The CA SOLVE Approach to Word Problems for CBEST Exam Study Guide

L Stands for Live

Living the problem means pretending you're actually in the situation described in the word problem. To do this effectively, make up details concerning the events and the people in the problem as if you were part of the picture. This process can be done as you are reading the problem and should take only a few seconds.

V Stands for View

View the problem with different numbers to help you get a better sense of the steps you will need to take in order to solve it. This tactic is especially helpful when the sight of a large or complex number is so overwhelming that you just don't know where to start. For example, you might be intimidated by being asked to calculate how long it would take a rocket traveling 650 miles per hour to go 1,300,000 miles. To view the problem differently, you might think of how long it would take a car traveling 10 miles per hour to go 50 miles. Write down the steps you will take to solve the simpler problem, and then apply them to the more complex problem in just the same way.

E Stands for Eliminate

Eliminate answers you know are wrong. You may also spend a short time checking your answer if there is time.

Sample Question

Solve this problem using the CA SOLVE steps.

1. There are 651 children in a school. The ratio of boys to girls is 4:3. How many boys are there in the school?
   1. 40
   2. 325
   3. 372
   4. 400
   5. 468

Answer

1. Subject Experience: You know that 4 and 3 are only one apart and that 4 is greater. You can conclude from this that boys are a little over half the school population. Following up on that, you can cut 651 in half and eliminate any answers that are less than half. Furthermore, since there are three numbers in the problem and two are paired in a ratio, you can conclude that this is a ratio problem. Then you can think about what methods you used for ratio problems in the past.
2. Organize: The clue word total means to add. In the context in which it is used, it must mean girls plus boys equals 651. Also, since boys is written before girls, the ratio should be written Boys: Girls.
3. Live: Picture a group of three girls and four boys. Now picture more of these groups, so many more that the total would equal 651.
4. View: If there were only 4 boys and 3 girls in the school, there would still be a ratio of 4 to 3. Think of other numbers that have a ratio of 4:3, like 40 and 30. If there were 40 boys and 30 girls, there would be 70 students in total, so the answer has to be more than 40 boys. Move on to 400 boys and 300 girls—700 total students. Since the total in the problem is 651, 700 is too large, but it is close, so the answer has to be less than 400. This would narrow your choices to two.
5. Eliminate: Since you know from the previous step that the number of students has to be less than 400, you can eliminate choices d and e. Since you know that the number of boys is more than half the school population, you can eliminate choices a and b. You are left with choice c, the correct answer.

Quick Tips and Tricks

Below is a miscellaneous list of quick tips to help you solve word problems.

Work from the Answers

On some problems, you can plug in given answers to see which one works in a problem. Start with choice c. Then if you need a larger number, go down, and if you need a smaller answer, go up. That way, you don't have to try them all. Consider the following problem:

1. One-fifth of what number is 30?
   1. 6
   2. 20
   3. 50
   4. 120
   5. 150

Try c: of 50 is 10. A larger answer is needed.

Try d: of 120 is 24. Not yet, but getting closer.

Try e: of 150 is 30—Bingo!

Problems with Multiple Variables

If there are so many variables in a problem that your head is spinning, put in your own numbers. Make a chart of the numbers that go with each variable so there is less chance for you to get mixed up. Then write your answer next to the given answer choices. Work the answers using the numbers in your chart until one works out to match your original answer. In doing this, avoid the numbers 1 and 2 and using the same numbers twice. There may appear to be two or more right answers if you do.

Sample Multivariable Question

2. A man drove y miles every hour for z hours. If he gets w miles to the gallon of gas, how many gallons will he need?
   1. yzw
   2. 
   3. 
   4. 
   5. 

Answer

Picture yourself in the situation. If you drove 4 (y) miles every hour for 5 (z) hours, you would have driven 20 miles. If your car gets 10 (w) miles to the gallon, you would need 2 gallons. Since 2 is your answer, plug the numbers you came up with into the answer choices and see which one is correct. Choice b equals 2 and is therefore correct.

Let the Answers Do the Math

When there is a lot of multiplication or division to do, you can use the answers to help you. Suppose you are asked to divide 9,765 by 31. The given answers are as follows:

1. 324
2. 316
3. 315
4. 314
5. 312

You know then that the answer will be a three-digit number and that the hundreds place will be 3. The tens place will be either 1 or 2.Your division problem is practically worked out for you.

Problems with Too Much or Too Little

When you come across a problem that you think you know how to answer, but there seems to be a number left over that you just don't need in your equation, don't despair. It could very well be that the test writers threw in an extra number to throw you off. The key to not falling prey to this trick is to know your equations and check to make sure that the answer you came up with makes sense.

When you come across a problem that doesn't seem to give enough information to calculate an answer, don't skip it. Read carefully, because sometimes a question asks you to set up an equation using variables, and doesn't ask you to solve the problem at all. If you are expected to actually solve a problem with what seems like too little information, experiment to discover how the information works together to lead to the answer. Try the CA SOLVE tips.

One Success Step for If Problems

1. Pick some numbers and try it out!

More Than One Way to Solve a Problem

Some questions ask you to find the only wrong way to solve a problem. In this type of question, do the computation yourself, and work from the answers. The choice that gives an answer different from the others has to be the wrong answer. Consider these choices:

1. 5% of 60
2. × 60
3. 0.05 × 60
4. 5 × 60 ÷ 100
5. 5 × 60

All of the answers compute to 3 except choice e, which turns out to be 300. Therefore, choice e must be the correct answer.