# 4 Math Problem Solving Strategies

These useful Math problem-solving strategies will help you pass the GED Math test.

We created this lesson to show you how to take a multiple-choice math test intelligently. Become a successful test-taker by using these simple, yet, powerful strategies.

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The four problem-solving strategies discussed here come with examples as well and include:

• Working backward
• Making a table or list
• Solving a simpler problem
• Guess & check

## Problem-Solving Strategy 1: Work Backward

Usually, in Math problems, you are given a set of facts or conditions after which you must find the end result. But there are also Math problems that begin with the end result and ask you to find something that occurred earlier.

To solve this type of Math problem, you can very well use the strategy of working backward. If you use this strategy, you begin with the result and then undo each of the steps.

Example:

Annie spent half of the money she had in the morning on lunch. Then, she gave her best friend one dollar. Now Annie has \$1.50. Now, what was the amount of money that Annie had initially?

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So we start with our end result, \$1.50. Then, we work our way back to find the amount of money Annie had initially. Annie now has an amount of \$1.50. First, we undo the one dollar she gave her best friend. That gives us \$2.50, right?

Annie spent half of her initial money on lunch. So we have to multiply what she has by two to undo her spending half what she had initially. Well, that gives us \$5.00 as Annie’s starting amount.

Let’s check this. Annie began with \$5.00. If she spent half of this amount (\$2.50) on lunch and then gave her friend \$1.00, she would have exactly \$1.50 left, right? Because this result matches what is stated in our given problem, this solution is correct! So we worked our way backward to solve this Math problem without having to use all sorts of Math formulas. Great, isn’t it?

## Problem-Solving Strategy 2: Make a List or a Table

Another strategy for solving Math problems is to make a list or a table. Lists or tables allow you to organize information or numbers in an easy-to-understand way. Let’s look at a few examples.

Example 1:

A fruit vending machine accepts dollars. Each piece of fruit will set you back 65 cents. The machine returns only quarters, dimes, and nickels. Now, which combinations of coins are options as change for one dollar?

What we know is that a piece of fruit costs \$0,65 and that the machine will return 35 cents in change. The combination is quarters, dimes, and nickels.

So let’s make a list of different possible combinations of quarters, dimes, and nickels that will total our 35 cents. Let’s organize our table by beginning with the combinations, including the most quarters.

We know that the total for each possible coin combination is 35 cents. If we list the combinations, we see that there are six (6) possible combinations:

quarters   dimes   nickels
1                 1           0
1                 0           2
0                 3           1
0                 2           3
0                 1           5
0                 0           7

This table gives us a clear overview of all possible combinations, right? We can use this strategy is to list a number of possibilities. When making a list or table, we use a highly organized approach so leaving out any important items should be avoided!

Example 2:

The Math problem is: Determine how many options or possibilities there are to receive change for one quarter when at least 1 coin is a dime.

So, let’s list the possible options. Let’s begin with the options that use the fewest coins.
Option 1: dime-dime-nickel
Option 2: dime-dime-5 pennies
Option 3: dime-nickel-nickel-nickel
Option 4: dime-nickel-nickel-5 pennies
Option 5: dime-nickel-10 pennies
Option 6: dime-15 pennies

So you see, there are in total 6 possibilities. Making a table gives us a clear picture of possible options. If you understand this sort of Math problem, chances are you’ll earn your GED fast.

## Problem-Solving Strategy 3: Solve a Simpler Problem

A very useful strategy to solve Math problems is to first solve a far simpler problem. When we use this strategy, we first solve a more familiar or simpler case of a similar problem. Then, we can use the same relationships and concepts to solve the original Math problem.

Example 1:

The Math problem is: What is the sum of the integers 1 through 500.
We begin by considering a much simpler problem, for example, finding the sum of the integers 1 through 10.

What you should notice is that we can group the addends in this list into partial sums. Check out this:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

Notice the following:
1 + 10 = 11
2 + 9 = 11
3 + 8 = 11
4 + 7 = 11
5 + 6 = 11

In total, we have 5 (five) sums, right? This is half our total number of addends. Do you notice that all partial sums are 11? This is the sum of our first and last integers! So the sum of our list is 55 (5 x 11).

Now, we can use this same concept to come up with the sum of the integers 1 through 500. Use the same principles and we’ll get:

1 + 2 + 3 … 499 + 500 = 250 x 501 = 125,250

So we multiply half the total number of addends (250) by the sum of our first and last integer (501), which gives us 125,250.

Example 2:

We can apply a similar problem-solving strategy by using subgoals. Let’s consider the following:

Two industry workers can produce two chairs in exactly two days. What’s the number of chairs that 8 workers can produce in 20 days when they work at exactly the same rate?

We begin by determining the number of chairs one worker can produce in two days. So we divide our two chairs by the two workers, which gives us 1 (2 divided by 2).

So now we know that one worker can produce one chair in 2 days. If we want to determine the number of chairs one worker can produce in 20 days, we have to divide 20 (days) by 2 (number of days needed to make one chair). Well, 20 divided by 2 gives us 10, right?

Now, when we have to determine the number of chairs that 8 workers can produce in 20 days, we have to multiply 8 by 10 which gives us 80 (8 x 10).
So the correct answer is that 8 workers can produce 80 chairs over a period of 20 days.

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## Problem-Solving Strategy 4: Guess & Check

Let’s take a look at one more useful strategy to solve Math problems. Sometimes, it is helpful to come up with a reasonable guess after which you can check if it solves the problem.

Simply use your guess results to get closer to improve the problem’s solution. This strategy is what we call the ‘Guess & Check’ Strategy.

Example:

The problem asks us the following: Determine two even consecutive integers if the product of these integers is 1088. So what are these two integers?

Well, we know that the product of our integers is pretty close to 1000. So let’s make a guess. What happens if we use 24 and 26?
The product of 24 and 26 is 624, so far too low.

We have to adjust our guess upward, so what about 30 and 32?
The product of 30 and 32 is 960, still too low, but we’re getting closer, right?

Let’s adjust our guess upward one more time. Let’s see what happens if we use 34 and 36. Well, the product of 34 and 36 is 1224, which is too high.

So we’ll have to try even consecutive integers between 30 and 34 and we already tried 30 and 32! This leaves us with 32 and 34. And indeed, the product of 32 and 34 is 1088! So this is our correct answer. The integers we’re looking for are 32 and 34. So we guessed and checked until we came up with the correct solution.

Last Updated on June 14, 2022.