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**MATH FORMULAS **

**The most powerful EMPOWER tactic for the Quantitative section of the GMAT**

**WHY Learn GMAT Math Formulas?**

1. Including Geometry, more than half the questions in the Quant section involve a speciﬁc math formula (or more than 1), so knowing the formulas is a must to solving the problem.

2. Math formulas can be used to answer many different versions of the same question.

3. TRIAGE can become easier in some cases by using the formula to estimate the approximate answer to a question.

__Area & Perimeter Formulas__**Square:**

- Area = length
^{2} - Perimeter = 4*length

**Rectangle:**

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

**Parallelogram:**

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

**Circles:**

- Area = πr
^{2}^{ } - Circumference = 2πr

**Triangle:**

- Pythagorean Theorem: a
^{2}+b^{2}=c^{2}

**Trapezoid:**

- Area = where a and b are the length of the parallel sides

**Circle Formulas**

Central angle = 2*(inscribed angle)

Area of a sector = where x is the measurement of the central angle of the circle portion in degrees

**Volume formulas**

Cube: (length)^{3}

Cylinder: πr^{2}*h** **

Pyramid: 1/3 (base length*base width*height)

__GMAT Arithmetic Formulas__

Arithmetic concepts are one of the most heavily tested content areas on the GMAT quant section, making up nearly 50% of GMAT quant question types. These GMAT quant formulas address the majority of concepts covered on the GMAT.

**Order of operations**

Parentheses – Exponents – Multiplication – Division – Addition – Subtraction (PEMDAS)

**Number properties**

(Positive Number) * (Positive Number) = (Positive Number)

(Positive Number) * (Negative Number) = (Negative Number)

(Negative Number) * (Negative Number) = (Positive Number)

(Positive Number) / (Positive Number) = (Positive Number)

(Positive Number) / (Negative Number) = (Negative Number)

(Negative Number) / (Negative Number) = (Positive Number)

(Odd Number) + (Odd Number) = (Even Number)

(Odd Number) – (Odd Number) = (Even Number)

(Odd Number) + (Even Number) = (Odd Number)

(Odd Number) – (Even Number) = (Odd Number)

(Even Number) + (Even Number) = (Even Number)

(Even Number) – (Even Number) = (Even Number)

(Odd Number) * (Odd Number) = (Odd Number)

(Odd Number) * (Even Number) = (Even Number)

(Even Number) * (Even Number) = (Even Number)

**Permutations and Combinations**

Permutation formula:

Combination formula:

**Probability**

Probability = (Number of favorable outcomes) / (Number of all possible outcomes)

Probability of events A & B happening = (Probability of A) * (Probability of B)

Probability of either event A or B happening = (Probability of A) + (Probability of B)

__GMAT Algebra Formulas__

Algebra questions make up about 20% of the question types you’ll see on the GMAT quant section.

**Absolute Value**

|x| depicts absolute value.

|x| = x

|-x| = x

|x| = |-x|

|x| ≥ 0

|x| + |y| ≥ |x+y|

**Exponent Rules**

In the expression x^{n}, ‘x’ is the base and ‘n’ is the exponent. The way to interpret is that the base ‘x’ gets multiplied ‘n’ times. For example, 2^{3}=2*2*2.

Some key rules and formulas for exponents:

0^{n}=0

1^{n}=1

x^{0}=1

x^{1}=x

xm*xn=x(m+n)

**Quadratic Equations**

ax^{2}+bx+c=0

**Interest**

All interest formulas use the following variables: P = starting principle; r = annual interest rate; t = number of years.

Simple Interest = P*r*t

Annual Compound Interest = P(1+r)t

Compound Interest = P(1 + r/x)^(xt); x = number of times the interest compounds over the year

**Other Algebra Formulas**

Distance = Speed * Time

Wage = Rate * Time

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