GMAT REVIEW - GMAT REVIEW Read pgs 43-44 before exam MATH...

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GMAT REVIEW Read pgs. 43-44 before exam MATH REVIEW ALGEBRA Integers: whole or natural numbers; can be negative or positive but do not include fractions (3,2,1,0,-1,-2) Positive and Negative Numbers: + * + = + + * - = - - * - = + Digits: All intefers are made up of digits. In the integer 246 there are 3 digits: 2,4,6. Each of the digits has a different name: 6=unit or one digit, 4= tens digit, and 2= hundreds digit. 27.63 => 2=tens digit, 7= units digit, 6= tenths digit an 3=hundredth digit Odd/Even: Even numbers are integers that can be divided evenly by 2, leaving no remainder (-6, -4, -2, 0, 2,4,6) . Odd numbers are integers that cannot be divided evenly by 2 (-5, -3,-1, 1, 3, 5). Even*even=even odd*odd=odd even*odd=even even + even=even odd+odd=even even + odd= odd Consecutive Integers: are integers listed in order of increasing value without any integers missing in between -3, -2, -1, 0, 1, 2, 3 Distinct numbers: if 2 numbers are distinct, they cannot be equal Prime numbers: positive integer that is divisible only by 2 numbers: itself and 1 Divisibility Rules: if there is no remainder when integer x is divided by integer y, then x is said to be divisible by y. Prime Factors: if an integer, x, that is a factor of an integer, y, is also prime then x is called a prime factor of y. 12 12 3 4 2 6 2 2 3 2 Average or mean= total sum of items/ total number of the items Median (middle number) = 4, 7 , 12, 14, 20 4, 12, 14, 20 => (12+14)/2= 13 Mode= pick the number that is repeating the most: 5, 6, 3, 9, 3, 28, 3, 5 => 3 Range= 4, 3, 8, 12, 23, 37 = 37-3 = 34 Exponents: Multiply numbers with the same base: 6^2 * 6^3 = 6^ 5 Dividing numbers with the same base: 6^5 * 6^3 = 6^2 Raising a power to a power: (4^3)^2 = 4^6 Distributing exponents: (4y)^2 = 4^2 * y^2 = 16y^2 Radicals: √x * √y = √xy √x/y = √x /√y Distance= Rate * Time Probability Formula = # of outcomes you want / total # of possible outcomes = Probability that A or B will happen : A+B = The odds that something doesn’t happen: Won’t = 1 – Will n(n-1)(n-2)….*(n-r+1) => n! => 9*8*7*6*5 r! r!(n-r)! 4*3*2*1
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GMAT REVIEW GEOMETRY Basic Tools: π = 3 √1 = 1 √2 = 1.4 √3 = 1.7 90degree A 180 deg d c b Equilateral Triangle: 3 sides that are equal in length Isosceles Triangle: 2 sides that are equal in length. The angles opposite the 2 equal sides are also equal Triangle: Perimeter: add all 3 sides Area: (height * base)/ 2 Pythagorean theorem: a^2 + b^2 = c^2 side√2 side x 2x sid side x√3 Circles: Rectangular Square Parallelogram Perimeter add all sides together side*4 add all sides Area: πr^2 length*width side *side base *height Circumference: 2πr Rectangular Cube Cylinder Volume Length*Width*Depth same as Rect 36π Area Slope: y=mx+b Example: 2/-3x + 2
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GMAT REVIEW Data Sufficiency: Pieces of the puzzle You will find problems involving integers, percent, averages, ratios, algebra, and geometry. 1. When working with equations, you generally need as many equations as there are variables in those equations: A single equation with 2 wariables cannot be solved But 2 distinct equations with the same 2 variables can be solves, using simultaneous equations ( x=y+1 and 2x= -y-6 2. Just because there is only one variable doesn’t mean that an equation has just one solution Generally, equations have as many solutions as the greatest exponent in the solution. So
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