Formulas You’ll Need for the GMAT™ Quantitative Section’s Arithmetic and Geometry Questions

The GMAT™ is a very special kind of test. You will not be able to skip any questions, and the penalty for skipping them is greater than that for getting them wrong. The questions go above and beyond just plugging in values in an equation. You need to be able to think critically, but it would be a very sad scenario if your thought process is hindered by not remembering the proper formula for the problem you’re solving.

Thankfully, we are here to help you! In the following chart, you’ll find the essential arithmetics and geometry formulas you’ll need for the GMAT™ Quantitative Section, so you will not forget them when the test comes. You’ll find formulas relating to the other types of questions on this section of the test here:

Algebra

Statistics and Problem Solving

You can practice for the test by solving our FREE sample test.

Arithmetic and Geometry Formulas

Category	Formula	Symbols	Comment
Arithmetic	\(a+b=b+a\) \(a \cdot b = b \cdot a\)	a, b = any constant or variable	Commutative Property
Arithmetic	\(a+(b+c)=(a+b)+c\) \(a \cdot (b \cdot c)=(a \cdot b) \cdot c\)	a, b, c = any constant or variable	Associative Property
Arithmetic	\(a \cdot (b+c)=a \cdot b + a \cdot c\)	a, b, c = any constant or variable	Distributive Property
Arithmetic	\(a+0=a\)	a = any constant or variable	Identity Property of Addition
Arithmetic	\(a \cdot 1 = a\)	a = any constant or variable	Identity Property of Multiplication
Arithmetic	\(\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{(a \cdot d)+(c \cdot b)}{(b \cdot d)}\)	a, b, c, d = any real number	Remember to simplify the fraction if possible.
Arithmetic	\(\dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{a \cdot c)}{(b \cdot d)}\)	a, b, c, d = any real number	Remember to simplify the fraction if possible.
Arithmetic	\(\dfrac{a}{b} \div \dfrac{c}{d}=\dfrac{a \cdot d)}{(b \cdot c)}\)	a, b, c, d = any real number	Remember to simplify the fraction if possible.
Arithmetic	\(a\dfrac{b}{c}=\dfrac{(a \cdot c)+b}{c}\)	a, b, c = any real number	Remember to simplify the fraction if possible.
Percents	\(a \cdot b\%=a \cdot \dfrac{b}{100}\)	a = any real number b% = any percent	Remember to simplify the fraction if possible.
Percents	\(\% = \dfrac{\vert b-a \vert}{b} \cdot 100= \dfrac{c}{b} \cdot 100\)	% = % increase or decrease a = new value b = original value c = amount of change
Geometry	\(A=\frac{1}{2} \cdot b \cdot h\)	A = area of triangle b = base h = height
Two Dimensional Shapes	\(a^2+b^2=c^2\)	a, b = legs of a right triangle c = hypotenuse of a right triangle
Two Dimensional Shapes	\(P=4 \cdot s\)	P = Perimeter of a square s = side length
Two Dimensional Shapes	\(P=(2 \cdot l)+(2 \cdot w)\)	P = Perimeter of a rectangle l = length w = width
Two Dimensional Shapes	\(A=s^2\)	A = Area of a square s = side length
Two Dimensional Shapes	\(A=l \cdot w\)	A = Area of a rectangle l = length w = width
Two Dimensional Shapes	\(A=h \cdot \frac{(b_1+b_2)}{2}\)	A = Area of a trapezoid \(b_n\) = base n h = height
Two Dimensional Shapes	\(C=2 \cdot \pi \cdot r\) or \(C=\pi \cdot d\)	C = Circumference of a circle r = radius d = diameter
Two Dimensional Shapes	\(S=r \cdot \theta\)	s = arc length r = radius \(\theta\) = central angle (radians)
Two Dimensional Shapes	\(A=\pi \cdot r^2\)	A = Area of a circle r = radius
Three Dimensional Shapes	\(V=l \cdot w \cdot h\)	V = Volume of a rectangular prism l = length w = width h = height
Three Dimensional Shapes	\(SA= \Sigma A_{fi}\)	SA = Surface Area of a prism \(A_{fi}\) = Area of face i
Three Dimensional Shapes	\(V=\frac{1}{3} \cdot (l \cdot w \cdot h)\)	V = Volume of a pyramid with rectangular base l = length w = width h = height
Three Dimensional Shapes	\(SA=\Sigma A_{fi}\)	SA = Surface Area of a pyramid \(A_{fi}\) = Area of face i
Three Dimensional Shapes	\(V= \pi \cdot r^2 \cdot h\)	V = Volume of a cylinder r = radius h = height
Three Dimensional Shapes	\(SA=2B+(C \cdot h)\)	SA = Surface Area of a cylinder B = Area of the Base C = Circumference of the Base h = height
Three Dimensional Shapes	\(V= \frac{4}{3} \cdot \pi \cdot r^3\)	V = Volume of a sphere r = radius
Three Dimensional Shapes	\(SA=4 \cdot \pi \cdot r^2\)	SA = Surface Area of a sphere r = radius of the sphere