### 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: nPr=n!(n−r)!

Combination formula: nCr=n!((r!)(n−r)!)

#### FRACTIONS

(a/b)/(c/d) = (a/b) * (d/c)

#### PERCENTS

Percent Change, as a decimal = (New – Old)/Old

N = (1 + G)O; N = New Value, 0 = Old Value, G = Growth Rate as decimal

#### 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)