GRE Algebra Practice Questions

Last Updated on January 12, 2024

As I like to say, algebra is the king of the GRE Quant section. I say this because algebra concepts appear in many question types, such as multiple-choice questions and Quantitative Comparison questions. Algebra is also a key tool that is used to solve many word problems.

In this article, we will cover some general rules involving algebra on the GRE, and then present a number of GRE math practice questions related to algebra.

Here are the topics we’ll cover:

• Linear Equations with One Variable
  • Solving a Linear Equation with One Variable
  • Example 1: Linear Equation with One Variable
• Linear Equations with Two Variables
  • Using the Substitution Method to Solve a System of Linear Equations
    • Substitution Method Practice 1
    • Substitution Method Practice 2
• Algebra Can Show Up Almost Anywhere in GRE Quant
  • Algebra Example 1: General Word Problems – Two Variables
  • Algebra Example 2: Exponents – One Variable
  • Algebra Example 3: Work Problems – One Variable
  • Algebra Example 4: Ratios – One Variable
  • Algebra Example 5: Statistics – Two Variables
  • Algebra Example 6: Geometry – Two Variables
  • Algebra Example 7: Probability – Two Variables
  • Algebra Example 8: Percents – One Variable
• In Summary
• Frequently Asked Questions (FAQ)
  • Is There Algebra on the GRE?
  • How Many Algebra Questions Are on the GRE?
  • What Is the Most Popular Math Question on the GRE?
  • How Can I Improve My GRE Algebra Skills?
• What’s Next?

Before diving into GRE algebra practice questions, let’s cover some basics of how to deal with equations with one variable and simultaneous equations. We’ll start with how to deal with solving equations when we have just one variable.

Linear Equations with One Variable

In the GRE Quantitative Reasoning section, the most basic algebra questions contain just one variable. Your goal will generally be to solve for the value of the variable. For example:

• 2x + 5 = x
• 4 = 5n
• 2v + 5 = 3v – 7

It’s important to note that even if you see the same variable twice in a single equation, we are still working with a single-variable equation. As we will see in the next section, we combine the variables before solving.

TTP PRO TIP:

Even if a single equation has multiple occurrences of the same variable, it’s still a single-variable equation.

Let’s practice simplifying and solving an equation with one variable.

Solving a Linear Equation with One Variable

When we see a single-variable question in the GRE Quant section, we have one job: combine like terms and determine the value of the given variable. If done correctly, we will simplify the equation such that we end up with the variable isolated by itself, and it will be equal to a particular value. Let’s practice a basic example and explain the steps to solve it.

If 5n – 1 = 10n – 16, then what is the value of n?

Step 1: We can combine our non-variable terms.

So, we add 16 to both sides of the equation. Thus, we have:

5n – 1 + 16 = 10n – 16 + 16

5n + 15 = 10n

Step 2: We can combine variable terms.

So, we subtract 5n from both sides of the equation. Thus, we have:

5n + 15 – 5n = 10n -5n

15 = 5n

Step 3: Finally, divide both sides of the equation by 5 to isolate the variable. So, we have:

15 / 5 = 5n / 5

3 = n

KEY FACT:

When solving for a single variable, we combine like terms and isolate the variable we are solving for.

Now, let’s practice with an example.

Next, let’s discuss equations with two variables.

Linear Equations with Two Variables

As you may expect, two-variable equations have not just one variable but two different variables. Let’s look at a few examples:

• v – u = 12
• 2x + y = 10
• 5z – 3y = 42

As we already discussed, these are two-variable equations because they contain two different variables. So, to solve these problems, we’d need a second equation that has one or both of the two variables. The two equations are called a system of linear equations. One popular way to solve for the values of the variables is by using the substitution method. So, let’s discuss the substitution method for solving a system of two linear equations.

Using the Substitution Method to Solve a System of Linear Equations

Everything we learned in the previous sections will help us solve a system of two linear equations.

When dealing with two equations, the essence of substitution is that we isolate one variable in one of the equations, and then substitute whatever that variable is equal to into the other equation.

If this sounds complicated, don’t worry—it’s not! Let’s practice with a couple of examples.

Substitution Method Practice 1

In the system of linear equations below, determine the value of m.

m = 3n (equation 1)

m + n = 12 (equation 2)

Solution:

Looking at our two equations, we see that m is already isolated in equation one. So, we can substitute 3n (from equation one) for m (in equation two). This gives us:

3n + n = 12

Now we can simplify and determine n:

4n = 12

n = 3

Substitution Method Practice 2

Using the system of linear equations below, what is the value of x?

5x + y = 14 (equation 1)

3x + 4y = 22 (equation 2)

Solution:

Unlike for the previous problem, we will have to do some work to isolate a variable. Looking at our equations, we can easily isolate y in equation 1.

Let’s do that below by subtracting 5x from both sides of the equation:

y = 14 – 5x

Next, we can substitute 14 – 5x for y in equation 2. This gives us:

3x + 4(14 – 5x) = 22

3x + 56 – 20x = 22

-17x = -34

x = 2

KEY FACT:

We can use the substitution method when solving a system of linear equations.

Next, let’s discuss the many topics on the GRE in which we see algebra problems.

Algebra Can Show Up Almost Anywhere in GRE Quant

Thus far, we have covered how to deal with algebra in one- and two-variable equations. Understanding the processes we’ve covered is very important because you’ll also need to use them when solving algebra in many more complicated and sometimes “wordy” GRE Quant topics:

• Exponents and Roots
• General Word Problems
• Rate Problems
• Work Problems
• Ratios
• Percents
• Overlapping Sets
• Combinations and Permutations
• Probability
• Geometry
• Coordinate Geometry
• Functions
• Sequences

As you can see, there are many Quant topics that require the use of algebra! The key when solving these problem types is first to use the various “topic-specific” rules to set up your equations, and then fall back on your algebra principles to solve for what the question asks for. If you are nervous, don’t be! We will practice with various algebra practice questions below.

TTP PRO TIP:

Be prepared to see algebra questions in many shapes and sizes.

Next, let’s see how algebra can be presented in an exponent question.

Algebra Example 6: Geometry – Two Variables

If lines a and b are parallel, what is the value of y?

• 30
• 45
• 50
• 60
• 65

Solution:

Since we have two parallel lines and a transversal, we can create the following two equations:

x + 60 = 2x

60 = x

and

2x + 2y = 180

x + y = 90

Since 60 = x, we now have:

60 + y = 90

y = 30

Answer: A

In Summary

Having great algebra skills is paramount for earning a good GRE score! Algebra is tested in a variety of question types, so mastering basic algebra is critical.

In this article, we presented two fundamental algebra problems to teach the basic skills for solving equations when we have (1) a linear equation with one variable or (2) a system of two linear equations. Mastery of these two equation-solving techniques will help you solve a variety of GRE math questions, including general word problems, exponents, work, ratios, statistics, geometry, probability, and percents.

Clearly, solid knowledge and understanding of algebra is crucial for getting a high GRE score.

Frequently Asked Questions (FAQ)

Is There Algebra on the GRE?

As you have seen in this article, the GRE is littered with algebra!

How Many Algebra Questions Are on the GRE?

Algebra can pop up in many different problem types on the GRE. So, there is a very real chance that you could have to use algebra in as many as 20 of the 27 Quant questions on the GRE.

What Is the Most Popular Math Question on the GRE?

Because algebra is so important in so many questions, I would say algebra is the most important math skill you must have for GRE quant.

How Can I Improve My GRE Algebra Skills?

When thinking about how to improve your GRE algebra skills, it’s important to realize that you must walk before you run. In other words, make sure you first learn how to deal with single-variable equations and simultaneous solution of equations before using those skills in the context of word problems. Learning in this way will make you an ace when solving algebra questions on the GRE.

You can find some additional study tips in our article about the best way to study for the GRE.

What’s Next?

I hope that you walk away from this article with a much better understanding of how to deal with algebra questions on the GRE. However, if you need some more help with GRE Quant, I welcome you to check out our article providing the top 10 tips for a top GRE Quant score. And if you want some additional algebra practice, check out the 5-day trial of our GRE self-study course

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