GMAT Math Ultimate| 211 Questions and Answers with complete solution

Common Factors - Break down both numbers to their prime factors to see what factors they have in common. Multiply all combinations of shared prime factors to find all common factors. Gross Profit - Gross profit = Selling Price - Cost Combined Events - For events E and F: • not E = P(not E) = 1 - P(E) • E or F = P(E or F) = P(E) + P(F) - P(E and F) • E and F = P(E and F) = P(E)P(F) Multiplication Principle - The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event. 1st Rule of Probability: Likelihood of A - Basic rule: The probability of event A occurring is the number of outcomes that result in A divided by the total number of possible outcomes. 2nd Rule of Probability: Complementary events - Complementary Events: The probability of an event occurring plus the probability of the event not occurring = 1. P(E) = 1 - P(not E) 3rd Rule of Probability: Conditional Probability - Conditional Probability: The probability of event A AND event B occurring is the probability of event A times the probability of event B, given that A has already occurred. P(A and B) = P(A) × P(B|A) 4th Rule of Probability: Probability of A OR B - The probability of event A OR event B occurring is: the probability of event A occurring *plus* the probability of event B occurring *minus* the probability of both events occurring.P(A or B) = P(A) + P(B) - P(A and B) Probability of Multiple Events - Rules: • A *and* B < A *or* B • A *or* B > Individual probabilities of A, B • P(A and B) = P(A) x P(B) ← "fewer options" • P(A or B) = P(A) + P(B) ← "more options" Indistinguishable Events (i.e., anagrams with repeating letters) - To find the number of distinct permutations of a set of items with indistinguishable ("repeat") items, divide the factorial of the items in the set by the product of the factorials of the number of indistinguishable elements. Example: How many ways can the letters in TRUST be arranged? (5!)/(2!) = 60 5! is the factorial of items in the set, 2! is the factorial of the number of repeat items ("T"s) Combinations (Order Does Not Matter) - nCr = n! / (r! (n - r)!) Where n is the total number of items in the set and r is the number of chosen items.