The 4 Basic Principles of Problem Solving

Let’s tackle problems!! Follow these four principles to become a master at solving problems.  You got this.

By adopting a systematic approach to Problem Solving, you will have a clear, concise method for thinking your way to a response. You won’t waste time by attacking a problem in a tentative or haphazard manner. A systematic approach will ensure that you find the most efficient solution to the problem and that you make as few careless and unnecessary errors as possible.

1. Develop the ability to decipher question stems quickly.

Learn to quickly recognize exactly what you’re being asked.

2. Decide how much effort to put into each question.

Depending on where you are on the test, you might be better off guessing and saving time for other questions. Only you know what type if questions give you a particular trouble. If you’re not that good at ratios and hit a ratio question in the second half of the test, you should move through it quickly to allow time to answer other questions more completely.

3. Consider alternative methods.

If the question seems as if it will take too long to solve, look for shortcuts. There are many different ways to solve a given math question. Remember, you’re not looking for an ideal method for everybody but the fastest method for you. Time is a key element on standardized exams, so you should maximize the value of your time with shortcuts or alternative methods. The Kaplan Method is all about time management. The right method is whatever method is quickest for you.

-Picking Numbers

Picking Numbers is a powerful alternative to solving problems by brute force. Rather than trying to work with unknown variables, you pick concrete values for the variables. Any answer choice that does not work for the concrete values cannot be the correct answer.

How does Picking Numbers work?

-Pick simple numbers to stand in for the variables. The usefulness f the strategy depends in large part on your ability to pick convenient numbers.

-Try all the answer choices, ditching those that don’t agree with the question information. Remember to keep the values you’ve picked for the variables constant throughout the problem.

-Try different values when more than one answer choice works. Sometimes more than one choice will give the right answer. If that happens, pick some new numbers. The correct choice must work for all possible numbers.

When you encounter a problem that contains variables, think of Kaplan alternative approaches to Problem Solving. Very often, Picking Numbers and substituting is quicker than any mathematical calculation.


Backsolving is a strategy that allows you to use the answer choices to work backward through the question stem. You plug the answer choices into the question to see which one works. The answer choice that agrees with the information in the question stem is correct. You’ve probably used this strategy unconsciously when you ran into a multiple-choice question that you found difficult. Backsolving can save a great deal of time if you use it wisely. It is an exceptional method for solving questions when you have no idea where to begin on a problem.

4. Guess if you’re stumped.

If you simply cannot solve an equation using regular math or an alternative method, sometimes that’s the time to make an educated guess. The key to good guessing is the elimination if wrong answer choices. Many questions will have answer choices that are obviously wrong or don’t make sense. If you can eliminate some wrong choices using common sense, make a good guess and move on.

Kaplan’s 4-step method for problem solving.

Now that you’ve got a grip on the basic principles of Problem Solving, let’s look at how to attack the questions you’ll see on the test.

1. Read through the whole question.

Determine exactly what the question is asking. Is the question or situation complicated?

2. Decide how much effort to put into question.

Is this the sort of question you normally do well on? Will you be able to solve it quickly? Be aware of where you are in the test and how much time you have left.

3. Choose the fastest approach to the answer.

Choose the approach that you feel most comfortable with. Questions are often deliberately confusing and contain traps for the unwary.

4. Select an answer.

Answer every question. Eliminate answer choices whenever you can. The more unlikely answer choices you can eliminate, the better your chances of guessing correctly. And if you’re running out of time and several questions remain, make sure to answer each question by guessing something.

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