Formulas You’ll Need for the GMAT™ Quantitative Section’s Algebra Questions

Who likes algebra? The perfect student that always sits at the front, or that guy who is crazy about math? What if you can become a lover of algebra? To ace the algebra-related questions in GMAT™ Quantitative Section, you’ll need way more than just “knowing” algebra. You have to develop a close relationship with the procedures and methods for solving algebra problems and, here at Union Test Prep, we want to help you develop that relationship.

The first step in getting close to someone is getting to know everything about them. That’s why, in the following chart, you’ll find the most important algebra formulas you’ll need to get close and personal with algebra. If you use them to solve the FREE problems we also have for you here at Union Test Prep, we’re sure you won’t dread Algebra anymore, but, instead, you may even long for her!

You’ll find formulas relating to the other types of questions on this section of the test here:

Arithmetic and Geometry

Statistics and Problem Solving

Algebra Formulas

Category	Formula	Symbols	Comment
General Algebra	\(x+a=b \Rightarrow x=b-a\) \(x-a=b \Rightarrow x=b+a\) \(x \cdot a=b \Rightarrow x=b \div a\) \(x \div a=b \Rightarrow x=b \cdot a\) \(x^a=b \Rightarrow x = \sqrt[a]{b}\) \(\sqrt[a]{x}= b \Rightarrow x= b^a\) \(a^x=b \Rightarrow x=\frac{log\ b}{log\ a}\)	a, b = constants x = variable
General Algebra	\(x^a \cdot x^b = x^{a+b}\)	a, b, x = any real number
General Algebra	\(\frac{x^a}{x^b}=x^{a-b}\)	a, b, x = any real number
General Algebra	\((x^a)^b = x^{a \cdot b}\)	a, b, x = any real number
General Algebra	\((x \cdot y)^a = x^a \cdot y^a\)	a, b, x = any real number
General Algebra	\(x^1 = x\)	x = any real number
General Algebra	\(x^0 = 1\)	x = any real number
General Algebra	\(x^{-a} = \frac {1}{x^a}\)	a, x = any real number
General Algebra	\(x^{\frac {a}{b}} = \sqrt[b]{x^a} = (\sqrt[b]{x})^a\)	a, b, x = any real number
General Algebra	\(\frac{x}{\sqrt{y}} \cdot \frac {\sqrt{y}}{\sqrt{y}} = \frac{x \sqrt{y}}{y}\)	x, y = any real number
Linear Equations	\(A \cdot x + B \cdot y = C\)	A, B, C = any real number y = dependent variable x = independent variable	Standard form
Linear Equations	\(y = m \cdot x + b\)	y = dependent variable m = slope x = independent variable b = y axis intercept	Slope-intercept form Try to convert any linear equation to this form.
Linear Equations	\(m = \frac{(y_2 - y_1)}{(x_2 - x_1)}\)	m = slope \(y_n\) = independent variable (point n) \(x_n\) = dependent variable (point n)	This is a rearrangement of the point-slope form.
Linear Equations	\(y-y_1 = m(x-x_1)\)	\((x_1,y_1)\) = point on the line m = slope y = independent variable x = dependent variable	Point-slope form
Quadratic Equations	\(x= \frac{-b \pm \sqrt{b^2-4 \cdot a \cdot c}}{2 \cdot a}\)	a, b, c = constants c = y axis intercept x = variable	Quadratic formula for equation in the form \(a^2+bx+c=0\)
Quadratic Equations	\((a \pm b)^2 = a^2 \pm 2 \cdot a \cdot b + b^2\)	a, b = constants or variables	Square of a sum or difference
Quadratic Equations	\(a^2 - b^2 = (a-b) \cdot (a+b)\)	a, b = constants or variables	Difference of two squares
Cubic Equations	\(a^3 - b^3 = (a-b) \cdot (a^2+ab+b^2)\)	a, b = constants or variables	Difference of two cubes
Cubic Equations	\(a^3 + b^3 = (a+b) \cdot (a^2-ab+b^2)\)	a, b = constants or variables	Sum of two cubes