Top 10 Most-Tested GRE Math Concepts
To get better GRE scores and get into the best graduate schools, you’ll need a strong understanding of the underlying math concepts—arithmetic, algebra, geometry, and data interpretation—as they are tested on the GRE. Even if you’re good at math, a little basic review is a great refresher. Even the best GRE test taker needs a quick review of the concepts tested on the exam.
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- Number Properties: Review odd and even numbers, integers, fractions, positive and negative numbers, zero, factors, multiples, prime numbers, and divisibility. In Quantitative Comparison questions, variables may represent different types of numbers unless the problem provides restrictions. Number properties can also appear in questions about large powers or trailing zeros. Recognizing these patterns can make a problem easier to solve without calculating the entire expression.
- Plane Geometry: Triangles are the most-tested shape on the GRE. You should know the Pythagorean Theorem, Triangle Inequality Theorem, the special right triangle ratios (45-45-90 and 30-60-90), as well as the properties of isosceles and equilateral triangles. Also review the types of angles, circles, and polygons. Make sure you know how to find the perimeter, area, and volume of these shapes.
- Word Problems: The GRE Problem Solving questions often contain challenging word problems – you’ll need to know how to “translate” English to Math.
- Rates and Work: The most important need-to-know formulas on the GRE are D = R x T, Distance = Rate x Time, and the concept of Average Speed. Average Speed = Total Distance / Total Time.
- Probability: The probability of an event occurring is the desired outcomes/total possible outcomes. The probability of two events occurring together is the product of the two probabilities. Memorize the combination and permutation formulas. Combination: n! /n-k! k! Permutation: n! / n-k!
- Ratios and Proportions: A ratio is a relationship, such as 3x:y. Given a ratio and one “real world” number, you can always set up a proportion to solve for the other missing “real world” number. Sometimes you will need to do this for similar triangles in Geometry, and sometimes in algebraic word problems.
- Percents: For percent questions on the GRE with unknown starting values, always pick 100. Make sure to review profit and interest concepts and know the formulas for simple and compound interest.
- Data Analysis:The GRE will present you with graphs, tables, or charts and ask specific questions about the data trends. Always identify what is being presented and what the information suggests BEFORE moving onto the questions. Don’t rush through these questions!
- Functions: A function is a simply a different way of writing an equation; we simply replace the “y” with a symbol,“f(x).” The GRE may also present made-up symbol functions; pay attention to any definitions you are given, and expand accordingly.
- Systems of Equations: You will need to be able to solve for a system of equations. Remember the “n equations with n variables” rule. If you have 2 variables, x and y, then you will need 2 equations with those 2 variables to solve for both. Familiarize yourself with Substitution and Combination.
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GRE Number Properties Example: Counting Trailing Zeros
A GRE number properties question may ask about a feature of a large number rather than its exact value. For example, finding how many zeros appear at the end of a positive integer does not require multiplying out every factor.
Each trailing zero corresponds to a factor of 10. Since 10 = 2 × 5, the number of trailing zeros equals the number of pairs of 2 and 5 in the integer’s prime factorization.
Example: How many trailing zeros does 2⁵ × 3 × 5³ have?
The expression contains five factors of 2 and three factors of 5. Only three pairs of 2 and 5 can be formed, so the number ends in three zeros.
The smaller count determines the answer. Extra factors of 2 cannot create another trailing zero without another factor of 5.
If a question includes addition or subtraction between large products, factor out any common factors first. Then check whether the remaining expression contributes additional factors of 2 or 5. Counting factors in each term separately does not establish how many trailing zeros their sum or difference has.
How to Recognize GRE Number Properties Questions
Reviewing a practice question should reveal both the rule being tested and the clue that points to it. A flashcard can connect those two pieces: place the question’s clue on one side and the next step on the other.
| Clue in the question | Useful next step |
|---|---|
| A positive integer ends in zeros | Count pairs of 2 and 5 in its prime factorization. |
| A question asks about factors, multiples, or divisibility | Break relevant numbers into prime factors, keeping track of repeated factors. |
| An expression contains large powers and subtraction | Look for common factors before calculating. |
During review, students should explain why a method works and then try it on a new problem. Recognizing the same structure with different numbers is more useful than memorizing a single solution.
If an approach is not producing progress during timed practice, students can eliminate any clearly incorrect choices, make a guess, and move on. Reviewing the problem afterward provides an opportunity to identify the missing concept or clue.
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