Top 5 Tips for GRE Algebra Questions

Here are the top five(5) tips that are almost guaranteed to appear on Test Day.

Top 5 Tips

1. For n equations, you need n variables to solve.
2. Substitute carefully for Functions
3. Know your number properties.
4. Flip the inequality when you multiply or divide by a negative number.
5. Remember that Quadratic equations have two solutions.

1. For n equations, you need n variables to solve.

The GRE will often present you with two or more equations with multiple variables. If there are 2 variables in an equation (for example, x and y), then there must be 2 equations that each contain those variables in order to solve. The two common ways to solve are Substitution and Combination.

2. Substitute carefully for Functions.

It’s helpful to think of (x, f(x)) as another way of writing (x, y). For many function questions, you can Pick Numbers or Substitute for the variables to solve! For example, if a question provides a Function such as f(x) = 3x + 2, and wants to know what f(x – 1) is when x = 3, first rewrite the function, substituting x – 1 in for x. We would get: f(x – 1) = 3(x – 1) + 2, or f(x – 1) = 3x – 3 + 2. That becomes f(x – 1) = 3x – 1. Now the question asks what f(x – 1) will be when x = 3. Substitute in x = 3 to solve. f(x – 1) = 3(3) – 1 becomes f(x – 1) = 9 – 1. The answer is f(x – 1) = 8.

3. Know your number properties.

The GRE tests number properties heavily, and you must be comfortable with words like integers, rational numbers, primes, etc. The properties of odds and evens, integers, fractions, positives, and negatives will all appear in various questions on your GMAT test as well. Don’t ever make assumptions about unknown variables. Unless you are told otherwise by the limitations in the question, variables can be negative integers, negative fractions, zero, positive fractions, or positive integer. You may need to Pick Numbers from multiple categories, especially for Quantitative Comparisons questions.

4. Flip the inequality when you multiply or divide by a negative number.

Remember that when you multiply or divide by a negative number, you must reverse the direction of the inequality. The non-flipped version will almost always be one of the wrong answer choices (of course!).

-4x + 5 > 17
-4x > 12 (When we divide by the negative 4, the sign is flipped)
x < -3

5. Remember that Quadratic equations have two solutions.

You’ll need to be able to FOIL and Reverse-FOIL on the GRE.

x^2 – 7x + 6 = 0 This is called the “quadratic equation”
(x – 6) (x – 1) = 0 These are called the “factors.”
x = 6, x = 1 These are called the “roots” or the “solutions.”