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### 38 Cards in this Set

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 Steps to solving Age problems? Make an age chart. It helps assign variables you can use to write equations. What is the GMAT's favorite Word Translation problem? Rate problems. The most common rate problem is the work problem. Rate problems come in five forms: Basic Motion, Average Rate, Simultaneous motion, Work, and Population. How do you solve an average rate problem? Lucy walks to work at a rate of 4 mi/hr, and walks home at 6 mi/hr. What is Lucy's average walking rate round trip? To find the average rate, you must first find the TOTAL combined time for the trips and TOTAL combined distance for the trips. Pick any number for the distance = 12. Figure out 3 hours + 2 hours = 5 total hours for 24 miles. Rate is 24 miles/5 hrs. More difficult rate problems involve _______ More than one rate. Simultaneous Motion. When two vehicles travel at different rates in opposite directions, eventually meeting somewhere in between….what tactic can you use? Clicking charts If Train A leaves 10 min after Train B ____________________(assign variables) then Train A's time is t minutes and Train B's time is t+10. If two people are moving TOWARDS each other, then what happens to the rates? Combined rate…(Rate1 + Rate2) = combined rate…. If two people are moving AWAY from each other, then happens? They travel for the same TIME, but for different DISTANCES. (2 charts, add distances) If two people are moving along the SAME PATH, then what happens? They travel for different TIIMES, but the same DISTANCE. (make 2 charts = d ) In work problems, distance is replaced by _____ work If two people are working together, then….. add their rates. The population of a certain bacteria triples every 10 minutes. If the population of a colony 20 minutes ago was 100, in approximately how long from now will the bacteria population reach 24,000? 20 min ago - 100. 10 min ago - 300. Now - 900. In 10 min - 2700. In 20 min - 8100. In 30 min - 24,300…just make a chart. For population problems, often use ______ Benchmark values / estimates. Combinatorics: Different sources _______ Just multiply Larry has 3 shirts, 2 pants, and 3 hats. How many different outfits could he have? 3*2*3 If there are 4 people and 4 chairs in a room, how many different seating arrangements? 4! Or 4*3*2*1 If there are 7 people in a room, but only 4 chairs available, how many different arrangements are available? 7! / 3! (Divide factorial by number of repeated letters). Or 7c4 = 7*6*5*4 If order does not matter, what would the anagram look like? Use Y/N. Or, know combinations and divide by number of choices… If a team of 4 is chosen from 7 people in a room, how many different teams are possible? YYYYNNN => (7!)/(3!4!) OR 7 choosing 4 and divide by # ways to arrange => 7*6*5*4 / (4*3*2*1) 6 people go to movies. If two of them will not sit next to each other, in how many different arrangements can the 6 people sit? Total - #ways to sit as couple = ways not sit as couple. Total = 6!. Ways could sit = 2! (ways to arrange the two) * 4! (ways to arrange the other 4) * 5 (seating pairs)…6! - (2! * 4! * 5) Convert all probability problems to ______ instead of percents, decimals, fractions Probability that x AND y will happen? MULTIPLY probabilities Probability that x OR y will happen? ADD probabilities Find the probability that something will not happen => what rule? 1-x. Pwill + Pwon't = 1 Renee has a bag of candy. Bag has 1 candy bar, 2 lollipops, 3 jellybeans, and 4 truffles. Jack takes one piece of candy out of the bag at random. If he picks a jellybean, he chooses one additional piece of candy and then stops. If he picks any non jelly bean candy, he stops picking immeidately. After Jack picks his candy, Renee will pick a piece of candy. What is the probability tha Renee picks a jellybean? List all winning scenarios. JB, notJB, JB. JB, JB, JB. Not JB, ____, JB. Then find individual probabilities and MULTIPLY b/c AND. Then you have 3 scenarios for Renee to get 1 jellybean. 3/10 is the answer. Kate and Amy want to be on the same team. 6 girls in the group, and only 4 of them will be placed on the team. What is the probabilty that Kate and Amy will both be on the team? Total number of 4 person teams / Total number of teams that include Kate and Amy. # of different 4 person teams => 6c4 or 6! / 2!*4! => 15 possible groups. Total number of 4 person teams include all the winning scenarios in which Kate, Amy, and 2 other people get on the team. 4c2 or 4! / 2!*2!. => 6 winning scenarios. Average = Total / number of terms Sam earned \$2,000 commission on a big sale, raising his average commission by \$100. If Sam's new average commission is \$900, how many sales has he made? Make two average pies: Before the sale and after the sale. Before the sale => 800n = Total or Sum. After the sale => 800n + 2000 / (n+1) = 900. If n=11, then total sales = 12. For any set in which terms are spaced evenly apart, the average => Middle Number For any evenly spaced set of numbers {101, 111, 121…581, 591, 601} find the middle number? Add first and last terms and divide that sum by 2. 101 + 601 / 2 => 351. (Only works for evernly spaced set of numbers) Given ascending set x,x,y,y,y,y, what is greater, the median or the mean? Median is larger b/c median is y, and the mean is x + y / 2 which is less than y. What does standard deviation measure? How far data points in distribution fall from the mean. 34:14:2 If data points in a set are close to the mean, then there is a _____SD small standard deviation Translation problems that involve 2 or more given sets of data that partially intersect are called_______ Overlapping sets What can you use to visualize the categories of overlapping sets? Use A, Not A and B, Not B and Totals… OR G1 + G2 - Both + Neither = Total Overlapping sets involving percents - what is your strategy? Use 100 Smart Number to represent Total! Problems involving 3 overlapping sets can be solved by using a Venn Diagram - work from the inside out…