GRE Algebra: Pattern, Syllabus, Questions, Preparation Tips & More

The GRE quant section might seem challenging, but you’re in familiar territory when it comes to algebra. Unlike other areas of math, GRE algebra focuses on concepts you’ve likely come across in high school. There’s no need to panic about memorising complex formulas or esoteric GRE vocabulary. The key to success lies in refreshing your memory and strategically practicing the application of these core principles.

The GRE isn’t trying to stump you with entirely new algebraic concepts. Instead, it tests your ability to apply your existing knowledge to solve problems. It covers a range of topics, including linear algebra, elementary algebra, number theory, and even a touch of abstract algebra. But don’t worry; these areas only make up about 25% of the GRE quantitative reasoning section. These problems might appear complex at first glance, but with a little practice, you’ll be solving them with ease.

Importance of the GRE Algebra

GRE algebra plays a critical role in your overall Quantitative Reasoning score. It makes up a significant portion of the math section, often accounting for 25% of the questions. This means you can expect to see anywhere from 6 to 12 algebra-based problems on the entire test. Mastering core concepts like linear and quadratic equations, inequalities, and functions is essential for solving these questions effectively.

Beyond its direct impact on your score, a strong foundation in GRE algebra strengthens your critical thinking and problem-solving abilities. Algebra on the GRE isn’t just about memorising formulas; it’s about strategically manipulating variables and equations to reach solutions. This analytical approach is valuable across various GRE practice question types, even those that seem unrelated to algebra at first glance. So, honing your GRE algebra skills goes beyond just answering those specific questions. It allows for a strong foundation in algebra and allows you to approach these problems strategically and efficiently.

GRE Algebra Exam Pattern

The GRE Quantitative Reasoning section assesses a wide range of mathematical abilities, and algebra is a crucial one. Around 25% of the questions on the GRE will test your understanding of algebraic concepts, which range from elementary algebra learned in middle school to linear algebra typically encountered in high school. These questions may appear in various formats, including quantitative comparison, problem-solving, numeric entry, or multiple answers.

It’s important to remember that not all 20 questions in each quantitative reasoning section will be algebra-focused, and only a select few (around six) will significantly impact your score. However, possessing strong foundational algebraic skills will prepare you to solve these questions effectively and show your quantitative reasoning capabilities.

GRE Algebra Syllabus

The GRE algebra syllabus covers a wide range of topics, testing your ability to apply fundamental formulas in various contexts. While the overall GRE quant section might seem challenging due to its connection to data analysis and other areas, the core of GRE algebra lies in manipulating expressions and solving equations. Unlike some areas of the GRE quant section, you won’t come across advanced math concepts like calculus or trigonometry here.

One key aspect of GRE algebra is its reliance on variables represented by letters. These word problems might appear complex at first glance, but with a solid grasp of the underlying algebraic concepts, you can break them down and solve them efficiently. Now, let’s dig deeper into the specific topics that make up the GRE algebra syllabus:

• Three types of factoring

• Simplifying algebraic expressions

• Basic equations

• Expanding equations

• Quadratic equations

• Systems of equations

• Equations with fractions

• Equations with exponents

• Equations with absolute values

• Equations with square roots

• Equations of lines

• The coordinate plane

• Graphs of quadratics

Read also: 10 Tips to Increase Your GRE Quant Score

GRE Algebra Question Types

The GRE algebra section tests your understanding of various algebraic concepts and your ability to apply them to solve problems. Here’s a breakdown of the areas you might encounter:

• Algebraic expressions: These are single terms or sums of terms that can include variables. You’ll need to be familiar with manipulating these expressions, such as combining like terms or simplifying complex expressions.

• Basic equations: This section involves formulating equations based on the given information and solving for the unknown variable. You might need to set up tables to organise your approach.

• Rules of exponents and radicals: The GRE assumes knowledge of the three basic rules of exponents and their application to radicals. Understanding these properties is crucial for simplifying expressions and solving equations.

• Solving equations in one variable: Here, you’ll be presented with equations containing one unknown variable. Your task is to manipulate the equation algebraically to isolate the variable and solve for its value.

• Linear/quadratic inequalities: This area deals with comparing expressions using inequality symbols like “<” or “>”. You’ll need to understand how these inequalities work and be able to solve them to find the values that satisfy the conditions.

• Simultaneous equations in two variables: These involve systems of equations with two unknowns. You’ll likely be tested by using substitution or elimination methods to solve for both variables.

• Word problems: The GRE presents word problems that can be solved using algebraic principles. Each problem might require a different approach, so it’s important to be familiar with various problem-solving strategies.

• Coordinate geometry: This section might involve the use of a coordinate plane where two number lines intersect at a right angle. You might need to interpret points on the plane or use them to solve equations.

• Functions and their graphs: While the focus isn’t on advanced calculus, the GRE might introduce basic concepts of functions and their graphical representations. You’ll need to understand how functions relate to numbers and interpret their behaviour through graphs.

• Symbolism: The GRE uses various mathematical symbols. However, most problems involve straightforward substitution, so a strong understanding of basic algebraic symbols is sufficient.

• Sequences: Sequences are ordered lists of numbers. The GRE might test your ability to recognise patterns and formulas within sequences to find specific terms or their properties.

Read also: 21 Most Difficult GRE Math Formulas for 2024

GRE Algebra Practice Problems

Question 1: What is the value of t if: 3x2 + tx - 21 = (3x - 3)(x + 7)?

1. 18

2. 21

3. -18

4. -3

5. 24

Explanation: Use the foil method: (3x - 3) (x + 7) = 3 x 2 + 21x - 3x - 21 = 3 x 2 +18x -21 so t = 18.

Answer: (a) 18

Question 2: Darius has 20 more coins than Rucker. If Darius and Rucker have a combined total of 38 coins, how many coins does Rucker have?

1. 4

2. 6

3. 8

4. 9

5. 12

Explanation: Before creating our equations, we can define two variables:

We can let D = the number of coins Darius has and R = the number of coins Rucker has.

Next, we can create two equations:

Since Darius has 20 more coins than Rucker, we have:

D = R + 20 (equation 1)

Since Darius and Rucker have a combined total of 38 coins, we have:

D + R = 38 (equation 2)

Since we have D isolated in equation 1, we can substitute R + 20 for D in equation 2, and we have:

R + 20 + R = 38

2R + 20 = 38

2R = 18

R = 9

Rucker has 9 coins.

Answer: (d) 9

Question 3: Working at a constant rate, Felix can complete a job in 4 hours, and his father, when working at a constant rate, can complete the same job in 5 hours. Working together at their same constant rates, how long will it take Felix and his father to complete the job?

1. 2

2. 20/9

3. 3

4. 24/9

5. 4

Explanation: Since Felix can complete a job in 4 hours, his rate is 1/4.

Since his father can complete the same job in 5 hours, his rate is 1/5.

Since they are working together to complete the job, we can let the time they work together = t.

Thus, the work done by Felix is t/4, and the work done by his father is t/5.

Next, we can use the combined work formula to solve for t.

Work of Felix + Work of Father = 1

t/4 + t/5 = 1

Multiplying both sides of the equation by 20, we are left with:

5t + 4t = 20

9t = 20

t = 20/9 hours

Answer: (b) 20/9

Question 4: A box contains only blue pens, black pens, and red pens. If the ratio of blue pens to black pens to red pens is 2 to 5 to 8, and if there are 24 more red pens than blue pens, how many black pens are in the box?

1. 8

2. 15

3. 20

4. 24

5. 30

Explanation: First, we can express the ratio using the ratio multiplier.

blue : black : red = 2x : 5x : 8x

Since there are 24 more red pens than blue pens, we have:

8x – 2x = 24

6x = 24

x = 4

The number of black pens is 5x. Thus, the correct answer is 5 * 4 = 20 black pens.

Answer: (c) 20

Question 5: A particular data point of 12.5 was 1.5 standard deviations above the mean, and another data point of 4.5 was 2.5 standard deviations below the mean. What is the mean of the data set?

1. 5

2. 6.5

3. 7.5

4. 8

5. 9.5

Explanation: We can let m = the mean and d = the standard deviation. Now let’s create our equations:

Since 12.5 was 1.5 standard deviations above the mean, we have:

12.5 = 1.5d + m

m = 12.5 – 1.5d (equation 1)

Since 4.5 was 2.5 standard deviations below the mean, we have:

4.5 = m – 2.5d (equation 2)

Next, we substitute 12.5 – 1.5d from equation 1 for m in equation 2, giving us:

4.5 = 12.5 – 1.5d – 2.5d

4d = 8

d = 2

Finally, we can find the mean as follows:

m = 12.5 – 1.5(2)

m = 12.5 – 3

m = 9.5

Answer: (e) 9.5

Question 6: A carnival stand has only pink cotton candy and red cotton candy. The probability of selecting a pink cotton candy is 1/5. If there are 12 more red cotton candies than pink cotton candies, how many red cotton candies are at the stand?

1. 4

2. 8

3. 12

4. 16

5. 18

Explanation: We can let the number of pink cotton candies = p and the number of red cotton candies = r.

Since the probability of selecting a pink cotton candy is 1/5, we have:

p / (p+r) = 1/5

5p = p + r

4p = r (equation 1)

Next, since there are 12 more red cotton candies than pink cotton candies, we have:

r = p + 12 (equation 2)

From equation 1, we know that 4p = r. So, we substitute 4p for r in equation 2. This gives us:

4p = p + 12

3p = 12

p = 4

We substitute 4 for p in equation 2:

r = 4 + 12

r = 16

Answer: (d) 16

Question 7: The price of a certain television was marked down by 50 percent. Because it still had not sold, the price was eventually marked down another 25 percent before selling for $600. What was the original price of the television?

1. $1,400

2. $1,600

3. $1,700

4. $1,800

5. $2,000

Explanation: We can let the initial price of the TV = p.

After being marked down 50%, the new price is 0.50p.

After being marked down an additional 25%, the new price is 0.75 * 0.50p = 0.375p.

Since the final price is $600, we can create the following equation and use it to determine p:

0.375p = 600

375p = 600,000

p = 1,600

Answer: (b) $1,600

Read also: 15 Hardest GRE Math Questions with Answers

GRE Algebra Preparation and Preparation Books

If you’re looking to ace the algebra section of the GRE, several resources can help you with the best strategies and practice problems. Here’s a breakdown of some popular options:

Kaplan’s GRE Maths Workbook

This workbook goes beyond just practice problems. It offers a personalised study program with expert reviews to pinpoint your strengths and weaknesses in math skills relevant to the GRE. You’ll also find concise introductions to key areas like algebra, , GRE data interpretation and GRE probability, providing a well-rounded foundation.

Princeton Maths Workout for the GRE

This book caters specifically to the quantitative reasoning section of the GRE. It digs deep into essential test topics, providing reviews, insights from top scorers, and a wealth of practice questions. With this comprehensive guide, you’ll gain valuable strategies and hone your problem-solving skills for success.

Nova’s GRE Maths Bible

This aptly named book is a comprehensive resource that covers a wide range of topics and practice questions. It effectively helps you identify areas that need improvement and provides you with the necessary tips and strategies to excel in the GRE. Nova’s Maths Bible offers a variety of practice problems, ranging from beginner to challenging levels, ensuring you’re prepared for anything on the test.

GRE Prep by Magoosh

If you’re looking for a user-friendly approach, Magoosh’s GRE Prep might be the perfect fit. This resource is known for its exceptional set of practice questions accompanied by thorough explanations. The book guides you through a logical progression, starting with clear introductions and explanations, followed by GRE practice test and expert reviews. These well-defined steps help solidify your understanding of key concepts and help you solve problems efficiently.

GRE Algebra Scores

The GRE quant section, though named math, covers a broader range of topics than just basic arithmetic. However, algebra roughly covers a quarter of the quant section that specifically focuses on algebra, including concepts from linear algebra, abstract algebra, and number theory. This means you’ll come across questions on matrices, inequalities, exponents, and more. While a strong grasp of calculus is also important, performing well in the algebra portion will position you to solve the other quant problems effectively.

Suggested: GRE Mathematics Subject Test

From the Desk of Yocket

The GRE Algebra section, while not the most difficult part of the quant section, plays an important role in your overall score. Understanding core algebraic concepts like manipulating equations, working with variables, and interpreting expressions is foundational for many other quant topics on the GRE. Even seemingly non-algebraic problems might require these skills to translate the worded problem into a mathematical form you can solve.

The good news is that the GRE Algebra itself mostly focuses on linear equations and inequalities, which are generally less complex than higher-order algebra. However, don’t be carried away by the seeming simplicity. The GRE cleverly disguises these concepts within worded problems, so you’ll need to have a strong grasp of the underlying algebra to break them down effectively. For comprehensive preparation, consider using Yocket Prep Premium to enhance your skills and boost your confidence.