Real GMAT® Problems - Ep. 46 - Computation

Episodes Referenced: Watch On YouTube - Break Through Score Plateau - Algorithm Video - GMAT® Math Basics Long Multiplication - Decimal Long Multiplication - Long Addition - Decimal Long Addition - Decimal Long Division - Decimal Long Subtraction - Fractions - Reach your dream GMAT® score in 1/2 the normal time: https://thegmatstrategy.com/ ---
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Transcript

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Welcome to Real GMAP Problems episode 46. Doing Real GMAP problems is one of the most tried and true ways to make test A go well. So let's talk through a few examples. The problems that we're going to go through are from the 11th edition of the official guide for GMAT Review, and you can web search them if you would like to follow along visually. And we are also making a push for video in the feeds now where we can get it. So if video is available on this platform, you should also be able to follow along via video and we'll put the problems up on the screen and I'll be able to show you some scratch work, which we're really excited about. If that's not available yet, then it's it's in the pipeline for you. Okay. And you can always click the link below to go to YouTube if you want to see this stuff worked out. Just so you know, the 11th edition of the official guide is out of print. And that's partly why I'm going through questions from that book, because that way, if you purchase this year's official guide, there shouldn't be any overlap between the questions that we're going to work through. The official guide contains retired problems that have appeared on past GMAT exams. So these are going to be extremely similar to what you're going to see on your official GMAT. I'll give you a chance to work through the solution on your own if you'd like, and then I'll discuss my thoughts on what to take away from each one. I recommend pausing after I read through each problem and trying to solve it. At the very least, visualize how you would solve it if you're on the go. You might not be able to execute all the steps in your head, but just do your best. It's a good little mental workout. And if you are in a situation where you can physically write down what you would on test day, that's that's for sure ideal. So we're going to start with some lower difficulty level, uh, just one warm-up problem today, and then we're going to bump up the difficulty level from there. We'll eventually end with like a tougher question. So if you find yourself struggling, it's okay to head back to an earlier episode number and work your way back up to this level when you're ready. And we're going to focus on computation questions today. It's a big pain point for a lot of folks. This is question number one, a little warm-up problem. The question says 0.1 plus 0.1 squared plus 0.1 cubed equals question mark. I'll read that again. The question is 0.1 plus 0.1 to the second power plus 0.1 to the third power. No parentheses anywhere. So it's just pure PEMDOS here. Option A is 0.1. Option B is 0.111. Option C is 0.1221. Option D is 0.2341. And option E is 0.3. Again, recommend pausing here and getting as far as you can. I'm just gonna jump into my commentary. So it's a really, really good warm-up problem for computation skills. There aren't too many steps, there aren't too many big traps in the question. And it's one of those questions where if you're solid with your skills, you're highly likely to get it right. And if you're a little shaky on your skills, it'll help reveal that and help guide the path toward toward fixing that. So it's a good good place to start with um getting better at computation. Let's start with a solid solution path. This isn't gonna be the only way to do the problem, but I think you'll find it useful. And then we'll we'll do a little light refresh on decimal multiplication, since obviously that's a huge component of this question, and then we can talk through a simple shortcut. Uh, if you if you're if you're just starting out with your GMAT studies and you're like, whoa, whoa, whoa, how do I add decimals again? How do I deal with exponents again? What does to the second power mean again? If if you're in that boat, uh that's pretty much where I started. It had been a many, many years when I started studying for the GMAT since I had done this kind of math, especially without a calculator. And so I just need to shake the rust off a little bit. We've got a whole math basics series linked below for you if you want some help reskilling, reskilling with those skills you probably had back in the day. And it just might have been a while since you've used them. So, first, there are probably a handful of you who could just look at this question and within a few moments like instantly know the answer with 100% confidence. And if that's you, that's amazing. And uh you probably have no worries here. If that's not you though, and it definitely was not me when I first started my journey with the exam, um, even if you have a tiny, tiny, tiny amount of doubt that maybe you're wrong. Like you're looking at the problem, and even if you're highly confident, like 97% confident, but not 100%, it's very worth doing the full computational process all the way end to end, using long multiplication in order to be sure you're getting it correct. I'm gonna talk about the philosophy behind that point a little bit more on this on this problem. Um, but for now, I went pretty long on the specific concept in our previous episode, which is called How to Break Through a GMAT score plateau. That's linked below as well if you want to check it out. Uh, but the short version is most people rush through the questions that they know how to do in order to make time for the questions that they don't know. And that can make sense on certain tests, but on the GMAT, partially because of how the scoring algorithm works, it's it's super hurtful. And that's because missing easy questions hurts your score more than missing hard questions. So it can be difficult to uh to make that transition since we're so used to thinking about our scores on tests, primarily in terms of accuracy only. Uh, but the GMAT also measures your performance based on the difficulty level of questions you see. So because of that, and because getting easy questions right is more important to high scores than getting hard questions right, which I know like might sound super, super counterintuitive, but it it is true. And I'll give you some more resources for learning more about that if you want to. But just staying at the high level here, doing out the actual math on a question where you're 90% sure is a great investment. Getting that extra 10% from 90 to 100 is really, really, really valuable because if I'm 90% sure I know how to do a question, I'm highly likely to be right about that. Like I probably do know how to do the question, and so I don't want to introduce 10% risk that I'm gonna get it wrong. That's gonna hurt my score more than just investing to get that extra 10%. Okay. So that that 10% chance that you might make a mistake on a question you know has an outsized negative effect. So as promised, if if you want to understand how the scoring algorithm works better and how you can capitalize on it, I would recommend checking out the the plateau episode that I just mentioned, that's linked below. And we've also got a video on our main site that goes into a bit more depth, and that'll be linked for you alo as well. You don't need the video, but I've found a lot of people find it really, really, really helpful. So if you're more of a visual learner, if you feel like listening to the plateau episode, you're still like, wait, I don't totally feel like I get this, I think the video will help a lot. But just to say at the high level and not get too in the weeds here, let's say for now you understand why it's so, so important not to miss questions you know how to do, uh then hopefully it makes sense why it's a good idea to do the full computation here and go from 90% certainty to 100. Um, even if that takes you a little bit more time. Uh if your first instinct is right, though, 100% of the time, I just want to reiterate this. If if you if that instinctual approach without doing all the math is right 100% of the time, then trust that. That's great. Um, what I'm saying is if you definitely know how to do the math and you have any doubt whatsoever that your first instinct could be misleading, then you want to just take the time to execute all the steps uh to get 100% certainty. Because again, missing questions you know how to do has a much larger negative impact than missing questions you sort of know how to do, which would be the questions you'd be saving time for by rushing through this question. So it might make intuitive sense to make those moves, but you'll want to train yourself over time to make more rational bets, especially under time pressure. So uh let's say that we do have a little bit of doubt here. The best bet is probably just long multiplication with decimals. Uh, we've got a full lesson on the technique in in the math basics series I mentioned before, uh, also linked below. So if you want more practice with this approach, that episode should help quite a bit. I'm just gonna gloss over the kind of short version of the approach is when you're multiplying decimals, you ignore all the decimal places first. You set up a regular long multiplication, and then you add the decimal places in at the end. So the way I would do that for this problem is for 0.1 squared, which is 0.1 times 0.1, I would just write um 0.1 out and then 0.1 right beneath that, as if I were going to do regular long multiplication on it, uh, just like stacking the numbers. Um if you forgot how to do long multiplication, we've got that how-to linked for you below as well. And uh now I'm just gonna ignore the decimal places and just do one times one, which is of course just one. And then I'll add in the total number of decimal places for all the numbers I was multiplying originally. So the way to do that is you count how many decimal places each number we multiplied has. So point one has one decimal place, the other point one has another decimal place, so that's two total decimal places in the original numbers we're multiplying. And then I'm gonna take the decimal place in the answer, and I'm going to shift it to the left that many decimal places. So if I have one point zero in the answer, then I'm gonna shift uh the decimal place once to the left, that would give me 0.1, and then another time to the left, that would give me 0.01. Okay, so 0.1 squared is 0.01. Again, that might be major overkill for some of you, maybe even a lot of you, especially if you've been studying for a while. But for those of you who might have felt the pressure to rush through that kind of thing, even though you technically know how to do it, hopefully this is going to help you uh have the conviction to execute well so you can at least get credit for the questions that you know how to do. And if you're having trouble scoring high, uh like you've studied a lot, you know all the material, but but it's not showing up in the score, or your score is fluctuating a lot, like it's sometimes high, sometimes low. This kind of consistent execution can really, really help with that. And it's just very, very counterintuitive. So that's why you see a lot of people on forums complaining like, hey, my score is going up and down. Why is my score so low, even though I know all the material, what the heck is going on? There's just uh a couple nuances to this exam that you might not have needed on a school test, and so you might not have built those skills. And that's why we're here. We're we're here to help you build those. So the good news is that if you study and practice a bit with the uh the long multiplication decimal approach, you should be able to execute that pretty quickly. And then the final step isn't too bad because now we want to know what the value of 0.1 cubed is, and we already know that 0.1 squared is 0.01. Uh so we can just multiply that by 0.1 a third time. So we can, again, just set it up like a regular long multiplication, 0.001 on top and then 0.1 on the right below that, and just ignore the decimal places. We do one times one again, obviously we get 1.0, and then we count up the three total decimal places from the things we were multiplying together, two point from 0.001 and one decimal place from point one, and we add those up to get three total decimal places, and then we shift the decimal place in the result three places to the left. So one point zero, I shift it over once, that's point one, shift it over twice, that's point zero one, shift it over three times, that's point zero zero one. And so now we can rephrase the problem as point zero one plus sorry point zero point one plus zero point zero one plus zero point zero zero one. Okay, so the original question was zero point one plus zero point one squared plus zero point one cubed. Now we've transformed that into zero point one plus zero point zero one plus zero point zero zero one. Uh for that, you might be able to intuitively understand that point one one is the answer, which is answer option B is in beta, which is correct. Or you could set up a long edition with decimals. Um to do that. Again, I'll just gloss over it. You line up the decimal places and use the standard long edition approach. We've got that linked below for you as well if you want to remind yourself how that works. Uh, because no calculator on G on the GMAT quant section, so that's why I'm doing all this math by hand and uh reminding you of all these long form approaches. They're they're quite important, quite helpful for the exam. Uh but the short version of how that would look would be I would write 0.100 on top, and then I would write 0.010 below that, and then at the bottom I would write 0.001. So that's 0.1 plus 0.01 plus 0.001. And that should help you see how each column sums to one and how the final result should be 0.111. Um, if you're on the pure audio feed, it might be a little tough to imagine, but if you worked the problem, you could probably see it. And again, we should have a visual aid for you either on YouTube immediately or hopefully on uh whatever platform you're on. It's just the the distributing video podcast thing is kind of an unsolved problem, everybody. So if you have a solution to that, let us know. Uh, but it's like even even like the big companies like Apple, they're having trouble bringing that stuff online, which is just uh just is what it is. So again, uh could be overkill here. Could definitely be overkill that approach I just talked through. But um listen, if if you can't get this question right, that's not good if you're aiming for a top score. Okay, so these are essential skills. And even if you are getting them right, but there's like that doubt in the back of your mind, I think in order to feel the way you want to feel during the exam, to have the confidence and conviction to be like, okay, I'm doing well here, ensuring that you have a structure for not missing questions you know how to do is gonna be super, super helpful, super foundational for that. So um again, the sh the short version of the algorithm is yes, missing easy questions hurts your score more, um, but missing hard questions hurts less. That's the counterpoint to that. So it's not that big of a deal if you're unsure how to do hard questions. You instead want to really focus your energy on not missing the gettable ones. If you're like, oh, I know this one, most people speed up. They're like, I gotta get this done fast, I know how to do this one. You want to practice, and this might feel super weird, going slower on the questions you know how to do. And I know that might make no sense right now. You're like, this guy's crazy. This guy's gonna destroy my score. I barely have time to get through the section as it is. If you, if you take time away from the questions you don't know how to do, you should have plenty of time to do the questions you do know how to do. And that's partly what the exam is measuring with the adaptive scoring algorithm. It's not just measuring, can you get questions right and can you reason through questions? It's also measuring, can you make difficult executive decisions under pressure? This, for most of us, our post-MBA role is going to be nothing but making decisions under pressure with finite resources. And that's that's partly what the exam is measuring is can you recognize a good investment and invest appropriately? And can you recognize a bad investment and let it go? Or do you just can you just are you emotionally unable to let go of a bad investment? Like that's a leadership skill that's worth working on. And this is just one, yeah, kind of maybe unrealistic version of that skill, but it's an opportunity to build those muscles. And I think the exam is um quite cleverly designed in that respect, but it's very poorly explained online uh because a lot of people sell a lot of GMAP prep on the back of the accuracy thing. Uh, because that just makes sense. You know, it just makes sense. Like you've been taking accuracy-based exams your whole life. You look at this, you're like, oh, cool, I got a thousand practice problems or 10,000 practice problems. Like, that's probably going to be enough. I'll just do a lot of practice problems and then I'll be great. And if that's working for you, don't stop. Don't stop. I'm I'm here to help. I'm not here to hurt. If that's working for you, then keep going with it. But it doesn't work for a lot of people. And I think that's super, super, super confusing to people. They're like, man, I did 2,000 practice problems and my score didn't move or my score went down. That was that's what happened to me. I mean, I did a lot more than 2,000 problems before I saw my score go down. You can imagine how that felt. So I'm just trying to give all of you what was missing for me that made me really doubt myself in the process. But it it was, I wasn't um, it wasn't that I wasn't smart enough or that I didn't have the capacity or that I didn't have the work ethic. It's that I didn't have the right map of the terrain. I didn't have the right map of the terrain. So that's that's what I'm trying to fill in because I know a lot of you are probably working with providers who are like probably good at certain parts of helping you with the exam. But if they don't give you the complete picture, then uh you can get stuck in this cycle where you're just paying these monthly fees over and over and over and over and over and over again and and not seeing the result, which um nobody wants that. Nobody wants that. So um the uh the shortcut here, the shortcut for this problem is not really much different from what we just did. Uh, it just comes from understanding what we just did so well that you don't even have to perform all the computation to have the certainty because you just know in your head one times one is one. You know that you're gonna move the decimal places based on how many decimal places there are in each step of the multiplication. So you just look at point one squared and you're like, oh, that's gonna be 0.001. But that intuition and that conviction in that intuition, you're either born with it, which is amazing, or you've developed it through many, many years of doing math in your job, which is the vast minority of us, but some people do, or you develop it now. You just you just sit down and you put in the practice to build that intuition. But if you're on a tight timeline, which uh which I was back in the day, and you don't have time to build that intuition, then you can just execute the math, and that's more than good enough. So uh the shortcut would be just having executed the math enough that you can just kind of do it in your head with 100% confidence. And then if if you're struggling with that, or that's just not you as a person, you don't have that confidence, then you just do the math and build the confidence over time. So again, just tying all this off. Check out those math basics episodes for more practice if you want practice with the basic skills. Um, check out the other links for a deeper understanding of the scoring algorithm and uh just focus on training yourself to invest more time in the questions you know how to do, even if it's very counterintuitive. And all the that should help quite a bit, whether you got this question right or not. Before we move on, if there's anything you feel is important for you to remember from that question, I'd recommend just pausing the episode here, making a quick note to self by either like texting or emailing yourself if you're on the go, or if you're at the desk just making a flashcard or however you're tracking your reminders, your notes to self, and then we'll uh bump up the difficulty a little bit for the next one. Okay, this is problem number two. The problem is a big fraction. The numerator of that fraction is zero point zero four five times one point nine. Okay, so the numerator of the fraction is zero point zero four times one point nine. The denominator of the fraction is zero point zero three times zero point zero zero five times zero point one. And I'll read that again. The numerator of the fraction is zero point zero four times one point nine. The denominator of the fraction is zero point zero three times zero point zero zero five times zero point one. Option A is five thousand seven hundred. So they're asking they're asking you th there's an equal sign to the right of the fraction, sorry. So uh they're basically asking you like what's the value of this? So option A is five thousand seven hundred, option B is five hundred and seventy, option C is fifty-seven, option D is five point seven, and option E is 0.57. Again, recommend pausing and getting as far as you can. I'm just gonna dive right in. Uh first things first. It's completely okay to just do this problem by converting every decimal into a fraction. In fact, that is a really viable strategy for the previous problem as well. I just didn't want to make a million points on the previous problem. I felt like I was already making a lot. So I wanted to use this problem to build on that. Obviously, the problem's more complicated. There's like more things, more decimal places. This is complicated by the fraction rather than the exponents. The numbers are a little trickier in the answers, you know. You can tell it's all about the decimal point moving, and like how do I get that exactly right? So there's just a few more pitfalls in this question, and um quite a few more of us get this one wrong. We'll talk about that in a second, which is fine. You know, we're all here to grow. Uh, but here's the bottom line. If you find you're fairly likely to make errors using decimal computation, which I definitely am, by the way, then it's an awesome idea to just do all of your decimal computation using fractions. Like just forget about everything decimal related. You can forget about the whole decimal long division, long multiplication, long addition thing on the previous problem. You can just do the previous problem all as fractions. You can make it one over 10 plus one over a hundred plus one over a thousand, find a common denominator. Like that's that's totally legit. Um having said that, there's a time and a place for decimal computation. It's a good workout. So that's why we let off with that. But it might sound like it's gonna really slow you down, but that's not too bad if you practice it a little bit. A little bit of practice goes a long way with the whole fraction thing. So let's walk through how that might look on this problem. And I think it does make this problem a lot more approachable for folks. So 0.45 on the top, we'll just start with the numerator, is just 45 divided by a thousand. And 1.9 is just 19 divided by 10. So I'm just gonna rewrite the numerator as those fractions. So I'll make it 45 over a thousand times 19 over 10 in the numerator. Let's do the same thing with the denominator. We'll turn 0.03 into 3 over 100. We'll make 0.005 into 5 over 1,000, and we'll make 0.1 into 1 over 10. Now if you write all that out in the original fraction form, it might feel a little overwhelming, since now you're getting like a really complicated double decker fraction, but Recall that if you're dividing by a fraction, that's the same as multiplying by the reciprocal. So let's transform the current state into all multiplication. So I'm going to take all the fractions on the bottom, invert them, and multiply by them instead of dividing by them. So dividing by a fraction, same as multiplying by the reciprocal. We've got a fractions math basics episode linked for you below as well if you're a little rusty on this. So the new version would be 45 over a thousand times 19 over 10 times 100 over 3 times 1000 over 5 times 10 over 1. And hopefully that starts to look a little bit more approachable, since you'll be able to cancel a lot of the zeros from the top and bottom. And if you're unsure how canceling and fractions work, just check out that math basics episode again. I'm not going to get us bogged down in the details of cross-canceling fractions here, but suffice to say that if you execute all of that well, you'll wind up with something like 45 times 19 times 100 times 1 over 3 times 1 over 5. And we could just reconvert that into a fraction if you wanted to. 45 times 19 times 100 divided by 3 times 5. Either way, either way, however that makes sense to you. And from there, I bet most of you would be able to arrive at the right answer or at least estimate your way there based on how far apart the answers are. It might not feel easy or natural yet if you're just starting out, but with a little bit of practice, I'm sure you can get there from here. So I think the the big point here is how you get past the potentially intimidating first look of uh of the problem. And the fraction thing can be huge for that. So we'll circle back on that in a second. Let me just not do the cliffhanger thing here. So 45 times 19 times 100. You um can cancel the three times five and the denominator with the 45. Um three times five is fifteen, fifteen times three is forty-five. So if we cancel that, we'd wind up with three times nineteen times a hundred, and that's that's five thousand seven. So that's option A. Uh as an alpha, which is the correct answer. So um just to just to finish that out. So if you um if you file a way to always do decimal computation in fraction form, I think that's a really nice, simple, memorable way to increase your odds of success without having to memorize a lot of things and go through a lot of decimal computation stuff. So if you if you're on a super tight timeline, like a few days from the exam and you're not feeling great with your decimal computation, you might have more success just transitioning all of that to fraction computation rather than trying to spend a lot of time learning decimal math. If you're six months away from the exam, then you might enjoy some of the advantages and flexibility that being good at decimal math gives you. Um and I would just follow your intuition there. There are definitely other potential solutions on this problem. And um if you're curious, they can be worth exploring. But what I've found for a lot of folks is uh they end up memorizing a bunch of really narrow, specific solutions that may only apply to a couple types of problems rather than memorizing one solution that will allow them to solve tons of problems. And there's no right or wrong with this, uh, like I was alluding to before, it's all about what works for you and your results. I'm never gonna argue with your results. Um, so whatever way gets you the result is the way to go strategically. But just in case you're feeling a little overwhelmed with a hundred decimal solutions for a hundred different types of decimal problems, I just gave you one solution that will work basically 99% of the time. Uh so if that's appealing, hopefully that was helpful. Again, don't need to do the problem that way, but I think it's a nice bet and it's a nice contrast to what we were doing by getting in the weeds on the previous problem. Both have their place, just trying to help you make good decisions about what you should do. So again, if if you're the type of person who's like, don't make me make any decisions here, Isaac, just tell me what to do. If you're that kind of person and you don't want to discover it on your own, then I'm just gonna say, do all your decimal computation as fractions. Just no negotiating, just make it happen every single time. If you're the kind of person who likes to experiment, maybe optimize, maybe find, oh, this, you know, one trick could work here, this other trick could work there, then just put this in your back pocket as something you can use in the future, and then try out the decimal computation episodes we have linked for you below, and you'll be able to invent your own solution and intuitively come up with, okay, in this kind of situation I use fractions, in this kind of situation I use decimals. And there's all kinds of learners out there. Okay, so once again, I just recommend pausing there, making any desired notes to self, and then we'll try one more question that's a little bit tougher. The problem says x equals one divided by a ton of stuff. So that ton of stuff is uh basically a fraction. X equals one is the numerator of the fraction, and then the denominator of the fraction is two to the second power times three to the second power times four to the second power times five to the second power. I'll read that first part again. So it says if x equals one divided by two to the second times three to the second times four to the second times five to the second, where x is a fraction with one in the numerator and all those exponents being multiplied together in the denominator, it says if x is expressed as a decimal, how many distinct non-zero digits will x have? I'll read that one more time, and again, feel free to check out the video feed for the visual here if you want. But if you're on the bike or you're at the gym, I'll read it for you one more time. If x equals one divided by two to the second times three to the second times four to the second times five to the second is expressed as a decimal, how many distinct non-zero digits will X have? Option A is one, option B is two, option C is three, option D is seven, and option E is far as you can. And I'll jump into my commentary in a moment. Okay, so an interesting kind of conglomeration of some of the stuff that we've been working on in the episode so far. We got some complicated fractions, we got some exponents, we got some decimals, it's kind of all colliding in this uh in this much more difficult problem. Um Yeah, so this one the the first question is about four times, sorry, the second question was about four times harder than the first one by the numbers, so quite a big jump there. This one's about 60% harder than the previous one. So a big range of difficulty levels here. Uh perhaps obviously more complicated conceptually. We got to transfer this weird fraction into a decimal. We gotta figure out how many non-zero digits the decimal is gonna have. If you're like, wait, what's a digit again? Then you want to go back to that first episode of the Math Basic series where we talk about some definitions that it might have been a while since you've thought about. So there's there's a lot of stuff going on here. So it's probably not the hardest GMAT question that you're gonna see, but uh it's certainly not easy for most of us. It's an interesting follow-up to the previous two, though, because of all the common threads. Having said that, I gave you some tactics and some tricks for the previous two. But this question is actually a really good one to make a different point, which is there are a lot of great tricks out there for a lot of decimal questions and a lot of computation questions, but sometimes, sometimes you may just have to brute force the computation. You may just have to sit there and do a ton of math. And I think that this question is actually a really good example of it. There's it's hard to just trick and trap your way to the answer unless you get lucky. There is a coincidence here where if you express the entire denominator of the fraction, like you just multiply it all out, that denominator of the fraction has three unique values in it, uh, one, four, and zero to be exact. Um, and you could luckily guess the correct answer from there, which is C. Uh, the correct answer is option C as in Charlie. It's there's gonna be three non-zero decimal places. But that's that's complete blind luck because um the question literally says how many distinct non-zero digits would X have. And so you should have picked two if you were thinking about the question that way. But there's all kinds of problems with that logic because that's not even a decimal. It's actually in fraction form. So yes, it kind of might appear on the surface that maybe there's a shortcut there, but it's it's it's actually not. It's it's just uh kind of like a coincidence there. Uh so instead, this is one where if you're gonna get to 100% certainty, you're gonna probably end up doing a lot of math, like a lot of math. So it's also a good opportunity to talk about the um the letting go, the guessing strategy I was talking about earlier of like if you get to a certain point in a problem and you're like, man, I'm I'm not sure I really know how to do this. Like I started at 90% and now I'm at like 30% certainty I'm gonna get this right, then it's a good opportunity to talk about how to make that decision well. Because again, if you let go of the problems that are hard for you, that hurts your score less than rushing through the questions that are easy for you and getting those wrong. Okay, so you can really undercut your score, shoot yourself in the foot if you are rushing through questions you know how to do. So instead, we do the opposite. We let go of the questions we don't know how to do, we invest more in the questions we do know how to do. Okay, so let's talk through all that. So again, some of you might be super insightful here. You might be able to just see through this question with very little effort, but in my experience, that's super rare on this problem, specifically this type of problem. So even at my level, this this is not a question where I would have any immediate insight into the question. I would look at it and be like, I'm not sure. I got to try a couple things and see what happens. Um, and I'd I'd at some point personally, just so you know, have to do a lot of computing in order to get to 100% certainty. So it's it's not like just because I got a 99th percentile score that I somehow like have this X-ray vision into this specific question. And that's why I think it's a good one to talk through. Because if you have a lot of experience like I do, I mean, seeing just like, I don't know, millions of GMAC questions at this point, uh, and just like an uncountable number of people dealing with them. Um like you you I tend to remember the the insights, the tricks, the shortcuts. Like when I'm working with people, that's like technically my job is to help them see that stuff. But it's good to know that even at my level where I've seen like almost every trick and trap that could possibly happen, there's still a time and a place where it's like, okay, we got to just sit here and do a lot of computation. So it's it's good to know that those questions are out there so that you're not like doubting yourself too much if that's the approach you take during the exam. Um, I've just found people can kind of get in their heads there, even though they knew how to do the math. And it's like, dude, if you just like sat there and did the math, you would have got it right. But instead you are looping on like, why am I not seeing the trick? Why am I not seeing the shortcut? I mean, if you see the shortcut, use it. Great. But if you don't, just get the problem right. Just do what you have to do to get it right. That's all the test care of is about at the end of the day. There's no style points on this thing. It's that you either got the question or you didn't. That's it. Uh so let's talk through how that might look, give you a little bit of peace of mind, and just try to make it as easy as it can possibly be. Um, while at the same time, again, just making the important point that it's okay to do a lot of math every once in a while. So the first move that's worth discussing and very likely to be helpful is consolidating the two squared and the five squared in that denominator, that complicated denominator. And we can do that because we can multiply things in any order. Again, math basics episode there for you if you need it. So two to the second times five to the second times four to the second times three to the second, that's exactly the same thing as two to the second times three to the second times four to the second times five to the second. I've just put the two squared and the five squared next to each other because if you do the math there, you would get two squared is four, five squared is twenty-five, four times twenty five is a hundred. And you can just separate that one over a hundred from the rest of the fraction. And the good news there is dividing numbers by 10 or 100 or 1,000, any power of 10, it just moves the decimal place around without adding any new non-zero digits. So there's a lot of deep, deeper theory behind that move in this question. But if you've been studying for a while, like you might be able to wrap your mind around that of like how that theoretically could be good. It might not be a natural move yet, but that could be a good takeaway for you on this question. Because maybe you want to be able to make that move in the future. So you could put this one aside, resolve it again over the next couple days at the beginning of your study sessions as a warm-up, and that move will start to become more natural. So we basically just ignore that part of the fraction for the moment because that's not going to add any non-zero digits. It's just going to be moving the decimal point around, and that's that's great news because things are complex enough as they are. Um, and so that that would then leave us with just having to deal with one over three squared times four squared. And that's that's a lot simpler. It's not the greatest news ever, but it's a lot less complex than where we began. So at that point, I'd be thinking, like, is there a shortcut? Is there a shortcut? And I'd really be coming up with like, no, I don't see a shortcut. And so I'd probably just multiply out three squared is nine, four squared is 16. I'd just multiply those together to get one over 144. That's that's honestly what I would do. I'd just be like, that's all I got, so that's what I'm doing. So I'd I'd wind up with re-expressing the problem as one over 100 times one over 144. And I know the one over 100 is uh gonna affect the ultimate value, but it's not gonna affect the answer to the question because it's not gonna add any non-zero digits. And so from here, I'm just gonna do long division of of one by 144, and we'll get to that in a second. But um, you know, it's worth mentioning you could split it up as one over nine with long division and then one over sixteen with long division, and that will make the long division part easier. And then you could multiply those decimals, but I've found for most folks it just makes things worse. I'm not a hundred percent sure why that is. Having said that, if you're really curious, you're welcome to give it a shot. But I've found people just they just kind of freeze for some reason when it comes to multiplying uh the decimals at the end. Um, so it's kind of like a false economy there. Like it seems like it's gonna be a shortcut and it's just uh it's just just kind of kicks you in the shins when you need at least, you know. So um I'd probably just do the one over 144 thing and just take the pain. And so this is where your decimal division and computation skills can get challenged. And that's part of the reason I let off with that. And the first question is it's it's helpful to know that stuff. Now, could you do this problem as all fractions and uh get all the way to the result? Probably not. Probably not, because it forces you to express it as a decimal at a certain point. And so if you're that person who's like, dude, just tell me what to do, don't make me think about this, then yeah, I'm gonna tell you do all your decimal computation as fractions, and you're just gonna live with missing this problem. You're just gonna give it away quickly, you're gonna be like, cool, I don't know how to do this one. That makes that decision easy. That buys you time to invest in questions you do know how to do. And I know that might sound super risky, uh, but the GMAT's engineered, so you're gonna miss a lot of questions. They just keep giving you harder and harder questions until you miss a lot of them. And so if you can accept, okay, I'm gonna miss some questions, then you can move on with the whole like perfectionism thing. You can just be like, okay, I'm gonna miss some questions. Let me miss some questions fast. Let me just find some questions I know I'm gonna get wrong anyway, and just miss them fast and then reallocate those resources. It's kind of like if you try to win every single game you play, you try to make every product you launch uh the ultimate success, you try to make every person you hire the ultimate success. Yes, you should put that energy into every project. But if you can't accept, like, hey, we were wrong about this product or we were wrong about this hire and you just never let those projects go, you can totally bankrupt your company. And that's that's a difficult decision to make. It's a difficult decision as a leader to be like, hey, this product didn't work, we were wrong. Market shifted, people didn't want it as much as we thought we did, or just, you know, environment shifted, it's not profitable anymore. We're losing money on this product. Uh, whatever. There's a lot of really, really difficult, hard decisions. But the absolute right thing is to be like, okay, we need to focus our energy elsewhere. And that's just hard to do. It's hard for people to let go of stuff in general. And that's that's why you get paid the big bucks to make those decisions in companies. Um, a lot of people aren't cut out for it, but you are, and that's that's why I want to support you doing this because your work in that regard is extremely, extremely important. We need people like you who are willing to endure that stuff, maybe even excited for it, you know. It's a really unique type of type of human. Um, so uh not not that not that like killing off products is is your number one job. It's just an example of a difficult decision. Obviously, the creative stuff, the growth stuff, the bringing products to market that are gonna make everybody's life better. That's the really, really key stuff. But in order to get to that next product that is gonna change the world and make it amazing, sometimes you have to make the difficult decision of not focusing on a certain product, and that's really, really hard. And that's I'm just using that as an analogy for it can be hard to let go of a question like, what do you mean you want me to not get the question right or not even try to get the question right? It's like if you spread your resources too thin, then you're gonna run out of resources and you won't have enough resources to do the projects that actually matter and move the business forward. And it's the same thing with your GMAT score. So again, go back to that last episode of Score Plateau. I'll go a little deeper on that philosophy, and then check out the video on the website if you if you're like, wait, technically, how does that work? How does the math work behind the scenes? How does my score get calculated exactly? And that'll clear up a lot of confusion from um yeah, just a lot of incorrect information on the internet that gets reposted all the time. I don't know what these people are thinking. I think they just don't even know how to take the GMAT and somehow they thought it was a good idea to start a GMAT business. I mean, I'm not understanding the logic there, but hey, you know, it's free country here. Um but I listened to those people when I was in your shoes and it just it just destroyed my results, guys. It it was thousands of questions for eight months. My score went down by 20 points. I mean, yeah, I just needed someone to tell me the truth. And it was just crazy to me how hard it was to find. So ergo. Here we are. Okay. Okay, so um again, decimal division computation skills. It's okay if you're feeling a little challenged on this question. Part of growing during your study time is challenging yourself, maybe even being wrong here or there. Um and for most of us, being wrong feels super bad. We don't want you to be wrong, but um, as long as you can learn from your mistakes and improve them over time, then being wrong can be an asset for your growth. So let's try to see it that way if you're feeling a little uh challenged by this question. So let's set up some long division here. Um if you have a hard time following my steps here, um you you will want to check out the decimal long division episode, which again should be linked for you below. We've done some decimal addition and multiplications today, but not division yet. So check that out for a primer if you're like, whoa, what's happening right here? Because I'm gonna gloss over a lot of the details and just kind of go through it so we can get to the main point. So I'm gonna set up 144 to the left of my division bars, and then to the right of my long division bar, I'm gonna put 1.0. And of course, 144 does not go into 10. And so I'm going to add another zero to be 1.00. 144 doesn't go into 100 either. And so I'm gonna wind up setting up 144 on the left of the division bar and 1.000 on the right. And then I'm I'm pretending I'm dividing 1000 by 144 and I'm just moving the decimal place up into the result area. Again, you can see this on the video feed if you want. Uh now, like I was hinting at earlier, if you're on the test and at this point you're realizing you're out of your depth, like, whoa, I don't, I don't even know how to begin figuring out if 144 goes into a thousand, or like, what's this decimal long division thing this guy's talking about? This this could be a harder question to guess on in order to make time for the ones you're more confident in. And you just want to pay attention to that feeling of like, if if you're ever telling yourself, like, wait, I should know how to do this, what you're really saying to yourself is I do not know how to do this. It's a difficult, difficult moment. I don't want to like make it sound too easy. But again, since being wrong on this question wouldn't hurt your score very much, whereas missing one of the previous two questions would hurt, hopefully it helps you start to build that mindset of like, okay, it's okay to let go of the ones I don't have traction on. And then hopefully the next one I am gonna know how to do, and it's okay. That's okay. It's part of the deal of like, okay, we made a bad hire. What's the worst thing we could do is just never ever uh give them a severance passage package and say, like, hey, you know, this is this has been great, but it's just not a fit. I'm really sorry. We tried everything we possibly could. You tried everything we possibly could. There's no hard feelings, we'll support you. If you want to start your own business down the line, we'll fund you. If you want us to introduce you to your contacts, we'll introduce you. Like, I mean, you you obviously want to do it gracefully, as gracefully as you possibly can. But like just staying in a bad relationship, I mean, we've all seen what that does. And and that's essentially what you're doing when you're keeping someone on the team who shouldn't be there and who doesn't want to be there, you know? And it's hard. It's hard. A lot of people don't want to deal with the the difficult stuff of letting go of things. But again, it's it's um if you want to, if you want to have a great business, you might make mistakes and you might have to deal with those mistakes. Hopefully you won't. Hopefully you'll be perfect and you'll never make mistakes and you'll be way better than I am at all this stuff. I really hope that. That's definitely my intention. But if we're being real, that will be hard to do, man. That will be hard to do. Sometimes you gotta clean up the mess and re-vector your resources. And that's what happens on some of these GMAP problems. Just see it as an opportunity to be like, okay, this question and I, we're just not a fit. We are just not a fit. The worst thing we can do is hang on to this relationship, this bad relationship that we're in with this question during this test where I have limited resources. Let me just see other questions. Let's just see other questions, Mr. Question. Okay, so how do we figure out how many times 144 goes into a thousand? So a little bit of benchmarking can help here. I'll talk through what I mean by benchmarking. So um I want to pick an easy multiple of 144. That might be somewhere close to a thousand. And then I'm gonna work my way up or down from there. So, for example, I'd probably think 10 times 144 is 1440. That's obviously way too big, but I'm at least in the ballpark and I can use it to kind of start my estimate. For example, if I cut that in half, which would be 144 times five, I can see that one uh 1440 divided by two is 720. That's not too hard for me to see. And with a little bit of practice, you'll get there as well. Um, and so 720 is too low, but 1440 is too high. So I know that 144 goes into 1000 somewhere between five and 10 times by just benchmarking that. And that's not amazing, but it's better than where I started. So from there, I could add 144 to 720 to get 864. I can just use some long addition or just do it in my head if I'm capable of that. And that's that's gonna represent 144 times six. So I'm just interchanging between addition and multiplication there to kind of like benchmark my way toward like. Okay, how do I get close? And then I can see that 860 plus 140, that's going to equal 1,000 exactly. And so 864 plus 144 will definitely be larger than 1,000. And so 864 is as close as I'm going to possibly get. And so that lets me know 144 goes in six times to a thousand. And so I can put a six in the result area above my division bar. So not the most fun I've ever had in my life doing all this computation here, but at least I have some traction. And so I'd be comfortable continuing to invest in the problem. Like I'm not sure it's going to pay off, but I'm not, I'm not like, whoa, I'm totally lost. I got to get out of here. So if I'm here, I would probably think to myself, all right, um maybe I can get this connect to connect. Uh let me just do the best I can with the math. So I'm going to just um keep going with the uh with the long division here. So I figured out that 144 times six is 864. So I'm going to write that under 1,000 and then subtract. You can check out our decimal uh long subtraction episode linked below as well if if you need some more help there. And again, not gonna go too in depth with decimal subtraction here, but basically 1,000 minus 864 is gonna get me 136, 136. And then I'm gonna bring down the zero from 1.0000. Again, I can add as many zeros to the right of 1.0 as I want to, and that's gonna give me 1,360. Okay, again, I can use some benchmarking here to figure out how many times does 144 go into that. Um so again, 1440 is 144 times 10. That's pretty close to 1360. So let me just subtract 144 from 1440, and it looks like that gets me 1296. So that's great. That's great. So apparently 144 times nine is 1296, and that's less than 1360, and so it's gonna go in evenly. So my next non-zero digit in the result column is gonna be nine. Okay, so I'm gonna write that in there. And again, if you're having trouble following this on the audio feed, it's the principles I'm talking through of like how to benchmark, how to skip questions you don't know how to do, how to invest in questions that are going well. Those are the important points here. Um, and then yeah, if you want to dig into the specific decimal computation stuff, we've got the video there for you. Okay, so we know that nine times 144 is 1296. So let's write that under 1360 and subtract, and that's gonna get us 64. Then I'm gonna bring down another zero. And yes, this is kind of gnarly, but again, I'm making progress, and so I'm okay continuing to invest. And uh I can even check the answers and say, okay, it's definitely not A. It could be B. So let me just see if I can prove C. And if not, you know, maybe trying to get to seven or 10 decimal places with D and E, that's gonna take too long. So maybe I'll just get to C and see where I'm at and then guess. And that's still not too bad of a position to be in. I can still make my time kind of pay off there by getting a good strategic guess down. And at this point, I'd be honest with myself. I'd probably be pushing the time limit. I'm glossing over how long it would take me to do all this math by hand just to make these points. But uh yeah, just to make it more realistic, like I would probably be coming up against what I'd be comfortable investing in the problem at this point. And again, the algorithm expects me to miss some questions. So guessing on some questions I find hard is not that big a deal. Again, guessing on a hard question doesn't hurt my score that much. Um, missing an easy question that I knew how to do hurts a lot. So I should be comfortable just being like, ah, this wasn't a fit, no big deal. Um, but it might take some time to get comfortable with that. And again, we got that video for you on the site to help give you the technical aspect to like think through that a little more logically in case this is tough. I know it can be a big ask to change your mindset on this stuff. Okay, so now I've got 640. Earlier I figured out that 144 times five is 720, so that's a helpful benchmark. Um I could think about more benchmarking, like 640 is is less than 100 units below 720. So definitely 720 minus 144 is is gonna go into 640. So I'll just use 144 times 4 instead of 144 times 5. And uh I'll do that math real quick. Um we'll just do some long long uh multiple uh long multiplication there. Yeah, 144 times four, and that um that gets us 576. Or you could do it sub subtracting 720 by 144 if you're more comfortable with that. That would also get you 576. Uh so I'll go ahead and write a four in my result column. And now I've proven that it's for sure not A and not B, because I've got three non-zero digits in my decimal result. I've got six, nine, and four. And I'm in a good position to guess if I needed to. But if I keep going, I do get a lucky break at this moment because six forty minus five seventy-six is sixty-four again. And you can see if you have enough experience with long division that you're gonna bring down another zero and have to divide into six forty again. And then you're gonna get five, seven, six, you're gonna subtract, get sixty four, and then you're gonna bring down a zero, and you're gonna get into this loop where you're just getting four, four, four, four, four, four, four, four, four forever for the rest of the decimal. And so that could get you to that 100% level of certainty where you're comfortable picking C. So again, kind of a painful problem to go through, certainly to talk through, but a helpful point on a lot of fronts. Number one, how to know if you should let go of problems. I give you some tools there. Number two, how to sidestep the pure computation and use benchmarking to speed up heavy-duty computation a little bit. And number three, the time and the place to just brute force a question with computation, as long as you're getting traction and as long as you're getting closer to the answer, you can go up to whatever time limit you set. I think for most people, it's around three minutes would be the absolute maximum that I'd be comfortable spending, unless you have extended time, in which case it'd be about four and a half minutes with 50% extended time. And at that point, it's just not worth it anymore. If you if you're dropping four minutes on a question, even if you get it right, that's one point for the price of two. That gamble just usually does not pay off. So I think three minutes is a good upper limit for everybody. And then yeah, you need to average around two minutes, but that that doesn't mean you have to spend two minutes on every question. Sometimes you might spend one, sometimes you might spend three. So, a lot of points there. Once again, I just recommend pausing and making any notes to self. If there's anything you feel like would be important for you to remember for the future there, if you want to put that problem aside and come back to it once a day for the next few days, get a little bit more comfortable with it. Highly recommended. If you're like, there's no way I'm ever getting that question, and I just want to get a 615 and get into, you know, graduate school of my choice or a 595, you definitely don't need to get a question that hard right. But if you're going for a 705, like 99th percentile score, and you want to get a scholarship to a top school, then you might have to put in a little more time up front. Okay. Once uh well, I guess I didn't mention this yet. If you do have questions about anything that we presented here, you can always reach us anytime at the GMAT Strategy on current social channels. You can DM, or you can email us. Our email address is contact C O N T A C T at the GMAT Strategy.com. As always, my greatest hope is that this material will make your studies as easy and as painless as they can possibly be. If you'd like more tips and strategies for optimizing your performance on the exam, just head to our website, thegmatstrategy.com, which is linked below, and check out our free video on how you can reach your dream G Mat score in half the normal times. Totally free, no obligation for the video. It's just there for you to learn and improve and get results faster. In the meantime, this is a regular show. So if you like it, please subscribe and please, no matter what, stay positive and stay consistent with your studies, everybody. You can do it. Talk to you soon.