Foundations of GMAT Math

Manhattan GMAT

• Publisher: Manhattan Prep Publishing
• Year: 2011
• Print ISBN: 9781935707592
• eBook ISBN: 9780979017599
• Topic: Study Aids
• Subtopic: GMAT Study Guides

Manhattan GMAT's Foundations of Math book provides a refresher of the basic math concepts tested on the GMAT. Designed to be user-friendly for all students, this book provides easy-to-follow explanations of fundamental math concepts and step-by-step application of these concepts to example problems. With ten chapters and over 700 practice problems, this book is an invaluable resource to any student who wants to cement their understanding and build their basic math skills for the GMAT. Purchase of this book includes six months online access to the Foundations of Math Homework Banks consisting of over 400 extra practice questions and detailed explanations not included in the book.

Chapter 1:

Arithmetic

Our goal in this book is not only to introduce and review fundamental math skills, but also to provide a means for you to practice applying these skills. Toward this end, we have included a number of “Check Your Skills” questions throughout each chapter. After each topic, do these problems one at a time, checking your answers at the back of the chapter as you go. If you find these questions challenging, re-read the section you just finished.

In This Chapter:

• Quick Start rules of numbers

• PEMDAS

• Combining like terms and pulling out common factors

Quick-Start Definitions

Whether you work with numbers every day or avoid them religiously, give a good read to this first section, which gives “quick-start” definitions for core concepts. We'll come back to many of these concepts throughout the book. Moreover, bolded terms in this section can be found in the glossary at the back of the book.

Basic Numbers

All the numbers that we care about on the GMAT can be shown as a point somewhere on the number line.

Another word for number is value.

Counting numbers are 1, 2, 3, and so on. These are the first numbers that you ever learned—the stereotypical numbers that you count separate things with.

Digits are ten symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) used to represent numbers. If the GMAT asks you specifically for a digit, it wants one of these ten symbols.

Counting numbers above 9 are represented by two or more digits. The number “four hundred twelve” is represented by three digits in this order: 412.

Place value tells you how much a digit in a specific position is worth. The 4 in 412 is worth 4 hundreds (400), so 4 is the hundreds digit of 412. Meanwhile, 1 is the tens digit and is worth 1 ten (10). Finally, 2 is the units digit and is worth 2 units, or just plain old 2.

412	=	400	+	10	+	2
Four hundred twelve	equals	4 hundreds	plus	1 ten	plus	2 units (or 2).

The GMAT always separates the thousands digit from the hundreds digit by a comma. For readability, big numbers are broken up by commas placed three digits apart.

1,298,023 equals one million two hundred ninety-eight thousand twenty-three.

Addition (+, or “plus”) is the most basic operation in arithmetic. If you add one counting number to another, you get a third counting number further out to the right.

7	+	5	=	12
Seven	plus	five	equals	twelve.

12 is the sum of 7 and 5.

You can always add in either order and get the same result.

5	+	7	=	12
Five	plus	seven	equals	twelve.

Subtraction (–, or “minus”) ...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Table of Contents
• 1. Arithmetic
• 2. Divisibility
• 3. Exponents & Roots
• 4. Fractions
• 5. Fractions, Decimals, Percents, & Ratios
• 6. Equations
• 7. Quadratic Equations
• 8. Beyond Equations: Inequalities & Absolute Value
• 9. Word Problems
• 10. Geometry
• Glossary