**Last Updated: Jun 11, 2015**

The GRE and the GMAT are the gateways to graduate school, and both tests require strong algebra skills. Here are six concepts that are almost guaranteed to appear on the GRE and the GMAT! Even if it has been awhile since you’ve cracked a math textbook, you’ll be surprised by how much comes back to you! Start by exploring the free Quantitative PDF study guides on the official GRE and GMAT websites. You’ll soon be rocking these concepts (and many others) on your next practice test! And if you need a little review, you can learn All About the GRE and All About the GMAT on Learnist!

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

It’s easy to forget this rule, especially when the GRE combines inequalities with other topics such as absolute value. The non-flipped version will be one of the wrong answer choices (of course!).

-2x + 7 > 15

-2x > 8 (When we divide by the negative 2, the sign is flipped)

x < -4

## A “number” is not an integer.

It may sound obvious, but don’t make assumptions about unknown quantities on the GRE. “Numbers” can be positive integers, negative integers, decimals/fractions, or 0. Choose ½ and -½ to test for different outcomes, especially in Quantitative Comparisons.

## Quadratic equations have two solutions.

x^{2} - 5x + 6 = 0 This is called the “quadratic.”

(x – 3) (x – 2) = 0 These are called the “factors.”

x = 3, x = 2 These are called the “roots” or the “solutions.”

## x, f(x) can be thought of as (x, y).

Functions look intimidating because we often aren’t sure what to plug in and where. What is inside the parentheses should be plugged in for x. What is equal to f(x) should be plugged in for f(x).

f(x) = 8x – z , and f(4) = 10. What is the value of z?

Here we are told that x = 4, and f(x) = 10.

10 = 8(4) – z

10 = 32 – z

-22 = -z

22 = z

## Non-prime integers >1 can be written as a product of primes.

The GRE tests number properties heavily, and you will be required to rewrite numbers as a product of their factors.

Example: find the greatest common factor of 210 and 63.

210 = 2 x 3 x 5 x 7

63 = 3 x 3 x 7

The prime factorizations have 3 x 7 in common. The GCF is 21.

## 2 is the only even prime number and the smallest prime.

When you use the strategy Picking Numbers, you will often want to choose 2 for one of your values. Often 2 will produce a different result than all the other prime numbers because it is even.