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Foundations of GMAT Math Review

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Joined: 11 Nov 2011
Posts: 46
Concentration: Finance
GMAT Date: 08-04-2012
GPA: 3.3
WE: Accounting (Non-Profit and Government)
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New post 28 Jan 2012, 15:11
Chapter 1-Arithmetic (40 Practice Problems but there are more problems after each section of the chapters)

This chapter focused mainly on arithmetic. Below are the topics covered.
Chapter one focused on the basics of arithmetic math on the GMAT such as addition and subtraction on the number line as well as the direction of positive and negative numbers on it. The book also breaks down the terminology so you can gain a better understanding of the concepts. For example, it stated to focus on “like terms” which meant it contains very similar “stuff.” Then it explains how an expression does not contain any addition or subtraction and how a term is just a bunch of things multiplied together.

• Basic numbers, Digits(0,1,2,3,4,5,6,7,8, and 9), and Units Digit, and Place Value (how much a digit in a specific position is worth)
• Number Line
• Multiplying (negatives and positives) and Dividing
• Distributing and Factoring
• PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition,Subtraction)

There is a section in the book that really helps the reader because it breaks down the concepts. Below is an example. It kept the explanations simple and it broke it down so it didn’t confuse the reader.
What you see.............................What you say...............................What it means
x+y.............................................x plus y..............................x plus y, or the sum of x and y

Chapter 2-Divisibility (42 Practice Problems)
• It covered divisibility by 2,3,5,9, and 10.
• It links factors and divisibility-Factors are Divisors.
• Prime numbers and Prime Factorization using prime trees.
• Factor Foundation Rule-every number is divisible by the factors of its factors.
• How to factor with unknown numbers.
• Factors of X with No Common Primes

Chapter 3-Exponents and Roots (63 Practice Problems)

• What is an Exponent
• It tells you to memorize certain Perfect Squares and Cubes
• Also it tells you to memorize Powers of 2,3,4,5 and 10.
• Multiplying Exponential Terms with Same Base
• Dividing Exponential Terms with Same Base
• Negative Powers
• Applying Two Exponents
• Applying an Exponent to a Product
• Adding or Subtracting Terms with the Same Base
• Square Roots and Cube Roots
• Multiplying Square Roots and Simplifying Roots
• Addition and Subtraction with Roots

Here is another example of how the authors did a really good job. They used the format below to better explain and break down the concepts. This helped the most when I was studying the chapters.
If you........................................................................Then you.......................................Like this:
Raise something to two successive powers...............Multiply the powers............................(a²)^4=a^8

Chapter 4-Fractions (66 Practice Problems)
• Numerator and Denominator
• Adding Fractions with the Same Denominator and Adding Fractions with Different Denominators
• Cross Multiplying and Improper Fractions
• How to change a Mixed Number To an Improper Fractions
• Simplifying Fractions and Multiplying them
• Squaring Fractions means it gets Smaller
• Dividing by a Fraction and Addition in the numerator and denominator

Chapter 5-Fractions, Decimals, Percents, and Ratios (77 Practice Problems)

Chapter was very useful because it helps you convert decimals, fractions, and percentage making them easier to work with.
• Converting Decimals to Percentages and vice versa (Very Helpful)
• Converting Fractions to Decimals or Percents
• Multiplying a Decimal by a Power of 10
• Addition and Subtraction of Decimals as well as Multiplying Two Decimals
• Multiplying a Decimal and a Big Number and Dividing by Two Decimals
• How to determine Percentages of Dollars
• Percent Change
• Ratios (Part:Part:Whole Ratios)

Chapter 6-Equations (49 Practice Problems)

Chapter 6 covered equations and expressions. This chapter was very helpful for me because I needed to brush up on equations.

• Deals with simplifying equations
• How an equation is a complete sentence
• Golden Rule of Equations-Changing the value of the left and right sides
• Isolating a Variable and Cleaning Up a Variable
• Variables in the Exponent
• Solving Two Equations and Two Unknowns by Isolating (then Substitute) or Combining Equations
• Working with Three or More Variables

Chapter 7-Quadratic Equations (25 Practice Problems)

• What is a Quadratic Expression
• FOIL (First, Outer, Inner, Last)
• Factoring expressions such x2+5x+6
• Solving Quadratic Equations with No X Term, with Squared Parentheses (y+1)2

Chapter 8-Inequalities and Absolute Values (55 Practice Problems)

• Inequalities with Variables
• Solving Inequalities
• Multiplying Inequalities by a Negative

Chapter 9-Word Problems (55 Practice Problems)

• It gives Four Steps to Turning Words Into Math-What do they want, What do they give me, How do I turn this information into equations, and How do I solve those equations for the desired value.
Refer to GMAT Club on Word Problems

Chapter 10-Geometry (60 Practice Problems)

• It covered the Radius, Diameter, Circumference, and Area of a Circle
• Sectors of a Circle including the Arc Length and Central Angle
• Triangles (Sum of Any Two Sides > Third Side)
• Sum of Three Angles=180 Degrees
• Same Sides=Same Angles
• Isosceles and Equilateral Triangles
• Perimeter of a Triangle
• Identifying the Base and height of a Triangle
• Parallelograms and Rectangles
• Coordinate Plane (X and Y Coordinates)

Most of the chapters were very helpful because I haven't done Algebra or Geometry in over 12 years! They also provide a lot of practice questions, which can be good and bad. The most useful chapters were chapter 2,3,4,5,6, and 8 except Chapter 9 on Word Problems. It did not really help me as much as I thought. I would check out this thread (word-problems-made-easy-87346.html). He should have wrote Chapter 9. LOL. I also completed all the practice problems (or drill sets) at the end of each chapter. It took about two weeks for me to complete Foundations of GMAT Math but I took notes while reading. I would definitely recommend this book to someone that needs to re-learn the basics for the GMAT. Now I am going through the Number Properties book more easily. Let me know if this format is helpful or not. I am sick at this moment so my thoughts are scattered everywhere. I feel bad I can't study but nothing beats a cold better than rest. :)
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New post 04 Jul 2013, 01:35
I know this thread is more than a year old but I must ust say, thank you for the review! Im soon done with the chapter on fractions, I really appreciate your review and the link to number properties here on the site.

I just want to ask: How has your math skills evolved since this review? Im asking because I want to see if it is reasonable to think that people like us who are THIS rusty in math in the initial stages of our GMAT studying can really get good enough such that on test day we can have a great quant score. I know everything is based on determination and ability to eliminate flaws, but still a indication would be invaluable to me!
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New post 06 Jul 2013, 16:32
No problem at all. I just wanted to help others in case someone else thought about purchasing this book. The foundation book is good for people that haven’t seen math in years. Also, Manhattan GMAT is the best out there. I went to a trial class and the instructor was awesome. If I take another GMAT class then I will take the Manhattan GMAT class.

Yes and no. The book will help you in the beginning but you will need the set of Manhattan GMAT books if you plan to study on your own. My biggest mistakes were getting frustrated with the GMAT because the test is about applying your knowledge. It doesn’t matter if you know the formula for polygons because the test makers will not make the test that easy. For example, you might be given the diagonal of a square and asked to find the perimeter. You will have to know that a square is two right triangles and the diagonal is the hypotenuse. Then you might have to use the Pythagorean Theorem (a2+b2 = c2). What I have learned from my mistakes is that you need to know what the GMAT is testing for each problem and how to solve the problem in multiple ways. A good site for Official GMAT math problem explanations is listed below. I like the way he explains the problems because the Official Guide answers can be convoluted. Most people on this board will recommend an “error log” and it is very useful. I use pen and paper instead of an Excel spreadsheet but it helps you to track your mistakes. I hope this helps and if you need some more advice just message me. ... ur-errors/
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New post 27 Oct 2019, 01:04
Hey y'all,

I might be 6-7 years late in replying to this thread, but are the earlier versions of this book (currently using the 5th Ed. that was written back in 2011...LOL) still worth using for test-takers nowadays?

Thanks in advance and appreciate any feedback!
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New post 27 Oct 2019, 18:48
Hi pauloracho,

To start, the rules of math have not changed, so if you're using this book to (re)learn math concepts, then that's fine. While the Quant section of the GMAT has gone through some adjustments over the last 8 years, it's still the same consistent, predictable section that it's always been, so you CAN train to Score at a higher level. That ultimately means that you have to remember that the Quant section of the GMAT is NOT a 'math test' - it's a critical thinking test that requires lots of little calculations as you work through it (so to score at a really high level, you need to be more of a 'strategist' and less of a 'mathematician').

Before I can offer you any additional advice for your studies, it would help if you could provide a bit more information on how you've been studying and your goals:

1) How long have you studied? How many hours do you typically study each week?
2) What study materials have you used so far?
3) On what dates did you take EACH of your CATs/mocks and how did you score on EACH (including the Quant and Verbal Scaled Scores for EACH)?

4) What is your overall goal score?
5) When are you planning to take the GMAT?
6) When are you planning to apply to Business School?
7) What Schools are you planning to apply to?

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New post 29 Oct 2019, 18:43
Hi Pauloracho,

You should not have any issues using that book; however, you may need additional resources for your prep. Since you seem to be just starting out with your GMAT studying, do you need any advice regarding your study plan?

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New post 29 Oct 2019, 21:15
geomatry subjects i hard in abroad but in India it is become easier way to study with parctical and digital way to understand every chapter of this subject
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Re: Foundations of GMAT Math Review   [#permalink] 29 Oct 2019, 21:15

Foundations of GMAT Math Review

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