GMAT Club Math Book - Number Theory - Study Notes

Sep 22, 2026

Uploaded by Jasmine

GMAT Club Math Book provides structured study notes for GMAT quantitative topics, beginning with Number Theory and its core number types: integers, rational (fractions), and irrational numbers. It defines key concepts such as even and odd integers, positive and negative real numbers, and prime versus composite numbers, clarifying exclusions like decimals in integers. The material also covers foundational arithmetic rules for parity and sign, plus examples for irrational values such as √2 and π.

LanguageEnglish

CategoryExam

FormatPDF

Pages126

Reading Time5 h 18 min

AccessFree to download

Number Theory

GMAT Number Types

Integers

Positive and Negative Numbers

Prime Numbers

For the latest version of the GMAT.BUI \#Pok, please visit: [http://gmatclub.com/NBUICPPL](http://gmatclub.com/NBUICPPL) GMAT Club’s Other Resources: GMAT Club CAT Tests [gmatclub.com/tests](gmatclub.com/tests) The Verbal Initiative [gmatclub.com/verbal](gmatclub.com/verbal) GMAT Club Math Book [gmatclub.com/mathbook](gmatclub.com/mathbook) GMAT Toolkit iPad App [gmatclub.com/iPhone](gmatclub.com/iPhone) GMAT Course & Admissions Consultant Reviews [gmatclub.com/reviews](gmatclub.com/reviews) Facebook [facebook.com/](facebook.com/)[ ](facebook.com/)gmatclubforum Table of Contents Number Theory .................................................................................. 3 INTEGERS.................................................................................................. 3 IRRATIONAL NUMBERS ................................................................................... 3 POSITIVE AND NEGATIVE NUMBERS .................................................................... 4 FRACTIONS ................................................................................................ 9 EXPONENTS .............................................................................................. 12 LAST DIGIT OF A PRODUCT ............................................................................ 13 LAST DIGIT OF A POWER ............................................................................... 13 ROOTS .................................................................................................... 14 PERCENT ................................................................................................. 15 Absolute Value .................................................................................. 17 Factorials ......................................................................................... 21 Algebra............................................................................................ 23 Remainders ...................................................................................... 27 Word Problems Overview ..................................................................... 33 Distance/Speed/Time Word Problems ...................................................... 37 Work Word Problems ........................................................................... 45 Advanced Overlapping Sets Problems....................................................... 49 Polygons .......................................................................................... 66 Circles ............................................................................................. 72 Coordinate Geometry .......................................................................... 81 Standard Deviation ........................................................................... 101 Probability ..................................................................................... 105 Combinations & Permutations .............................................................. 111 3‐D Geometries ................................................................................ 118 GMAT Club Math Book ‐ 2 ‐ part of GMAT ToolKit iPhone App Number Theory Definition Number Theory is concerned with the properties of numbers in general, and in particular integers. As this is a huge issue we decided to divide it into smaller topics. Below is the list of Number Theory topics. GMAT Number Types GMAT is dealing only with Real Numbers: Integers, Fractions and Irrational Numbers. INTEGERS Definition Integers are defined as: all negative natural numbers , zero , and positive natural numbers . Note that integers do not include decimals or fractions ‐ just whole numbers. Even and Odd Numbers An even number is an integer that is "evenly divisible" by 2, i.e. , divisible by 2 without a remainder. An even number is an integer of the form

FAQs

What number types does GMAT focus on for Number Theory?

GMAT deals with real numbers: integers, fractions (rational numbers), and irrational numbers. These types are treated as distinct categories with no overlap between rational and irrational numbers.

How are integers defined in this material?

Integers are all negative natural numbers, zero, and positive natural numbers. Integers are whole numbers and do not include decimals or fractions.

What is the difference between prime and composite numbers here?

A prime number has exactly two distinct natural number divisors: 1 and itself. A composite number can be written as a product of two factors both greater than 1, and 1 is not prime because it has only one divisor.

Sep 22, 2026

Uploaded by Jasmine

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