GRE Math Study Guide Latest Update

GRE Math Study Guide Latest Update Consecutive numbers - Numbers of a certain type, following one another without interruption. Numbers may be consecutive in ascending or descending order. Consecutive integers: (-2, -1, 0, 1 ,2, 3) Consecutive even numbers: (-4, -2, 0, 2, 4, 6) Consecutive multiples of 3: (-3, 0, 3, 6, 9) COnsecutive prime numbers: (2, 3, 5, 7, 11) Cube - A number raised to the 3rd power. 4^3=64; 64 is the cube of 4 Decimal - A fraction written in decimal system format. 0.6 is a decimal; numerator divided by denominator 5/8=0.625 Decimal system - A numbering system base don the powers of 10. ONLY numbering system used on the GRE. 315.246 - (3)hundreds, (1)tens, (5)ones units. (2)tenths, (4)hundredths, (6)thousandths Denominator - The quantity in the bottom of a fraction Difference - The result of subtraction Digit - One of the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. A number can have several digits 542 - three digits: 5, 4, and 2 321,321,000 - nine digits, but four distinct digits: 3, 2, 1, and 0 Distinct - Different from each other. EX: 12 has three prime factors (2, 2, and 3) but only two distinct prime factors (2 and 3) Element - One of the members of a set Exponent - The number that denotes the power to which another number or variable is raised. 5^3 = (5)(5)(5) Fraction - The division of a part by a whole. Part/Whole = Fraction EX: 3/5 Integer - A number without fractional or decimal parts, including positive and negative whole numbers and zero. All integers are multiples of 1 EX: -5, -4, -3, -2, 0, 1, 2, 3, 4, 5 Number line - A straight line, extending infinitely in either direction, on which numbers are represented as points. Can contain irrational numbers such as √2 which is between 1 and 2. Numerator - The quantity in the top of a fraction. Operation - A function or process performed on one or more numbers. The four basic arithmetic operations are addition, subtraction, multiplication, and division. Part - A specified number of the equal sections that compose a whole. Product - The result of multiplication. Sequence - An ordered list of terms. The terms of a sequence are often indicated by a letter with a subscript indicating the position of the number in the sequence. EX: a3 is the third number in a sequence, an is the nth term in a sequence Set - A well-defined collection of items, typically numbers, objects, or events. The bracket symbols {} are normally used to define sets of numbers. EX: {2, 4, 6, 8} is a set of numbers Square - The product of a number multiplied by itself. A squared number has been raised to the 2nd power. EX: 4^2 = (4)(4) = 16; 16 is the square of 4 Sum - The result of addition. Whole - A quantity that is regarded as a complete unit. SYMBOLS - = is equal to ≠ is equal to is less than is greater than ≤ is less than or equal to ≥ is greater or equal to ÷ divided by π pi (the ratio of the circumference of a circle to the diameter) ± plus or minus √ square root PEMDAS - Parentheses Exponents Multiplication, Division (simultaneously from left to right) Addition, Subtraction (simultaneously from left to right) "Please Excuse My Dear Aunt Sally" EX: 66(3-2)÷11 = 66(1)÷11 = 66÷11= 6 Communicative Laws of Addition and Multiplication - Addition and multiplication are both communicative, which means that switching the order of any two numbers added or multiplied does not affect the result. a+b = b+a ; ab = ba Division and subtraction are NOT communicative Associative Laws of Addition and Multiplication - regrouping the numbers does not affect the result (a+b) + c = a + (b+c) ; (ab)c = a(bc) The Distributive Law - Allows you to "distribute" a factor over numbers that are added or subtracted; multiply the factor by each number in the group EX: a(b+c) = ab + ac ; (a+b)/c = (a/c) + (b/c) BUT when the sum or difference is in the denominator no distribution is possible! EX: a/(b+c) ≠ (a/b) + (a/c) Absolute Value - The distance a number is from zero on a number line. ALWAYS POSITIVE |-3| = |+3| = 3 ; -3 and 3 are 3 units from 0 so each have an absolute value of 3. if you are told |x| = 5 then x could be 5 or -5. Properties of Zero - Adding or subtracting zero to a number does not change the number. x + 0 = x Subtracting a number from zero changes the number's sign. Subtract 5 from 0: 0 - 5 = -5 The product of zero and any number is zero. 0(z) = 0 Division by zero is undefined. For GRE purposes this translates to " it cannot be done" Properties of 1 and -1 - Multiplying or dividing a number by 1 does NOT change the number. Multiplying or dividing a nonzero number by -1 changes the number's sign. Multiple - The product of a specified number and an integer. EX: 3, 12, and 90 are multiples of 3: 3 = (3)(1); 12 = (3)(6); 90 = (3)(30) Divisibility - A number is said to be evenly divisible by another number if the result of the division is an integer with NO remainder. A number that is evenly divisible by a second number is also a multiple of the second number. Rules of Divisibility & How to recognize MULTIPLES of a number - 2: (divisible) if its last digit is divisible by 2, (multiple) last digit is even 3: (both) if it's digits add up to a multiple of 3 4: (both) if its last two digits are a multiple of 4 5: (both) if its last digit is 0 or 5 6: (divisible) if it is divisible by both 2 and 3, (multiple) sum of digits is a multiple of 3 and the last digit is an even number 9: (both) if its digits add up to a multiple of 9 10: (multiple) last digit is 10 12: (multiple) sum of digits is a multiple of 3, and last two digits are a multiple of 4 Even - Integers that are evenly divisible by 2 Odd - Integers that are not evenly divisible by 2 Rules for Odds and Evens - Odd + Odd = Even Even + Even = Even Odd + Even = Odd Odd x Odd = Odd Even x Even = Even Odd x Even = Even Factors - The positive and negative integers by which a number is evenly divisible