn't have hit the brakes and created skid marks. Instead, he probably would have accelerated, in which case, his impact with the tree would have been harder and resulted in more damage. Similarly, if the driver had fallen asleep at the wheel and only woken up when he hit the fawn, there wouldn't have been skid marks leading up to the fawn.
So now you're down to two possibilities: c and d. Which is more likely to be true? While it is entirely possible that the driver was drunk, all of the evidence points to c as the most likely possibility. The skid marks indicate that the driver was trying to stop to avoid hitting the fawn. Unsuccessful, he hit the animal and swerved off the road into a tree.
Other questions that ask you to draw conclusions from evidence may vary in format, but don't let their appearance throw you. If you read the following practice problems, for example, you'll see that you can tackle them quickly and easily by applying the evidence that's provided and eliminating the incorrect answers as you go along.
Logical Reasoning and Problem Solving In Short
Tests that aim to measure your critical thinking and reasoning skills generally ask three types of questions: those that measure your common sense, those that measure your ability to recognize good evidence, and those that measure your ability to draw logical conclusions from evidence. You'll perform well on these tests if you remember to break down the parts of a problem and think about different possible scenarios, keep in mind the criteria for strong arguments and good evidence, and start inductive reasoning questions by working with the key facts. Use the process of elimination to help you arrive at the correct answer.
Skill Building until Next Time
- Stop in your local bookstore or go to the library and get a book of logic problems and puzzles. The more you practice them, the better you'll get at solving them.
- Write your own logic problems and puzzles. Test them out on your family and friends. Be sure you can clearly explain the correct answer.
Exercises for this concept can be found at Logical Reasoning and Problem Solving Practice.