Note: Greyscale scan with OCR.

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 nine chapters and over 600 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.

factors of 84 are 2, 2, 3, and 7. In other words, 2 x 2 x 3 x 7 = 84. The prime factors can be used to build all of the factors of 84. Because the question asks for even factors, only factors that are built with at least one 2 will be correct. Even divisors can be built using one 2. 2; 2 x 3 = 6; 2 x 7 = 14; 2 x 3 x 7 = 4 2 Even divisors can also be built using both the twos that are prime factors of 84. 2 x 2 = 4; 2 x 2 x 3 = 12; 2 x 2 x 7 = 28; 2 x 2 x 3 x 7 = 84 The even divisors of 84 are

the product, whatever x is. Exponents&Roots Chapter 3 T = 7 Seven to the first equals seven. Memorize the following powers of positive integers. Squares Cubes 12= 1 13=1 2 2= 4 23 = 8 32 = 9 33 = 27 42 = 16 43 = 64 52 = 25 53 = 125 62 = 36 103 = 1,000 72 = 49 82 = 64 Powers of 2 92 = 81 2' = 2 102 = 100 22 = 4 l l 2 = 121 23 = 8 122 = 144 24 = 16 132 = 169 25 = 32 142= 196 26 = 64 152 = 225 27 = 128 202 = 400 28 = 256 302= 900 29 = 512 210 = 1,024 Powers

a8 a to the fifth times a to the third equals a to the eighth. What happens to the exponents 5 and 3? They add up: 5 + 3 = 8. This works because we only have as in the equation. The two terms on the left {a5 and a3) have the same base (a), so we have eight as on each side of the equation. When you multiply exponential terms that have the same base, add the exponents. Treat any term without an exponent as if it had an exponent of 1. y ( y 6) = y xy 6 =y l X y6 = y 1+6 = f Adding

answers that are nega tive as these answers have lower values than any positive answers. (A) (-3)4 will result in a positive number because 4 is an even power. (B) - 3 3 = -(3 3) = -2 7 The exponent is done before multiplication (by -1) because of the order of operations. (C) (-3)-3 = — = = (-3 ) -2 7 27 (D) (-2)3 = - 8 (E) 2~6 = — The value of this expression is positive. - 2 7 has the lowest value of the three answer choices that result in negative numbers. The correct answer is (B). 23.

the phrase “what percent.” What percent of 125 is 25? You should still use x to translate “what.” The word “percent” by itself means “divided by 100.” You can show that as “ /100” or “ ”• x As a result, “what percent” can be translated as at/100, o r -----. 100 r Translate the question now. What percent — 100 of 125 is 25? X 125 = 25 You can now find the answer by solving for x. Solving equations for x will be covered in depth in the “Equations” chapter on page 257. MANHATTAN GMAT