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<\/p>\n<\/p>\n
Grab your <\/span>Official Guide<\/span><\/a> as we walk through 3 GMAT Quant problems (Problem Solving), hoping to drink every drop of knowledge from the problem before we say, \u201cYo, that keg is kicked.\u201d<\/span><\/p>\n In <\/span>part 1<\/span><\/a>, we discussed the process of maxing out the value of the GMAT Quant problems you do.<\/span><\/p>\n 1: Basic exposure, little to no clue what to do For any little blip of content or \u201crecognition \u2192 move\u201d we\u2019re trying to memorize, we should create a flashcard (and we should look at flashcards at least five times a week).<\/span><\/p>\n For any problem whose overall process felt heavy or halting, we should schedule at least one Redo Appointment between 2-20 days later (the lower our level of mastery was initially, the sooner we\u2019d schedule it).<\/span><\/p>\n —–<\/p>\n If you have a copy of the 2018 Official Guide, let\u2019s try a few GMAT Quant problems in Problem Solving and practice modeling what our inventory of each problem might look like. I\u2019m going to randomly pick three without looking: PS 75, 150, 225.<\/span><\/p>\n Go give them a try and then compare your breakdown to mine.<\/span><\/p>\n 1. Reframe the question: find the four possible numbers for total, or use some property that a legal answer needs (like \u201cmultiple of 16\u201d in this case) to spot an illegal number.<\/span><\/p>\n 2. Do we know, given a real number for some part of a ratio, how to scale up the rest of the numbers by the same multiplier?<\/span><\/p>\n 3. No real important constraints here, because the 30 does all the work for us. Ratios usually have an integer constraint, meaning that the real numbers the ratio scales up to usually have to be integers (because they usually represent a quantity like number of people or number of items). This ratio doesn\u2019t have an inherent integer constraint, because it\u2019s fine for hours to scale up to a decimal or fraction.<\/span><\/p>\n 4. No vocab translations needed here.<\/span><\/p>\n 5. Seeing the word <\/span>ratio <\/b>tells me it\u2019s a <\/span>Ratio <\/b>problem, and my First Move\/First Thought is, \u201cWrite the ratio horizontally, add a column for total and add up the ratio, and then look for a real number to pair up with a ratio number so that we can solve for the multiplier.\u201d<\/span><\/p>\n 6. I needed to add 2 + 3 + 5 + 6 = 16. I needed to be able to do 30\/2, 30\/3, 30\/5, and 30\/6 in order to get multipliers of 15, 10, 6, and 5. Then I needed to be able to do 16*15, 16*10, 16*6, and 16*5 to find the four possible numbers for the total.<\/span><\/p>\n 7. None of these answers are obvious bad ones.<\/span><\/p>\n 8. No obvious traps being laid here. Just seems to be a time-sucker in terms of executing four computations.<\/span><\/p>\n 9. I could definitely <\/span>work backwards<\/b>. Say I test (C) and say the total number of hours was 160. That would allow me to compute a multiplier of 10 and know that the four staff members worked 20 hrs, 30 hrs, 50 hrs, and 60 hrs. Since one of them worked 30 hours, this is a valid number for a total and I could eliminate (C) and test another answer.<\/span><\/p>\n 1. J (now) = ?<\/span><\/p>\n 2. No content needed other than Algebraic Translations.<\/span><\/p>\n 3. No constraints to worry about other than the Algebraic Translations.<\/span><\/p>\n 4. Two sentences to translate into algebra:<\/span> 5. It feels like Algebraic Translations because it\u2019s a story with two unknowns (Jake\u2019s weight and his sister\u2019s weight), and the story is providing us with relationships between the two unknowns.<\/span><\/p>\n 6. If we\u2019ve gone the Algebraic route, then we should be able to solve the system of equations in 45 seconds or less.<\/span> We can isolate one variable and then substitute the other side of that equation into the other equation. Or we can stack the two equations (possibly scaling them up in order to make the coefficients of a given variable match), and add or subtract the equations in order to eliminate one of those variables.<\/span><\/p>\n If we initially isolate s by saying s = 278 \u2013 J, then we\u2019ll have the unenviable task of doing J \u2013 8 = 2(278 \u2013 J). The burden of 2 * 278 should suggest to us that there\u2019s probably a friendlier route.<\/span><\/p>\n If we\u2019ve gone the <\/span>Working Backwards <\/b>route, we need to be able to subtract 8 from a three-digit number, divide that number by 2, and then add up a three-digit and two-digit number to see if it\u2019s equal to 278.<\/span><\/p>\n 7. Since they\u2019re asking us to solve for Jake\u2019s present weight, but the problem talks about Jake losing 8 pounds, there might be Evil Twin answers (one answer is Jake\u2019s real weight, the other is 8 less, in case someone accidentally solves for <\/span>that <\/span><\/i>number). 131 and 139 are Evil Twins, because they\u2019re 8 apart, as are 139 and 147. We\u2019d be ditching the lower one, since that one would be solving for Jake \u2013 8 rather than for Jake. So we wouldn\u2019t guess 131. But 139 appears as the bigger twin and as the lower twin, so we\u2019d probably not know what to do with that one.<\/span><\/p>\n 8. The big potential errors on Algebraic Translation are always botched translations. People might accidentally do (J-8)*2 = s.<\/span><\/p>\n 9. Since the answers are friendly integers, we could <\/span>Work Backwards<\/b>. If we started with (C), for instance, and said that Jake\u2019s present weight is 139, we could calculate that if he loses 8 pounds, he\u2019ll be 131. His sister would therefore be 65.5 lbs. That decimal weight is already enough to know this number is wrong, but going a step further and thinking, \u201ctogether, they weigh about 130 + 70 = 200 lbs,\u201d we know that this number was way too small. We\u2019d eliminate (A) and (B) and (C) and probably jump to (E) since 137 was way too small and (D) is only somewhat bigger. We also might recognize that if <\/span>J \u2013 8 = 2R<\/span><\/i>, then <\/span>J \u2013 8 = even<\/span><\/i> (since 2 * anything is even). If <\/span>J \u2013 8 = even<\/span><\/i>, then <\/span>J = even + 8<\/span><\/i>, which means that <\/span>J = even. <\/span><\/i>That makes (E) the only legal number to pick.<\/span><\/p>\n 1. Say whaaaaa? No, I don\u2019t know how to simplify this dumpster fire. This question SCREAMS out, \u201cUse one of your three free skips on me<\/i>!\u201d It\u2019s clear from the size of the paragraph, the number of variables or functions being named and defined, the complicated constraints (1\/3 of the decimals have a tenths digit that\u2019s even), the cryptic question (\u201cpossible value\u201d) and the three-case answer choices that this is a very hard problem.<\/p>\n 2. Anyone, including a teacher, who thinks that they are at level 4 of mastery on this problem the first time they try it is lying to you or themselves. Now that we\u2019ve established that it would take several times doing this problem to be able to answer these 10 questions, we\u2019ll pretend like we\u2019re already at THAT stage of understanding it.<\/span><\/p>\n There really isn\u2019t one compact reframing for this dense a question, but whenever questions are asking which is a <\/span>possible <\/span><\/i>value<\/span>, <\/span><\/i>then the question is either asking:<\/span><\/p>\n -which of these values adheres to the number property that any possible value would have?<\/span> In other words, you\u2019re either going to know that \u201call possible values are multiples of 11\u201d and pick accordingly, or you\u2019re going to know \u201call possible values are between 4 and 18\u201d and pick accordingly.<\/span><\/p>\n So we could reframe this question by asking ourselves, \u201cIs this asking me to infer a potential number property of E \u2013 S, or is it asking me to find the min\/max of E \u2013 S?\u201d<\/span><\/p>\n 2. There aren\u2019t any formulas or properties at work here (for example, we AREN\u2019T using the normal property we think of with rounding decimals: \u201cIf it\u2019s .5 thru .9, round up\u2026 if it\u2019s .4 thru .1, round down\u201d).<\/span><\/p>\n 3. Lots of vocab here.<\/span> 4. We need to apply the function rules to think about what\u2019s happening with E.<\/span> If we\u2019ve figured out that we\u2019re seeking the minimum\/maximum value of E \u2013 S, we are saying: Biggest E compared to S comes when the even tenths digits are all 0\u2019s, because the function forces us to round up, so we get more upgrade going from something like 0.01 to 1 than we would going from 0.81 to 1.<\/span><\/p>\n Also, we need the odd tenths digits to be 1\u2019s, because they will be rounded down, and we want to minimize the downgrade we get out of rounding down. We lose less when we go from 0.11 to 0 than when we go from 0.91 to 0.<\/span><\/p>\n Smallest E compared to S has the opposite logic. We\u2019d want to have all the even tenths digits be 8\u2019s so that we have as little rounding up as possible. And we\u2019d want the odd tenths digits to be 9\u2019s so that we have as much rounding down as possible.<\/span><\/p>\n 5. The big topic clues are DECIMALS, ODD\/EVEN, but the normal first moves don\u2019t apply.<\/span><\/p>\n The normal first move with DECIMALS is to \u201cclean it up into integers and powers of 10.\u201d For example, change 0.0034 into 34 * 10<\/span>-4.\u00a0<\/sup><\/span>The normal first move for ODD\/EVEN is to \u201cthink about the rules of adding\/subtracting\/multiplying two evens, two odds, or a mix.\u201d For example, seeing 3x + 4y is odd and thinking \u201cif 3x + [even] is odd, then 3x is odd, so x is odd.”<\/span><\/p>\n The real topic is FUNCTIONS, and the giveaway there is \u201cThe estimated sum, E, <\/span>is defined as follows<\/i><\/b>.\u201d<\/span><\/p>\n Our first move on FUNCTION problems is usually just to think, \u201cShould I bail on this problem? Do I typically do poorly on function problems? I know it\u2019s a topic that skews hard, so it wouldn\u2019t hurt me to miss this.\u201d or \u201cCalm down, FUNCTIONS problems are designed to be brain-numbing the first time we read them. Read this multiple times and think flexibly about what process it\u2019s describing.\u201d<\/span><\/p>\n 6. It should be easy to take 1\/3 of 30 and getting that 10 of these numbers have even tenths digits (i.e. will be rounded up) and that 20 of these numbers have odd tenths digits and will be rounded down.<\/span><\/p>\n When we\u2019re calculating biggest E and smallest E, we will get to some ugly numbers that suggest we should switch over to approximating.<\/span><\/p>\n Biggest E: 10 of the numbers of a tenths digit of 0 and 20 of them have a tenths digit of 1. What\u2019s the net gain\/net loss, compared to what we would have gotten by just adding all 30 numbers (S)?<\/span><\/p>\n For each of our 10 round ups, we\u2019re getting something as big as 0.9999\u2026 since we can go from a 0.01 to a 1. Let\u2019s approximate and say that these 10 numbers are being rounded up by 1. So we get +10 from those. Meanwhile, we\u2019re losing 0.10 from each of the 20 odd numbers, because we\u2019re going from 0.1 to 0. We get a -2 from that (20 * 0.10).<\/span><\/p>\n For our Biggest E, then, we have a net gain of about +8.<\/span> To calculate our Smallest E, we\u2019re going from 0.89 to 1, and we\u2019re going from 0.99 to 0. So we have 10 gains of roughly 0.11 = +1.1. We have 20 losses of roughly 1 = -20.<\/span><\/p>\n So E could potentially be about 19 smaller than S.<\/span> 7. It would be weird for (D) to be right. It\u2019s the only answer that thinks case 1 fails. Since case 1 is in four of the answers, it\u2019s much more likely that it actually works.<\/span><\/p>\n It would be weird for the middle number NOT to work. Most of these \u201cpossible values\u201d questions are basically testing whether we\u2019ve solved for the mix\/max of possible values. The middle number is usually safe and one or both of the extreme numbers have gone beyond the legal range. Since the middle number probably works, (B) or (E) would be a smart guess.<\/span><\/p>\n 8. It\u2019s possible that people would rule out \u201c0\u201d as one of the potential even tenths digits, although it mercifully doesn\u2019t affect our getting the correct answer. People often forget to consider 0 when they think about even digits.<\/span><\/p>\n People might waste time trying to find a case where they land on E \u2013 S = 6, instead of realizing that 6 is just some arbitrary number they\u2019re picking that\u2019s somewhere within the legal range.<\/span><\/p>\n 9. There aren\u2019t really multiple ways of doing this problem. Subbing in each of the three cases as a possible value of E \u2013 S wouldn\u2019t allow us to calculate anything, so Backsolving is off the table. We sort of <\/span>do <\/span><\/i>need to Make Up Numbers to get through this, but this problem largely hinges on two things:<\/span><\/p>\n -sensing that a problem asking \u201cWhich of these are possible values of E \u2013 S\u201d is really asking us to figure out the min and max value of E \u2013 S Now\u2019s the REAL practice:<\/span><\/p>\n We\u2019ve dissected all three GMAT Quant problems. Which of those are you putting on your Redo Calendar and when? (Remember that PS 225 is a stupid problem for us to attempt on test day, so we should not prioritize getting better at it in practice.) Which little nuggets \/ moves \/ properties \/ translations we mentioned were ones that had escaped you? Go write some flashcard quizzes for each of those, so that you can reinforce those ideas a few more times in the next couple weeks. ?<\/span><\/p>\n Want some more GMAT tips from Patrick? Attend the first session of one of his\u00a0<\/i><\/b>upcoming GMAT courses<\/a>\u00a0<\/i><\/b>absolutely free, no strings attached. Seriously.<\/i><\/b><\/p>\n Grab your Official Guide as we walk through 3 GMAT Quant problems (Problem Solving), hoping to drink every drop of knowledge from the problem before we say, \u201cYo, that keg is kicked.\u201d In part 1, we discussed the process of maxing out the value of the GMAT Quant problems you do. As you review them, […]<\/p>\n","protected":false},"author":117,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[873,929,52871,930,2,24,8],"tags":[],"yst_prominent_words":[],"class_list":["post-15932","post","type-post","status-publish","format-standard","hentry","category-for-current-studiers","category-gmat-prep","category-gmat-strategies","category-gmat-study-guide","category-how-to-study","category-problem-solving","category-quant-on-gmat"],"_links":{"self":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/15932","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/users\/117"}],"replies":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/comments?post=15932"}],"version-history":[{"count":5,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/15932\/revisions"}],"predecessor-version":[{"id":15960,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/15932\/revisions\/15960"}],"wp:attachment":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/media?parent=15932"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/categories?post=15932"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/tags?post=15932"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/yst_prominent_words?post=15932"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}As you review them, classify your current level of mastery for that problem.<\/b><\/h4>\n
\n<\/span>2: Partial clue, knew how to do some stuff (may have even guessed the correct answer), but didn\u2019t know a \u201creal way\u201d to get a definite answer
\n<\/span>3: Got the answer correct through a legitimate process, but it felt hard
\n<\/span>4: Got it correct and felt totally in control and normal (you can even think of other problems it\u2019s similar to or more than one way to do the problem)<\/span><\/p>\nTake an inventory of all the component parts of a problem and assess whether you could be better at any of those parts.<\/b><\/h4>\n
\n
\u00a0Follow up on what you\u2019ve attempted to learn on GMAT Quant problems by testing yourself later<\/b>.<\/h4>\n
PS 75<\/b><\/h4>\n
PS 150<\/b><\/h4>\n
\n<\/span>Jake loses 8<\/span><\/i> \u2192 \u201cJ \u2013 8\u201d<\/span>
\n<\/span>(the verb) he will weigh<\/span><\/i> \u2192 \u201c=\u201d<\/span>
\n<\/span>twice as much as his sister<\/span><\/i> \u2192 \u201c2s\u201d<\/span>
\n<\/span>Together they weigh \u2192 <\/span><\/i>\u201csum\u201d<\/span><\/p>\n
\n<\/span>J \u2013 8 = 2s<\/span>
\n<\/span>J + s = 278<\/span><\/p>\nPS 225<\/b><\/h4>\n
\n<\/span>or
\n<\/span>-which of these values is within the range of possible values?<\/span><\/p>\n
\n<\/span>\u201c30 positive decimals, none of which is an integer\u201d = must have some nonzero digit to the right of the decimal
\n<\/span>\u201ctenths digit is even\u201d = tenths digit is .0, .2, .4, .6, or .8<\/span>
\n<\/span>\u201ctenths digit is odd\u201d = tenths digit is .1, .3, .5, .7, or .9<\/span>
\n<\/span>S = sum of the non-rounded numbers<\/span>
\n<\/span>E = sum of the rounded numbers<\/span><\/p>\n
\n<\/span>\u201c1\/3 of the decimals have even tenths digits\u201d = 1\/3 of the numbers get rounded down<\/span>
\n<\/span>and we need to think about the complementary leftover<\/span>
\n<\/span>\u201c2\/3 of the decimals have odd tenths digits\u201d = 2\/3 of the numbers get rounded up<\/span><\/p>\n
\n<\/span>MAX VALUE: E is as big as it can be, compared to S<\/span>
\n<\/span>MIN VALUE: E is as small as it can be, compared to S<\/span><\/p>\n
\n<\/span>E \u2013 S < 8<\/span><\/p>\n
\n<\/span>-19 < E \u2013 S<\/span><\/p>\n
\n<\/span>-understanding that finding the min\/max of E \u2013 S means picking which odd or even tenths digit would achieve the most rounding up \/ least rounding down or the opposite.<\/span><\/p>\n
\n
\n![\"patrick-tyrrell\"](\"https:\/\/cdn2.manhattanprep.com\/gmat\/wp-content\/uploads\/sites\/18\/2018\/03\/patrick-tyrell-150x150.png\")
Patrick Tyrrell<\/a>\u00a0is a Manhattan Prep instructor based in Los Angeles, California.<\/strong>\u00a0He has a B.A. in philosophy, a 780 on the GMAT, and relentless enthusiasm for his work. In addition to teaching test prep since 2006, he\u2019s also an avid songwriter\/musician.\u00a0Check out Patrick\u2019s upcoming GMAT courses here!<\/a><\/em><\/p>\n","protected":false},"excerpt":{"rendered":"