GRE Quantitative Exam Study Guide with Complete Solution

GRE Quantitative Exam Study Guide with Complete Solution What are digits? - Numbers the make up other numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) What are integers? - Counting numbers Are fractions integers? - No Can integers be even or odd? - Yes Is zero positive or negative - It's neither Is zero even or odd? - Even Can you divide a number by 0? - No What are consecutive integers? - Numbers listed in order (increasing or decreasing). Can count by 1s, 2, 3s, etc. What is the absolute value of a number equal to? - The number's distance away from) on the number line. Can the absolute value of a number be negative? - No, it's always positive. |-5| = 5 and |5| = 5 How many factors does a prime number have? - Only 2 factors, 1 and itself Are 0 and 1 prime numbers? - No Are there any even prime numbers? - Yes, the number 2 Can negative numbers be prime? - No, prime numbers are only positive What is the quotient? - The result of division What is the product? - The result of multiplication What are the orders of operation? - PEMDAS Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction Distributive Property: a(b+c) is the same as... - ab + ac Distributive Property: a(b-c) is the same as... - ab - ac Exponent Rule: a2 is the same as... - a x a Exponent Rule: a2·a3 is the same as... - a2+3 = a5 Exponent Rule: (a2)3 is the same as... - a2·3 = a6 Exponent and Cube Root Rule: - 3√a12 = (a12)1/3 = a 12/1 x 1/3 = a12/3 = a4 Exponent Rule: a6/a2 is the same as... - a6-2 = a4 A number raised to the first power (10001) is always _________. - The number itself (10001 = 1000) What is 00? - Undefined What is a number raised to the power 0 (10000)? - 1 no matter what the number is (10000 = 1) What happens to a number raised to a negative power? 2-2 - It becomes 1 over the number raised to a positive power (2-2 = 1/22 = 1/4) Does a negative number raised to an odd power become negative or positive? (-23) - It stays negative -23 = -8 Does a negative number raised to an even power become negative or positive? (-22) - It becomes positive -22 = 4 If you raise a fraction between 0 and 1 to a power greater than 1 will the number become larger or smaller? - Smaller (1/2)2 = 1/4 If you raise a number other than 1 to a power greater than 1 with the number become larger or smaller - Larger. 22 = 4 Can you simplify 274? - 3x3x3=27, so (3x3x3)4 which equals (3x3x3)(3x3x3)(3x3x3)(3x3x3), so 312 How do you divide and multiply square roots? - Just like any other number √3 x √12 = √36 √16 = √16 = 4 = 2 4 √4 2 Can you add or subtract square roots? - Only if the roots are equal √2 + √2 = 2√2 (same root = 1√2 + 1√2) but √2 + √3 ≠ √5 Estimate √32 - √32 is in between √25 and √36, so we can guess that √32 is somewhere between 5 and 6 Simplify √32 - 32 has a factor that is a perfect square, 16, so √32 = √16x2 = 4√2 What is the absolute value of √a2 - √a2 = |a| for all value of a What is √1 - 1 What is √2 - 1.4 What is √3 - 1.7 What is √4 - 2 If ETS asks for the value of √16, do they want a positive or negative root? - They only want the positive root. Is x2=16 the same as √16? - No because in x2 = 16, x = ±4, but √16 = +4 (NOT -4) What is foil? - First, Outer, Inner, Last (x + 4)(x + 3) (x · x) + (x · 3) + (x · 4) + (4 · 3) x2 + 3x + 4x + 12 x2 + 7x + 12 What is the unfactored form of x2 - y2 - (x+y)(x-y) What is the unfactored form of (x+y)2 - x2 + 2xy + y2 What is the unfactored form of (x-y)2 - x2 - 2xy + y2 What is the factored form of (x+y)(x-y) - x2 - y2 What is the factored form of x2 + 2xy + y2 - (x+y)2 What is the factored form of x2 - 2xy + y2 - (x-y)2 Inequalities (ie: 12-6x0) What happens to the inequality symbol when you multiply and divide? - 12 - 6x 0 -12 -12 (+/- no change in direction) -6x -12 -6x -6x (x/div. change direction) x 2 When can you plug-in? - When there are variables in the answer choices How do you know when you can plug in the answer? (ie: plug-in one of the given answers) - 1. When the question begins with: How much..., How many..., What is the value of... 2. Answer choices are in ascending or descending order 3. Your tempted to make an algebraic equation When plugging in the answer, what answer should you assume is correct? - C. Use C as a starting point In Quantitative Comparison questions, how many times should you plug-in? - Always plug-in at least twice When you plug-in for a Quantitative Comparison, what should you start with? - Something nice and happy When you plug-in for a Quantitative Comparison, what should you plug in the second time? - Use ZONE F What is ZONE F - Zero One Negative Extremely small or big Fractions Percentages How do you set-up: 1. 5 is r percent of 25 2. s is 25 percent of 60 - r 1. 5 = 100 (25) 25 2. s = 100 (60) Percentage Increase/Decrease Formula - Difference Percentage Change = original x 100 What is the original number in a percentage INCREASE problem? - The smaller number What is the original number in a percentage DECREASE problem? - The larger number What is the difference in a percentage increase/decrease problem? - The larger number minus the smaller number Can you plug-in for fraction and percentage problems? - Yes. Plugging in for the missing value will make your life much easier! What is a Ratio? - A ratio expresses relationships in part to part What is the key to dealing with ratio questions? - Finding the whole or the total A ratio of 2:1 has how many total parts? - 3 How do you figure out what number to multiply by? - You take the total number of coins (24) and divide it by the total of the ration (2:1 = 3), so 24 divide by 3 = 8. Then you multiply each item (pennies and nickels) by 8 to figure out the total number of each coin in the pocket. What are proportions? - The equivalent relationship between two fractions or ratios What is the formula for finding the Average? - Total Average = # of things What is the mean? - The average Add all the numbers and divide the total by the number of numbers. ie: 5, 1, 4, 6 = 16/4 = 4 is the average What is the median? - The middle value in a set of numbers In the set {1,2,3,4,5,6,7), the median is 4 In the set {1,2,3,4,5,6), the median is the average of 3+4/2 (3.5) What is the mode? - They number in a set that occurs the most frequently What is the range - The difference between the biggest and smallest number in the set. In the set {2, 6, 13, 3, 15, 4, 9}, 15 is the biggest and 2 is the smallest, so 15-2 = 13 (the range) What is the formula to find the time in a rate problem? - t = d/r What is the formula to find the distance or amount in a rate problem? - d = rt