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:
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  \(\% = \dfrac{\vert ba \vert}{b} \cdot 100= \dfrac{c}{b} \cdot 100\)  % = % 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 
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