# Math definitions

GMAT Study Guide - a prep wikibook

No matter how brilliant you are, you need to know the conventions in the field. Math, and particularly GMAT math, has several conventions, definitions, and jargon terms. They are collected in this page.

## Top quirks

This is a short list of truisms knowing which can save you from the most common errors:

1. 0 is not positive, nor negative
2. 0 is a multiple of every number, and therefore is even
3. 0 and 1 are neither prime nor composite
4. 0 is greater than -1
5. $0^0$ is undefined
6. $\sqrt{x} \ge 0$
7. 2 is the only even prime number

## Number families

real
all numbers on GMAT are real
integer
{..., -3, -2, -1, 0, 1, 2, 3, ...}
fractional
non-integer reals, such as 3.1417
whole
{0, 1, 2, 3, ...}
even
{..., -4, -2, 0, 2, 4 ...}
odd
{..., -3, -1, 1, 3, ...}
positive
any number strictly greater than zero
negative
any number strictly less than zero
perfect squares
{1, 4, 9, 16, ...} - integer squares of other integers
prime
{2, 3, 5, 7, 11, 13, ...} - see below for a definition
composite
{4, 6, 8, 9, ..} - non-prime positive integers except 1

## Factors and multiples

Suppose $a=pq$ (all numbers are whole). Then:

1. $a$ is a multiple of $p$ and of $q$
2. $p$ and $q$ are divisors (factors) of $a$

## Prime and composite numbers

The positive integer $p$ ($p > 1$) is a prime if the only positive divisors of $p$ are 1 and itself. The first 10 primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. All other positive integers (except 1) that are not prime are composite numbers.