GMAT Number theory questions are part of GMAT problem solving section, in particular they belong to the Arithmetic type of questions. There are several important concepts involving number theory and properties that will help you succeed in writing your GMAT. Here we review these concepts.

Basic Number Properties

A number is an integer if it is a whole number with no fractions or decimals. For example, 1, -13, 752 are integers. 1.1, and are not integers.

An integer that is divisible by 2, such as 4, 16 or 299388456, is even. A number that is not divisible by 2 is called odd. Note:

• Odd + Odd = Even
• Even + Even = Even
• Even + Odd = Odd
• Odd * Odd = Odd
• Even * Even = Even
• Even * Odd = Even

A number is called prime if it has exactly two factors- 1 and itself. If the number has any other divisors or factors, it’s not a prime, and we call it composite. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, etc. are prime numbers.

Consecutive integers are integers that are separated by 1. For example, (1, 2, 3), (99, 100, 101) and (34563, 34564, 34565) are sets of consecutive integers. We can represented them as n, n+1, n+2, n+3, etc.

There are two important numbers that satisfy interesting properties. First, 0. For any number, , while . The second number is 1, which satisfies for all n.

Basic Operational Properties

You should know the basic properties of addition, multiplication, and absolute value:

• ,
• , and
• 
• if a is positive, and if a is negative. Basically, |a| is the magnitude of a and will always be positive regardless of a.
• If , either or or both.
• . This is called the triangle property.

The properties above make up the bulk of number-theory-related questions you may encounter in the GMAT. Don’t forget to review all of these, even if they’re basic- you will need to know them like the back of your hand.

Practice GMAT Number Thoery Problems

Practice makes perfect!

GMAT Arithmetic (10 problems) GMAT Number System (10 problems) GMAT Number Theory (10 problems), GMAT Number System (10 problems)

Related Concepts: GMAT Arithmetic and GMAT Algebra.