GRE Math Review Fundamentals

The Quantitative Reasoning sections of the GRE General Test are designed to assess your basic mathematical skills, understanding of elementary concepts, and ability to reason quantitatively. For many prospective graduate students, these topics haven't been practiced since high school, making a systematic review of fundamentals—paired with GRE-specific strategy—essential for achieving a competitive score. This review will rebuild that foundation, focusing on the core arithmetic, algebra, geometry, and data analysis you need, while training you to apply them under the unique pressures of the exam.

Arithmetic Fundamentals: The Bedrock of GRE Math

Success on the GRE quantitative section begins with rock-solid arithmetic. You must be able to manipulate numbers and their properties quickly and accurately without a calculator for the first section. Number properties include understanding integers, primes, evens/odds, positives/negatives, and the rules of divisibility. A common GRE twist is testing these concepts within inequalities or sequences.

Operations with fractions, percentages, and ratios form a huge portion of real-world word problems. Mastery here is non-negotiable. For fractions, be fluent in multiplication, division, addition, and subtraction, and always simplify to lowest terms. For percentages, remember that "percent" means "per hundred"; the formula "Percent = (Part/Whole) * 100%" is fundamental. Crucial GRE skills include calculating percent increase/decrease and solving for the original whole after a percent change.

Ratios express a part-to-part relationship and are often the key to solving complex proportion problems. If the ratio of apples to oranges is 3:5, you can represent the apples as $3x$ and oranges as $5x$. This technique of using a multiplier is invaluable for dividing a total into ratio parts or for combining ratios. Always distinguish between a ratio and an actual quantity; the GRE loves to test this distinction.

Algebra and Geometry: Translating Words into Equations

GRE algebra tests your ability to manipulate algebraic expressions and solve equations. The most critical skill is setting up an equation from a word problem. Identify the unknown, assign a variable, and translate the English phrases into mathematical operations step-by-step. Key concepts include factoring, expanding, simplifying expressions, and solving linear and quadratic equations. Remember the FOIL method for binomials and the quadratic formula: for $a{x}^2+bx+c=0$, the solutions are given by $$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$.

Coordinate geometry bridges algebra and visual reasoning. You must know the standard forms for lines (slope-intercept: $y=mx+b$, point-slope), how to calculate slope ($m=(y_2-y_1)/(x_2-x_1)$), and what slopes indicate (positive, negative, zero, undefined). Understand how to find intercepts, the distance between two points, and the midpoint of a line segment. The relationship between a line's equation and its graph should be second nature, as questions often ask for a line's equation given its graph or properties.

Data Analysis: Interpreting Statistics and Chance

The GRE's data analysis questions cover descriptive statistics and basic probability. For statistics, you'll need to calculate and interpret the mean (average), median (middle value), mode (most frequent value), range, and standard deviation (a measure of data spread). A classic trap is how the mean is affected by adding or removing data points, while the median is more resistant to extreme values. Reading data from tables, bar graphs, line graphs, circle charts, and scatterplots is a tested skill; always examine axes, scales, and titles carefully.

Probability measures the likelihood of an event, expressed as a number between 0 and 1. The basic formula is: Probability of an event = (Number of favorable outcomes) / (Total number of possible outcomes). Understand the difference between independent events (where you multiply probabilities) and mutually exclusive events (where you add probabilities). The "1 minus" trick is powerful: the probability that an event does not occur is 1 minus the probability that it does. Many GRE probability problems involve simple scenarios with dice, cards, or selections from groups.

Common Pitfalls

1. Misreading Ratio Problems: A problem stating "the ratio of A to B is 3:4" does not mean A is 3 and B is 4. They are multiples. The most reliable method is to set $A=3k$ and $B=4k$, then use other given information to solve for the multiplier $k$.

• Correction: Always introduce a variable multiplier when translating a ratio into actual quantities.

1. Percent Change Confusion: A common error is calculating a new value after successive percent changes. A 20% increase followed by a 20% decrease does not return you to the original amount. The multiplier for a 20% increase is 1.2; for a 20% decrease, it's 0.8. The net change is found by multiplying: $1.2\ast 0.8=0.96$, a 4% overall decrease.

• Correction: For sequential percent changes, use multiplication of decimal multipliers, not addition or subtraction of percentages.

1. Assuming Diagrams Are Drawn to Scale: In the GRE Quantitative sections, geometry diagrams are not necessarily drawn to scale unless explicitly stated. You cannot visually estimate lengths or angle sizes.

• Correction: Use only the information given in the text. If a line looks like a bisector but isn't labeled as one, you cannot assume it is.

1. Overcomplicating Probability: Test-takers often try to use advanced formulas for simple scenarios. The GRE primarily tests foundational probability.

• Correction: Break the problem down. List the total possible outcomes and the favorable ones. Often, systematically counting is safer than recalling a complex formula.

Summary

• A thorough, concept-based review of high school arithmetic, algebra, geometry, and data analysis is the cornerstone of GRE quantitative preparation, as the test assesses reasoning built on these fundamentals.
• Master the core operations with fractions, percents, and ratios, as they are central to solving a high percentage of GRE word problems. Use the multiplier technique for ratios.
• Your ability to translate a word problem into an algebraic equation is a critical skill. Practice identifying variables and relationships described in text.
• For coordinate geometry, be fluent in the relationships between a line's slope, its equation, and its graphical representation.
• In data analysis, know how to calculate and interpret basic statistics (mean, median, mode, range) and solve probability problems using the basic formula and rules for independent/mutually exclusive events.
• Always be strategic: use the exam's format to your advantage by plugging in answer choices, estimating, and eliminating trap answers that reflect common calculation errors.