Chapter 7 Math in the Real World TRYING TO RELATE The most common critique against the GRE is that it tests topics that have no direct connection to the topics most graduate school students will use So the Educational Testing Service makers of the GRE decided not to test too much abstract math Instead they try to make questions have actual real life connections Of course for people who spend their entire day writing standardized tests real life situations means something very different than it does for most normal people For the GRE this is a real world problem Here s How to Crack It A typical real world situation that we ve all been in You save and save but then forget how much you have in your account When you ask your bank how much you have you are informed that you put 227 50 more in your account this month than you did three months ago But how much do I actually have in my account you ask The bank teller types some numbers into her computer answers you put double the amount into your account each month for the past four months Since that answers your question thank you for banking with Oblique Bank and remember to sign up for an Obfuscation Checking Account and hangs up You mean you ve never been in that situation But it s a perfectly common situation Okay so it s not a common situation at all However it is a common style of GRE question and one that you may have seen before Notice all those numbers in the answers and how the question is asking for a specific amount You may have recognized the opportunity to PITA If so good for you If not feel free to look over Chapter 5 to learn more about Plugging In the Answers Write down A B C D E on your scratch paper copy the answers and label the column March Start with C If she saved 97 50 in March then she saved double that in April 195 doubled again in May 390 and doubled once more in June 780 The amount she saved in June was 780 97 50 682 50 more than what she saved in March which is way more than 227 50 Because C is too big cross off C B and A Try D If she saved 65 in March she saved 130 in April 260 in May and 520 in June She therefore saved 520 65 455 dollars more in June than in March which means D is too large as well Cross off D and pick E the only answer left Fictional World Examples So the questions on the GRE won t actually apply to the real world However they ll frequently use certain real world topics You should know exactly what to do when any of these topics come up so you don t get lost in all the extra word problem garbage As always focus on learning what you need to recognize in a problem to know what to start writing on your scratch paper THE THREE M S When it comes to crunching numbers there are three statistical terms that every GRE student should recognize and distinguish from each other The mean or arithmetic mean is just another word for the average The median is the middle number in a list of numbers when the numbers are listed in order from lowest to highest The mode is the term that occurs most frequently in a list of numbers To remember these last two terms you can think that 1 the median of a highway is in the middle of the highway and 2 if you say the word most as if you have a terrible head cold it comes out sounding like mode One final term you should know is range the range of a set of numbers is the difference between the greatest and smallest numbers in the set The Mean Average You calculate the average value of a list of numbers by finding their total value and dividing by the quantity of numbers in that list To find the average of 12 29 32 8 and 19 for example add them all up 12 29 32 8 19 100 and divide by the number of terms five The answer is or 20 The Average Pie Here s How to Crack It Based on the work you just did you know the answer is C However it s worth pointing out that you can eliminate a few answer choices right away In particular E stands out because the average of a list of numbers cannot be greater than the greatest number in the list To solve problems like these you can use the Average Pie All average problems involve three quantities the Total value the Number of things and the Average value of those things You can relate them in a diagram we call the Average Pie which looks like this The Average Pie helps you visualize the relationship between the three numbers It also helps you organize your thoughts by giving you three discrete compartments in which to put your information In order to solve the previous problem you would add up the elements to get 100 recognize that there were five numbers and place that information in the Average Pie like this When you divide 100 by 5 you see that the answer is 20 Try another example Here s How to Crack It Here you have two of the three elements that go in the Average Pie You know the Average and the Number of things and you re looking for the Total so set up your Average Pie like this To find the Total multiply the two bottom numbers 6 12 6 75 6 million which is slightly larger than the 75 million in Quantity B The answer is A Averages Quick Quiz Explanations for Averages Quick Quiz 1 During the seven days the hens produced a total of 301 eggs The Average Pie therefore looks like this The average value equals 301 7 or 43 The answer is A 2 You know the number and the average so set up your Average Pie like this Farmer Jones can expect to get 21 255 or 5 355 eggs over the course of a year 3 This time you know the total and the average so the Average Pie looks like this The number of hens equals 572 22 or 26 hens The answer is C 4 Average is used three times so set up three Average Pies and then start filling in what information is known to solve for what is not If 12 hens lay an average of 9 eggs apiece then the total number of eggs is 12 9 or 108 Once the top three egg layers are disqualified there are 9 hens left that lay an average of 7 eggs They account for 7 9 or 63 of the eggs The top three layers must therefore account for 108 63 or 45 eggs The average value among the top three is 45 …