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The Holistic Approach to Mods on the GMAT - Solutions  [#permalink]

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11 Nov 2014, 15:00
 FROM Veritas Prep Admissions Blog: The Holistic Approach to Mods on the GMAT - Solutions First, we would like to refer you back to a post we put up quite a while ago: The Holistic Approach to ModsIn this post, we discussed how to use graphing techniques to easily solve very high level questions on nested absolute values. We don’t think you will see such high level questions on actual GMAT. The aim of putting up the post was to illustrate the use of graphing technique and how it can be used to solve simple as well as complicated questions with equal ease. It was aimed at encouraging you to equip yourself with more visual approaches.We gave you two questions at the end of that post to try on your own. We have seen quite a bit of interest in them and hence will discuss their solutions today.The solutions involve a number of graphs and hence we have made pdf files for them.Question 1: Given that y = |||x – 5| – 10| -5|, for how many values of x is y = 2?Solution 1Question 2: Given that y = |||x| – 3| – x|, for what range of x is y = 3?Solution 2Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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11 Nov 2014, 18:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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SAT Tip of the Week: Breaking Down the Math Section  [#permalink]

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12 Nov 2014, 09:00
 FROM Veritas Prep Admissions Blog: SAT Tip of the Week: Breaking Down the Math Section Last week, we discussed how to break down the Writing Section of the SAT. Today, we’re focusing on Math.Anyone can get an 800 on SAT Math. It doesn’t matter if you struggle just to get through class in high school or you’ve tested out of advanced Calculus. The content of the SAT Math section is designed in a completely different manner than that of conventional math class. This is good news for anyone who wants a high score on the SAT. This means regardless of how you might fare in class, you can succeed on the math section . All it takes is knowledge of Algebra I and II, Geometry, and basic arithmetic. If you have all that down (and work hard to understand patterns of SAT questions) you will be on the road to success! Here are some helpful tips that will assist you dominate the SAT math sections.ORDER AND DIFFICULTY. There are three sections on the test. There is one twenty five minute, twenty question section (all multiple choice). There will be another twenty five minute, eighteen question section (eight multiple choice and ten grid in questions). Finally, you will have a twenty minute, sixteen question section near the end of the test composed solely of multiple choice questions.The SAT math questions follow the “order of difficulty rule.” More specifically, question one is the easiest and question twenty is the hardest. The same rule follows on the sixteen question, twenty minute section. The order of difficulty resets on the grid in section, with questions increasing in difficulty from one to eight and then restarting from nine to eighteen. The one caveat to this rule is when you have a graph of table and two questions referring to the example. In this case the first question is fairly easy and the second question is significantly more difficult. If you find yourself having trouble with these remember that the question is generally more challenging than the normal question for that stage of the test. These types of questions appear almost always near the middle of a section.TYPES OF QUESTIONS. It’s important to be aware of where each question lies on the spectrum of the test. If a question is in the early stages and you are having trouble with it, it is fair to say you are probably doing something wrong. These questions are usually pretty easy and only take a step or two to solve. On the other hand, if there is a question near the end of the test and you solve it pretty quickly, you might have fallen into a trap laid by the SAT. These questions are multi-step problems that require a level of critical analysis before using math to find the answer.In addition to the order of difficulty it is helpful to be cognizant of the type of questions that come up on the test. A lot of times, a more difficult question will deal with geometric figures. Occasionally, this will be asking for the volume of a cylinder or something of that nature. However, the bulk of these types of questions deal with circles. The circles can have circumscribed squares or triangles, they can be on graphs, or they can be asking for the arc, radius, or area of segments. Whatever the case may be, it will serve you very well to familiarize yourself with the difficult circle questions. Many students are able to solve one or two difficult questions each test just from practicing the multiple variations of these types of problems.CONCEPTUAL TRICKS. In addition to geometric figures, the SAT will also try to get you with abstract concepts through the use of multiple variables. The best thing to do in this case is to plug in numbers for the variables. Whenever you do this it takes abstract ideas and turns them into concrete concepts. Doing this helps you avoid traps the SAT sets knowing students will try to solve these problems using letters instead of numbers.If you understand the structure of the test, do enough practice tests and sections, and remember to study geometric figures and plug in numbers, there is no doubt you will succeed on the Math sections of the SAT.Still need to take the SAT? We run a free online SAT prep seminarevery few weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter!Jake Davidson is a Mork Family Scholar at USC and enjoys writing for the school paper as well as participating in various clubs. He has been tutoring privately since the age of 15 and is incredibly excited to help students succeed on the SAT.
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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1 Simple Way to Solve Puzzling GMAT Questions  [#permalink]

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13 Nov 2014, 13:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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14 Nov 2014, 11:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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GMAT Tip of the Week: Why Are You Here?  [#permalink]

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14 Nov 2014, 13:00
 FROM Veritas Prep Admissions Blog: GMAT Tip of the Week: Why Are You Here? This week’s video post brings you a tip for taking a closer look at the data in Data Sufficiency. Is what you know about Data Sufficiency statements really sufficient? There are certain points of information that are necessary to know for Data Sufficiency, but knowing those doesn’t mean you have sufficient information to correctly solve the problem.Watch this video to learn how you can find hidden hints within statements and how that can help you avoid any GMAT traps. You don’t want to leave any points on the table.Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!By Brian Galvin
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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How to Go from a 48 to 51 in GMAT Quant - Part V  [#permalink]

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17 Nov 2014, 10:00
 FROM Veritas Prep Admissions Blog: How to Go from a 48 to 51 in GMAT Quant - Part V First, let us give you the link to the last post of this series: Post IV. It contains links to previous parts too.Today, we bring another tip for you to help get that dream score of 51 – if you must write down the data given, write down all of it! Let us explain.If you think that you will need to jot down the data given in the question and then solve it on your scratch pad (instead of in your mind), you must jot down every single detail. It is easy to overlook small things which are difficult to express algebraically such as ‘x is an integer’. These details are often critical and could make all the difference between an ‘unsolvable’ question and a ‘solvable within 2 minutes’ one. Once you start solving the question on your scratch pad, you will not refer back to the original question again and again and hence might forget these details. Have them along with the rest of the data. Read every word of the question carefully, and ensure that it is consolidated on your scratch pad. For example, look at this question:A set of five positive integers has an arithmetic mean of 150. A particular number among the five exceeds another by 100. The rest of the three numbers lie between these two numbers and are equal. How many different values can the largest number among the five take?It is a difficult question because it incorporates statistics as well as max-min – both tricky topics. On top of it, people often overlook the ‘are equal’ part of the question here. The reason for that is that they are actively looking for implications of the sentences and the moment they read “The rest three numbers lie between these two numbers”, they go back to the previous sentence which tells us “A particular number among the five exceeds another by 100”. They then make a note of the fact that 100 is the range of the five positive integers. In all this excitement, they miss the three critical words “and are equal”. Ensure that when you go to the sentence above, you pick the next sentence from the point where you left it. Another thing to note here is that all numbers are positive integers. This information will be critical to us.Let’s demonstrate how you will solve this question after incorporating all the information given.Question: A set of five positive integers has an arithmetic mean of 150. A particular number among the five exceeds another by 100. The rest of the three numbers lie between these two numbers and are equal. How many different values can the largest number among the five take?(A) 18(B) 19(C) 21(D) 42(E) 59Solution:Let’s assume that the 5 natural numbers in increasing order are: a, b, b, b, a+100We are given that a < b < a+100.Also, we are given that a and b are positive integers. This information is critical – we will see later why.The average of the 5 numbers is (a+b+b+b+a+100)/5 = 150(a+b+b+b+a+100) = 5*1502a+3b = 650We need to find the number of distinct values that a can take because a+100 will also take the same number of distinct values.Now there are two methods to proceed. Let’s discuss both of them.Method 1: Pure Algebra – Write b in terms of a and plug it in the inequalityb = (650 – 2a)/3a < (650 – 2a)/3 < a+1003a < 650 – 2a < 3a + 300Now split it into two inequalities: 3a < 650 – 2a and 650 – 2a < 3a + 300Inequality 1: 3a < 650 – 2a5a < 650a < 130Inequality 2: 650 – 2a < 3a + 3005a > 350a > 70So we get that 70 < a < 130. Since a is an integer, can we say that a can take all values from 71 to 129? No. What we are forgetting is that b is also an integer. We know thatb = (650 – 2a)/3For which values will be get b as an integer? Note that 650 is not divisible by 3. You need to add 1 to it or subtract 2 out of it to make it divisible by 3. So a should be of the form 3x+1.b = (650 – 2*(3x+1))/3 = (648 – 6x)/3 = 216 – 2xHere, for any positive integer x, b will be an integer.From 71 to 129, we have the following numbers which are of the form 3x+1:73, 76, 79, 82, 85, … 127This is an Arithmetic Progression. How many terms are there here?Last term = First term + (n – 1)*Common Difference127 = 73 + (n – 1)*3n = 19a will take 19 distinct values so the last term i.e. (a+100) will also take 19 distinct values.Method 2: Using Transition PointsNote that a < b < a+100Since a < b, let’s find the point where a = b, i.e. the transition  point2a + 3a = 650a = 130 = bBut b must be greater than a. If we increase b by 1, we need to decrease a by 3 to keep the average same. But decreasing a by 3 decreases the largest number i.e. a+100 by 3 too; so we need to increase b by another 1.We get a = 127 and b = 132. This give us the numbers as 127, 132, 132, 132, 227. Here the average is 150Since b < a+100, let’s find the point where b = a+1002a + 3(a+100) = 650a = 70, b = 170But b must be less than a+100. If we decrease b by 1, we need to increase a by 3 to keep the average same. But increasing a by 3 increases the largest number, i.e. a+100 by 3 too, so we need to decrease b by another 1.We get a = 73 and b = 168. This gives us the numbers as 73, 168, 168, 168, 173. Here the average is 150Values of a will be: 73, 76, 79, ….127 (Difference of 3 to make b an integer)This is an Arithmetic Progression.Last term = First term + (n – 1)*Common difference127 = 73 + (n – 1)*3n = 19a will take 19 distinct values so the last term i.e. (a+100) will also take 19 distinct values.Answer (B)Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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18 Nov 2014, 10:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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SAT Tip of the Week: Breaking Down the Critical Reading Section  [#permalink]

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19 Nov 2014, 09:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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6 Reasons You Need at Least 6 Weeks to Finish Your MBA Applications  [#permalink]

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19 Nov 2014, 14:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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20 Nov 2014, 13:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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21 Nov 2014, 10:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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How To Tackle Vocabulary (And Actually Remember!)  [#permalink]

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21 Nov 2014, 11:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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Busting Some GMAT Sentence Correction Myths - Part II  [#permalink]

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24 Nov 2014, 10:00
 FROM Veritas Prep Admissions Blog: Busting Some GMAT Sentence Correction Myths - Part II A few weeks back, we wrote a postbusting some Sentence Correction myths. Let’s continue from where we left.  We discussed how we can have pronouns referring to different antecedents in different clauses of the same sentence. Let’s take another example illustrating that principle. Also, we learn how to use ‘being’ correctly in GMAT.Myth 3: Use of ‘being’ is always wrong on GMAT!Often, the way we use ‘being’ in our day-to-day communication, is incorrect. For example,Being a doctor, he is very well respected.But there are correct ways of using ‘being’. Since most students believe that ‘being’ is wrong, don’t trust the GMAC to not use this nugget of information to misdirect the test takers. The correct answers of questions at higher ability are worded in such a way that they make the test takers uncomfortable!So how is ‘being’ used correctly?‘Being’ is used to express a temporary state.The little boy started screaming when he saw his dog being impounded.‘Being impounded’ is a temporary state and would be over – unlike being a doctor. So the use of being is correct here.Let’s look at one of our own sentence correction questions now:Question: The data being collected in the current geological survey are providing a strong warning for engineers as they consider the new dam project, but their greatest importance might lie in how they influence the upcoming decision by those same engineers on whether to retrofit 75 bridges in the survey zone.A. The data being collected in the current geological survey are providing a strong warning for engineers as they consider the new dam project, but their greatest importanceB. The data being collected in the current geological survey provide a strong warning for engineers as they consider the new dam project, but its greatest importanceC. The data collected in the current geological survey is providing a strong warning for engineers as they consider the new dam project, but their greatest importanceD. The data collected in the current geological survey provides a strong warning for engineers in consideration of the new dam project, but its greatest importanceE. The data collected in the current geological survey provide a strong warning for engineers in consideration for the new dam project, but the greatest importanceSolution:  Let’s find the decision points:First decision point: being collected vs collected‘The data being collected’ is a temporary state here. Data won’t always be collected, but are being collected for a short time right now, so “being” is used properly here. Nothing wrong with ‘The data collected in …’ either so we retain all answer options.Second decision point: are/isTechnically, data is plural of datum. In academic writing it is almost always treated as plural. It is treated as singular in informal writing but GMAT favors treating it as plural.Even if you do not know this, the use of “they influence the upcoming” – in the portion of the sentence that is not underlined – should tell you that ‘data’ is used in plural form here.Hence the use of ‘are’ is appropriate. Hence, options (C) and (D) are eliminated.Third decision point: PronounsThere are many pronouns used here. Antecedent of each pronoun is present in the sentence. The usage clarifies which pronoun refers to data and which refers to engineers.Original Sentence: The data being collected in the current geological survey are providing a strong warning for engineers as they consider the new dam project, but their greatest importance might lie in how they influence the upcoming decision by those same engineers on whether to retrofit 75 bridges in the survey zone.they – only engineers can consider the new dam project so ‘they’ refers to engineerstheir/its  - greatest importance will be of data, which is plural, so ‘their’ would be the correct usage. Eliminate option (D)There is no ambiguity in the use of pronouns. The nouns are present and the usage clarifies the antecedent.Now we are left with options (A) and (E). In option (E), “in consideration for the new dam project” is bad diction.  Also, it doesn’t tell us ‘whose greatest importance?’.Answer is (A)Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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True or False: Do You Need to Take Calculus Prior to Business School?  [#permalink]

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25 Nov 2014, 09:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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SAT Tip of the Week: 3 Steps To Stay Sharp During The Holidays  [#permalink]

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26 Nov 2014, 09:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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How to Manage Unmanageable Numbers on the GMAT  [#permalink]

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27 Nov 2014, 21:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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28 Nov 2014, 14:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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What are the Weights in Weighted Averages?  [#permalink]

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01 Dec 2014, 09:00
 FROM Veritas Prep Admissions Blog: What are the Weights in Weighted Averages? We have discussed weighted averages in detail here but one thing we are yet to talk about is how you decide what the weights will be in weighted average problems. It is not always straight forward to identify the weights. For example, in a question such as this one,While traveling from Detroit to Novi, a car averaged 10 miles per gallon, and while traveling from Novi to Lapeer, it averaged 18 miles per gallon. If the distance between Detroit and Novi is half the distance between Novi and Lapeer, what is the average miles per gallon for the entire journey?We have two figures for mileage given here – 10 miles per gallon and 18 miles per gallon. We need to find the average mileage. So we can use the weighted average formula but what will the weights be? Will they be 1:2 since the distance between the two cities is given to be in the ratio 1:2? If you think that taking the distance to be the weights in this problem is correct, then you fell for the trap in this question.To explain the concept, let us use a simpler example first:When talking about average speed, what are the weights? We know that the weight given to each speed is the time for which that speed was maintained, right? Yes! But why?Let’s review our weighted average formula:Cavg = (C1*w1 + C2*w2)/(w1 + w2)Average Speed = (Speed1*Time1 + Speed2*Time2)/(Time1 + Time2)Average Speed = (Distance1 + Distance2)/(Time 1 + Time2)Average Speed = Total Distance/Total TimeThis is an accurate representation of average speed.Now see what happens when you use distance as the weights.Cavg = (C1*w1 + C2*w2)/(w1 + w2)Average Speed = (Speed1*Distance1 + Speed2*Distance2)/(Distance1 + Distance2)Speed*Distance doesn’t represent any physical quantity. So this doesn’t make sense. The units of the quantities will help you see the relation clearly.Cavg = (C1*w1 + C2*w2)/(w1 + w2)Average Speed = (Speed1*Time1 + Speed2*Time2)/(Time1 + Time2)Average Speed = (miles/hour * hour + miles/hour * hour)/(hour + hour)Average Speed = (miles + miles)/(hour + hour)Average Speed = Total miles/Total hoursWhat happens when you take distance as the weights?Cavg = (C1*w1 + C2*w2)/(w1 + w2)Average Speed = (Speed1*Distance1 + Speed2*Distance2)/(Distance1 + Distance2)Average Speed = (miles/hour * miles + miles/hour * miles)/(miles + miles)miles^2/hour doesn’t represent a physical quantity and hence doesn’t make sense here. Therefore, whenever you are confused what the weights should be, look at the units.Let’s go back to the original question now. Average required is miles per gallon. So you are trying to find the weighted average of two quantities whose units must be miles/gallon.Cavg = (C1*w1 + C2*w2)/(w1 + w2)The unit of Cavg, C1 and C2 is miles/gallon so w1 and w2 should be in gallons to getmiles/gallon = (miles/gallon * gallon + miles/gallon * gallon)/(gallon + gallon)miles/gallon = Total miles/Total gallonsSo how will we actually solve this question?Question: While traveling from Detroit to Novi, a car averaged 10 miles per gallon while traveling from Novi to Lapeer, it averaged 18 miles per gallon. If the distance between Detroit and Novi is half the distance between Novi and Lapeer, what is the average miles per gallon for the entire journey?Solution:Let the distance between Detroit and Novi be D. So the distance between Novi and Lapeer must be 2D.Amount of fuel used to cover distance D = D/10Amount of fuel used to cover distance 2D = 2D/18 = D/9So the two weights used must be D/10 and D/9Average miles/gallon = (10*D/10 + 18*D/9)/(D/10 + D/9) = 3D*90/19D = 270/19 = 14.2 miles/gallonOr simply, Average miles/gallon = Total miles/Total gallons = 3D/(D/10 + D/9) = 14.2 miles/gallonFood for thought: Which one of the following can you solve?- If a vendor sold 10 apples at a profit of 10% and 15 oranges at a profit of 20%, what was his overall profit%?- If a vendor sold apples at a profit of 10% and oranges at a profit of 20%, what was his overall profit% if cost price of each apple was \$0.20 and the cost price of each orange was \$.06?Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!
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01 Dec 2014, 17:00
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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