# 50+ GMAT Math Formulas

#### This article covers most frequently needed math formulas for GMAT exam. These GMAT Math Formulas will be helpful for beginners for getting quickly ready for the exam.

This is an All in one math formulas list for GMAT.

### Formulas for powers or indices

• $a^0 = 1 \mbox{, for all a }$
•  $a^m \times a^n = a^{m+n}$
• $a^m / a^n = a^{m-n}$
• $a^{-m} = \frac {1} {a^m}$
• $a^{b^c} = a^{bc}$

### Square Formulas

• $(a + b)^2 = a^2 + 2ab + b^2$
• $(a - b)^2 = a^2 - 2ab + b^2$
• $a^2 - b^2 = (a - b)(a + b)$
• $(a + b)^2 + (a - b)^2 = 2(a^2 + b^2)$
• $(a + b)^2 - (a - b)^2 = 4ab$

### Cube Formulas

• $(a + b)^3 = a^3+ 3a^2b + 3ab^2+ b^3$
• $(a - b)^3 = a^3- 3a^2b + 3ab^2- b^3$

### Special number zero

• 0/a = 0, where a is not equal to 0.
• $a^0 = 1$
• $0^a = 0$
• $a \times 0 = 0$
• a/0 is undefined

### Simple Interest Calculation

The formula to calculate simple interest is:

$\mbox{p }\times \mbox{t }\times \mbox{r }$

where,

p = principal
r = interest rate
t = time

### Compound Interest Calculation

Formula to calculate the Final amount for compound interest is :

$\mbox{A }= \mbox{p }(1+\frac{\mbox{r}}{\mbox{n}})^{\mbox{nt}}$

where,
A = final amount
p = principal
r = interest rate
t = time in years
n = number of times per year, interest is compounded

### Arithmetic Progression(AP)

Formula for finding nth term in an AP is :

$a + (n-1) d$

Formula for finding sum(S) of n terms in an AP is :

$S = \frac {n} {2} [\mbox{first term} + \mbox{last term}]$

or,

$S = \frac {n} {2} [2a + (n-1)d]$

### Geometric Progression(GP)

Formula for nth term in geometric progression is :

$ar^{n-1}$

Formula for sum of terms in geometric progression is :

if r >1, then

$S = \frac {a(r^n - 1)} {r - 1}$

if r <1, then

$S = \frac {a(1 - r^n)} {1 - r}$

### Logarithms

• $log_a (mn) = log_a m + log_a n$
• $log_a (m/n) = log_a m - log_a n$
• $log_a (m^n) = n log_a m$
• $log_n (m) = log_a m / log_a n$
• $log_n (m) = 1/log_m n$

### Statistics

• #### Mean

Mean or Average of n numbers is calculated as sum of the n numbers divided by n.

For example, in the list of numbers 13, 24, 3,24, 5 , Mean is (13+24+3+24+5)/5 = 13.8

• #### Median

For calculating Median, first sort the numbers from smallest to largest; then if n is odd, Median is the middle number. If n is even, the median is the average of 2 middle numbers.

For example, in the numbers 13, 24, 3,24, 5 , Median is 13.

• #### Mode

Mode is the number that is repeated more often than any other in the group of numbers.

For example, in the numbers 13, 24, 3,24, 5 , mode is 24.

• #### Range

Range is the difference between the largest and smallest number if the group.

For example, in the numbers 13, 24, 3,24, 5 , Range is 24-3 = 21.

• #### Standard Deviation

• Find squared difference between mean and each number
• Find the average of the square of the differences
• Take the nonnegative square root of average

### Sets

$|A \cup B| = |A| + |B| - |A \cap B|$

For disjoint sets,
$|A \cup B| = |A| + |B|$

### Permutations and Combinations

• $P(n,r) = \frac {n!} {(n-r)!}$
• $C(n,r) = \frac {n!} {r! (n-r)!}$

### Probability

$P(E) = \frac {\mbox{No of outcomes in E}} {\mbox{Total outcomes}}$

$P(not E) = 1 - P(E)$

$P(E \cup F) = P(E) + P(F) - P(E \cap F)$

The standard form of quadratic equation is :
$ax^2 + bx + c = 0, a\ne 0$

Its roots can be found as :

• $x = \frac {-b + \sqrt(b^2 - 4ac)} {2a}$
• $x = \frac {-b - \sqrt(b^2 - 4ac)} {2a}$

### Coordinate Geometry Formulas:

• Distance between two points (x1,y1) and (x2,y2) formula
$d = \sqrt {(x_2-x_1)^2 + (y_2-y_1)^2}$
•

• Midpoint formula:
$(\frac {x_1+x_2} {2} , \frac {y_1+y_2} {2})$

#### Parallels lines intersected by another line

If lines are parallel, then :

• Corresponding angles are equal.

$\angle {1} = \angle 5, \angle 2= \angle 6, \angle 3 = \angle 7, \angle 4 = \angle 8$

• Alternate Interior angles are equal.

$\angle 3 = \angle 6, \angle 4 = \angle 5$

• Alternate Exterior angles are equal.

$\angle 1 = \angle 8, \angle 2 = \angle 7$

• Same side interior angles are supp.

$\angle 3 + \angle 5 = 180, \angle 4 + \angle 6 = 180$

### Triangles:

By Sides

• Scalene – all sides different
• Isosceles – 2 equal sides
• Equilateral – 3 equal sides

By Angles:

• Acute triangle – all acute angles
• Right triangle– one right angle
• Obtuse triangle – one obtuse angle
• Equiangular – 3 congruent angles(60º)
• Equilateral ↔ Equiangular

Exterior angle of a triangle equals the sum of the 2 non-adjacent interior angles.

Mid-segment of a triangle is parallel to the third(opposite) side and half the length of the third side

#### Pythagorean Theorem:

If in a right triangle with sides a, b, c, where c is the hypotenuse, then

$c^2 = a^2 + b^2$

Conversely, If the sides of a triangle satisfy
$c^2 = a^2 + b^2$, then the triangle is a right triangle.

#### 30-60-90 triangle:

In 30-60-90 triangle, the sides are x, $x\sqrt {3}$ and the hypotenuse is 2x (double the
size of the smallest side)

### Circles

Equation of circle center at origin(0,0):

$x^2 + y^2 = r^2$, where r is the radius.

Equation of circle not at origin(0,0):

$(x-h)^2 + (y-k)^2 = r^2$, where (h,k) is the center and r is the radius.

### Sum of interior angles of Polygon

The formula for sum of the interior angles of a n-sided polygon is :

$(n-2) 180 \textdegree$

For example, the sum of angles in a triangle is (3-2)180° = 180°.

### Area and Perimeter

• #### Square

If length of each side of a square is a, then the area and perimeter can be calculated as :
$Area = a^2$
$Perimeter = 4*a$

• #### Rectangle:

$Area = length*width$
$Perimeter = 2(length) + 2(width)$

• #### Parallelogram:

$Area = base*height$
$Perimeter = 2(base) + 2(height)$

• #### Circles:

$Area = \pi r^2$
$Circumference = 2 \pi r$

### 3D figures

V=Volume, SA = Surface Area, B = Base, h = Height

• #### Cylinder:

$V = \pi r^{2}h$
$SA = 2 \pi rh + 2 \pi r^{2}$

•

• #### Cone:

$V = \frac{1}{3} \pi r^{2} h$
$SA = \pi rl + \pi r^2$

l = slant height

•

• #### Sphere:

$V = (4/3) \pi r^3$
$SA = 4 \pi r^2$

•

• #### Cube:

$V = a^3$
$SA = 6a^2$

References