Real GMAT® Problems - Ep. 29 - Algebraic Reasoning, Prime Factors, and More

What This Episode Covers

Three problems from the 11th edition of the Official Guide for GMAT® Review, each chosen because a surprisingly high percentage of test takers miss them. None of the three requires advanced math. The traps are about process: setting up a percent increase correctly, reading "other cars" vs "all cars," and understanding what "in terms of" actually means.

All three problems can be solved multiple ways, and Isaac walks through algebraic approaches, plugging in numbers, and logical reasoning for each one. The thread connecting them is that knowing the content is necessary but not sufficient. The questions are designed to exploit common process errors, and 30% of test takers fall into the trap on each one.

Problems Covered

Inequality with P and Q — If P/Q is less than 1 and both are positive integers, which expression must be greater than 1? A warm-up that rewards recognizing when answer choices are recombinations of the same variables. Three valid approaches (algebra, plugging in numbers, logical reasoning) all converge on the same answer. Read the worked solution →
Lunch price with gratuity — 15 people, $207 total including 15% gratuity. What's the average price per person excluding gratuity? The trap: 21% of test takers subtract 15% from $207 instead of setting up the percent increase equation correctly. The core lesson is that increasing a number by 15% and decreasing the result by 15% are not inverse operations. Read the worked solution →
Car dealer sales report — One third of cars sold were sedans, one fifth of the other cars were station wagons, N station wagons sold. How many sedans in terms of N? The trap: 20% of test takers read "other cars" as "all cars." The core lesson is understanding what "in terms of" means and using substitution to eliminate the variable you don't want. Read the worked solution →

Key Takeaways

Recognize when answer choices are recombinations of the same variables. If the problem gives you P and Q, and every answer choice is a different arrangement of P and Q, algebraic manipulation will likely get you there. Multiply or divide both sides to isolate what you're solving for.

Increasing by X% and decreasing by X% are not inverse operations. If a $100 item costs $110 after 10% tax, removing 10% from $110 gives you $99, not $100. The percentage applies to a larger base after the increase. To find the original, set up: (1 + rate) × original = final, then solve for original.

"In terms of N" means use only N in your answer. When a question asks you to express something in terms of N, you need to eliminate every other variable from your equation. That means substitution: isolate the variable you want to eliminate, then replace it in the equation for the thing you're solving for.

"Other cars" is not the same as "all cars." When a problem says one third of cars are sedans and one fifth of the other cars are station wagons, the station wagons are one fifth of the remaining two thirds, not one fifth of the total. Read carefully and double-check your transcription.

Prime factoring rescues you when fraction arithmetic gets ugly. When you're staring at 207/1 × 100/115 and can't see what cancels, prime factor each number. 207 = 9 × 23, 100 = 2² × 5², 115 = 5 × 23. The 23s cancel, the 5s partially cancel, and you're left with clean integers.

Plugging in numbers is a backup, not a crutch. It works best when variables appear in the answer choices or when a question uses "must be" language. Pick simple numbers that satisfy the constraints (2 is almost always a good start), test each answer, and if more than one works, pick new numbers and narrow it down.

Double-check your transcription. Reading the problem wrong and doing correct math on wrong information is the most preventable mistake on the GMAT®. After you write down what the problem says, look back at the screen and verify. This one habit saves 1-2 questions per exam.

Episodes Referenced

Transcript

Read the full transcript

Welcome to the GMAT Strategy Podcast. You're here because you believe there's a better way to study for the GMAT and so do we.

We created the GMAT Strategy to maximize your results and minimize your efforts so you can get to the fun parts about business score and life as quickly as possible.

My name is Isaac Pullia and I've been teaching GMAT classes and tutoring privately for the GMAT for almost a decade and I've achieved a 99% tell score on the GMAT and helped thousands of students get into the business schools of their choice.

I'm excited to be a part of your MBA journey since we all at TGS think our world can benefit from the best possible business leaders that we can find.

If this show is bringing new value, please share it with your friends and family who are studying so that together we can make this process as easy and as painless as it can possibly be.

Let's go!

Welcome to Real GMAT Problems episode 29.

Doing Real GMAT Problems is one of the best ways to make sure that test day is as easy as it can possibly be for you so let's talk through a few examples together.

The problems that we're going to go through are from the 11th edition of the official guide for GMAT Review and you're welcome to web search them if you would like to follow along visually.

Just so you know, the 11th edition of the official guide is out of print and that's partly why I'm going to go through questions from that book because that way if you purchase this year's official guide which is a good general recommendation there shouldn't be any overlap between the questions that we're going to work through here together.

The official guide contains retired problems that have appeared on past GMAT exams so these are going to be really really similar to what you're going to see on your official GMAT.

I'm going to give you a chance to work through the solution on your own if you'd like and then I'll discuss my thoughts on the problem and what I recommend that you take away from each one.

I would recommend pausing after I read through each problem and at least trying to solve it.

If you're on the go you might have to visualize a solution like if you're biking or running or at the gym or something like that and so you might not be able to execute every single step in your head in that case but just do your best it's a great mental work out.

If you are in a situation where you can physically write down what you would on test day that's definitely ideal.

Let's go.

I'm going to start us with a warm up problem today and then we'll jump into some stuff that's clearly a little bit more challenging for people.

We're going to start a little bit lower on the end of the difficulty spectrum and if you're just starting out this might be hard.

If you've been studying for a while hopefully this is going to be pretty smooth sailing and then of course a lot of us are going to be between those two extremes.

This is problem number 125.

The problem says if p divided by q that fraction if p divided by q is less than one and p and q are positive integers which of the following must be greater than one.

Option a is the square root of p divided by q.

So to be clear it's p over q that fraction and in the square root of that entire fraction.

Option b is p divided by q squared.

So to be clear it's p over q that fraction and in the square root of that entire fraction.

Option b is p divided by q squared.

Option c is p divided by two times q.

Option d is q divided by p squared and option e is q divided by p.

Again I recommend pausing and at least attempting to visualize your own solution path here.

This is a good warm up problem because there are a few pitfalls but there are also quite a few different approaches that can yield a good result.

So it's a good little stretch I guess and kind of like mind potential mind expander in the sense that like your default approach might be great or you might want to consider one of these alternate approaches that I'm going to discuss.

It's also good warm up problem because I think if you're solid on your basics you're very likely to get it right.

If you did miss it that's totally fine it's better to be wrong in practice than during performance and this is a good opportunity to sharpen your basic skills and get to the next level which of course is the whole point of studying and why we're here right now is to improve not necessarily to get everything right in practice although obviously it's it's great if you get everything right in practice I just don't know how realistic that is I certainly didn't.

And most of the time it was the questions I got wrong that I learned the most of and that I from excuse me and I ended up profiting from the most on on test day.

So let's jump in let's talk through an algebraic approach first since there's a few valuable points to make on the algebra side.

The first point is that all the same rules of equations apply to any qualities p divided by q is less than one that's called an inequality if you're just starting out or you're not familiar with that terminology we've got an entire math basics series linked in the description of this content to help you out with that and just reskill or upscale if you know it might have been a couple decades since you thought about the difference between an inequality and an equation and it happens.

It's probably important to note that there is one major difference when operating on any qualities that we don't have to think about when we're operating on equations which is that if you multiply or divide both sides of an inequality by a negative value you'll want to invert the sign so the greater than symbol becomes the less than symbol when you're multiplying and dividing by negatives and the less than symbol would become the greater than symbol so think about a simple example like five is less than six I think all of us would agree on that.

If I multiply both sides of that by negative one I would get negative five is less than negative six that would that's what would happen if I would if I didn't invert the inequality sign and if you think about it negative five is not less than negative six it's actually bigger so that's a good example of why you want to invert that sign when you multiply or divide both sides by a negative if I have five is less than six and I multiply both sides by negative one I should flip the inequality sign to get negative five is greater than negative six.

So most of you probably aware of that especially if you've been studying for a while but if not super super important what's interesting though on this problem is we don't actually need to worry about that because we're dealing with only positive numbers the problem tells us this directly it says P and Q are positive integers obviously one is a positive integer and if you're not familiar with that whole integer terminology that's also covered in the math basic series.

So in an algebraic approach to this question we are just going to use what I like to call the golden rule of algebra which is whatever you do to one side of the equation you do that exact same thing to the other side of the equation and that applies equally well to any qualities whatever I do to one side of the inequality I do that same thing to the other side.

So let's multiply both sides of our inequality here by Q that gets us P is less than Q then less divide both sides of the equation by P and that gets us one is less than Q divided by P and that's our correct answer which is option E as an echo so obviously it's a great approach let's talk about how you can recognize that that's going to work well because I don't know that that would necessarily be intuitive for most of us.

So we'll talk through a couple clues the first clue is that the problem presents you with something less than one but then it asks you for something that's greater than one so in situations like that it's really really likely that you'll be able to manipulate the expression to solve for what you want.

So if you're given something less than one you're asked for something greater than one or there's like a lot of similarity between what you're given and what you're asked highly likely you'll be able to use some algebraic manipulation to solve for what you want so that clue by itself could tip you off to be like let me just if I can multiply and divide here and then there's your answer.

The second clue that you can use is glancing at the answer choices which you might recognize are all recombinations of P and Q in a in a bunch of different ways so if you're presented with an expression involving P and Q and the answer options are all different variations of that expression like we have here that can be also a good signal that algebra is going to be a good approach to use.

Let's pretend you recognize it's a good situation for algebra and you execute well highly likely to get this one correct and probably fairly quickly at that.

But again if you didn't recognize that that's no problem like I said you're here to improve and hopefully you'll be able to recognize that type of situation in the future as a result of engaging with this material right now and that's the whole reason we want to do real GMAT problems together.

Now I mentioned that there are some other approaches that can work just going to briefly touch on those one technique we've spoken about in past episodes quite a bit is plugging in numbers and not approach generally works when you see variables in the answer options like we've got here.

I'm not going to go through the full solution on that just for the sake of brevity but quickly talking through it we need to just pick numbers for P and pick a number for Q as well and we just need to make sure that the value for P is less than the value for Q and that they're both positive integers basically we just need to obey the constraints of the problem and then that way we're obeying the rule that P over Q is less than one if I pick a P that's a hundred and Q is two a hundred over a two is not going to be less than one so I'm not allowed to do to do that the problem.

Tells me quite clearly P over Q has to be less than one so as long as I stick within those constraints I can pick any numbers that fit them and the techniques should work now from there all we have to do is plug our values into all five answers and see which one is greater than one because that's what the questions asking for asking is for which the following is going to be greater than one.

Depending on the values we picked we should get to option E fairly quickly again not going to go through the whole song and dance there you're welcome to try it out on your own if you're curious about it.

But it's worth noting that we're not really supposed to be able to plug in numbers on GMAT questions like the questions aren't designed to do that it's it's just a really helpful technique that that just happens to work in those situations.

So the reason I bring that up is sometimes you can get more than one answer that works and if that happens it's not that big of a deal just choose new numbers that fit the problem repeat the process and generally you're going to narrow it down to one option at that point but if you stay away from plugging in numbers like zero and one.

Like basically if you never plug into on one when you're using that plugging in numbers technique you'll avoid that pitfall I would say 99% of the time really really useful technique we've got a whole episode of fleshing out that technique of plugging in numbers if you're curious to learn more will link that for the for you in the description of this content as well it's very worth checking out if you're not familiar with it already.

Finally you can use some logical reasoning to get this question right for example if you know that P has to be less than Q in order for P over Q to be less than one.

Then you also know that Q over P is going to be greater than one so let's just reason through that together so think about an example like five over six if P is five Q is six five over six is less than one if I flip that six over five has to be larger than one.

So think about an example like 10 over 11 10 over 11 has to be less than one 11 over 10 would have to be bigger than one.

Again in order for the original fraction to be less than one the inverted fraction would have to be greater than one.

And I would say the majority of GMAT test takers are probably not automatically going to think of that and go to that kind of approach but some folks do and just want to mention that it is a totally viable approach if that resonates with you now.

It's not the natural place for you to go but it is appealing and you're like I would like to be able to think about problems like that.

I just want you to be really cautious with that kind of reasoning until you've practiced enough to have a lot of success with it because it can backfire quite easily it can sometimes lead to mistakes I think actually in the last couple episodes of this series I talked through a few examples of how that kind of algebraic reasoning can be dangerous.

And so it's definitely something you want to use with caution when it works it works so well that it's easy to sell ourselves on it like I want to do it that way all the time and that that sounds great.

In theory but in practice as you might have noticed from doing some of the more challenging questions that we've done in this series together and like some of the ones we're going to do later most of the time the slower way is the safer way and for a lot of us frankly the better way.

Now it's not that we want to prioritize loneliness or that we want to deprioritize speed is just we want to use fast approaches when we're not going to be fast and wrong and that sounds just so painfully obvious I know I've said it so many times if you've been a long time listener.

But it really does bear repeating because speed is just really seductive and it's easy to sell our sell sorry it's easy to over sell ourselves on techniques that are just too dangerous it would be like it would be like winning the lottery is your retirement plan you know that's maybe a kind of an extreme example and it's like hey if it works probably works great.

But we just want to be realistic about our odds there so I did want to mention that and also give that caveat having said that if you look for opportunities to use that kind of algebraic reasoning even if it's not natural for you and you practice a lot with it and you start to figure out the kinds of situations where it works well for you and the kinds of situations where you should slow yourself down and use a more methodical step by step approach.

Then you're studying the right way for sure but I just want to caution you against being like oh I'm just going to use that 100% of the time very very few techniques work 100% of the time on the GMAT everybody and that's why I'm taking so much time here to talk to you about all of this because I don't want you to go down the path that I went down which was super painful and just like took three times longer than it needed to and just was obviously things worked out but I mean holy smokes it was just really tough.

So if you're already a really comfortable and well rehearsed with that reasoning approach by all means keep using it.

If there are any notes to solve that you want to make regarding this question I'd recommend pausing and making those now if you have any questions about anything we're discussing here today or really anything at all GMAT related feel free to get in touch with us anytime we're at the GMAT strategy on current social channels or you can email us at contact at the GMAT strategy.com

and we should be able to help you out we've been through this tens hundreds of thousands of times at this point probably and if you're having an issue we've probably dealt with it and solved it before and we're happy to share as much as we can over DM an email just for the good of everybody basically.

So let's tackle some questions that seem a bit more challenging for folks just based on the numbers again don't stress about being wrong on these just focus on improving and eventually you will get where you want to go.

This is problem number 123. The problem says the price of lunch for 15 people was $207 including a 15% gratuity for service.

What was the average price per person excluding the gratuity?

Let me read that again the price of lunch for 15 people was $207 including a 15% gratuity for service.

What was the average price per person excluding the gratuity?

Option A is 11.73 option B is 12 option C is 13.8 option D is 14 and option E is 15.87

Again I'd recommend pausing here and working on your own because I'm just going to jump right into my explanation.

Great word problem to polish your percent and word translation skills.

We've got 21% of us all going for the exact same incorrect answer that's likely based on a percent calculation mistake so we're going to dig into that.

It's a very avoidable mistake but also very common and apparently very tempting so let's try to fix that kind of mix up for for everyone and you might be surprised to know that 30% of us are missing this question overall and only 70% of us are getting it right.

Which I thought was really really surprising given the nature of the math and like how short the problem is.

But if you've been listening for a while I think you probably heard me say that a bunch of times and it's these are some of the most important problems for us to talk through because all of you have a lot of experience learning stuff and there's also a lot of really really great products free and paid out there to help you learn the stuff like learn the material like I got a re-learn the quadratic formula here or like oh yeah like.

Totally forgot how to do the surface area of a cube you know good good to be reminded of that and it does come up or exponent rules things like that.

But eventually if you practice enough you you will have all of those things down and I don't think most people struggle with that piece most people feel like they know all this material like I feel like I know all this stuff why am I missing questions now.

There can be a lot of answers to that.

But one of the answers is this more process oriented stuff and part of the reason I started this whole project many years ago at this point is I just realized.

A lot of people just aren't talking about that they're not teaching it.

A lot of professionals in the space I mean bless their hearts they're they're probably really good people and most of the people I've met in the space on balance are really good.

But they just don't even realize how much people are struggling with this because a lot of them are a lot of the people who work in the industry are so intelligent they're so smart they just never struggled with the exam themselves so it's really hard for them to imagine what it's like to know all the content and still miss lots and lots of questions and yet.

Then we come to data sets like the one we have on this one we're out of I think is like 5,000 rep repetitions on this 30% of us are still missing it and you're thinking about like future MBAs you know this is a pretty competitive group here this these are people who know how to work hard there intelligent.

This isn't like you know the this isn't like like the riff rap here so what does that suggest I mean I think if we just look at that situation overall it just suggests that a conversation about this probably should be had.

So hopefully we're filling that fill that gap for all of you.

Okay so again great one to miss in practice definitely not something we want to be missing on test day so let's jump into the trap here let's jump right into the trap because the first important place where it looks like a lot of us are missing this is the creativity part.

So the good news is that it looks like the large majority of us realize that we do need to remove the creativity and in the problem the way it's written in the book the word excluding from excluding the creativity is in all caps.

So so the test writers are trying to help us out with that thank you for that everybody who writes these tests but the problem seems to be the way people are taking the creativity out is incorrect so let's let's work on that together.

Quite a few of us appear to be taking 85% of 207 okay so we're thinking like oh 207 is 100% of the price there was a 15% creativity if I just remove 15% of 207 then that's that's going to get me back where I started and that's not true the correct approach is increasing an unknown amount by 15% and then setting that equal to 207.

That's really really important so let's dig into that a little bit more we've discussed that type of situation and that type of mistake a few times in this series it's extremely common and also really really understandable.

A lot of you are going to be brand new here potentially going to be brand new to the exam potentially going to have just be doing this problem in a distracted environment or you're tired like that's fine there's still value you can get of studying when you're distracted and tired.

But you just want to accept like the hit rates going to suffer there a little bit so even those of you who are veterans might benefit from this question though because it's just really really easy to slip back into old habits especially if you've been having success recently so you see a lot of post online about people getting a really good score and then the next score is really bad.

Sometimes that's the look of the draw but most of the time and I really hate to say this but I would want you to say it to me if our roles were reversed right now most of the time it's because you stopped doing the things that got you that good score in the first place.

It happens to the best of us it's a very natural part of the human condition things start going well we start to relax ease off the process a little bit we're not as hard on ourselves as we were when we were coming up the mountain as it were.

And it's a good it's a good lesson on a lot of really good good basic principles so just if you notice yourself getting complacent.

You want to start to build the skill set and it's okay if you're starting small and just working up from there and that's what I did if you start to notice yourself getting complacent you want to just start building up your discipline and your willpower we've got a whole episode on how to be more disciplined.

And we'll link that in the description of the content I didn't have that noted before so let me just make that note and then let me get back to the place in my notes where we were together.

Okay so that'll be linked for you below.

Let's talk about what's wrong with taking 85% of 207 think about a simpler example.

Let's say you're purchasing a hundred dollar item and you need to pay a 10% sales tax what's the total price including tax.

Hopefully you're thinking it's a hundred and ten dollars which is right but what if we're buying a hundred and ten dollar item that's on sale for 10% off.

Well 10% of 110 is 11 so if we discount by 11 dollars we get a final price of 99 dollars.

Notice that a 10% discount on a hundred and ten dollar item is not a hundred dollars.

What's the point there the point is that increasing a number by 10% is not the same as decreasing a larger number by 10%. Those are not the same things.

So if that happened to you on this problem or you've noticed that happened in the past you want to make like a bunch of flashcards on this.

You want to set this problem aside and redo it every single day until you can't forget it.

It's like you really want to re-condition yourself to think about percent differently if you are naturally thinking about them the incorrect way which again it's extremely common.

30% of us missing this question is hate keeps saying it's sorry if I sound like a broken record but it's just such a surprise.

So the reason that that percentage difference is there the reason that increasing a number by 10% is not the same as decreasing a larger number by 10% is because the increased number is bigger.

I know that might just sound like comically obvious but it's really really worth discussing and hammering home because it just seems really intuitive to do it the wrong way.

So the same percentage of a larger number is going to get you a larger result.

That can be a little confusing because it is the same percentage so some people feel like increasing 100 by 10% should be the same as decreasing the result by 10%.

But that's the whole point it's not the same.

And that's really important for problems like this one that we're working on right now because if I said an item's final price is $110 including a 10% sales tax we cannot just take 10% of 110 and get the right original price that way.

That's not going to work we have to increase an unknown amount by 10% and then set that equal to 110 and that's the key to problems like this.

So that equation would be something like 110 over 100 times P for whatever the price is equals 110 and then we can use algebra to solve for P and there's a math basics episode linked below on equations and algebra if you want some help re-skilling there.

In fact, we'll also link a math basics episodes on percents if that would be helpful.

That type of thinking is just critical and it's inescapably important because 207 is the price after the utility has been added and if you simply decrease that by 15% you're going to get an answer that's too small and that's why we've got so many of us 21% of us going for option A which unfortunately is not right.

The really painful thing about that is there's some pretty intense math and computation involved in getting to option A.

So a lot of people are executing after that blunder like perfectly and that's a super painful so that's why we're trying to get this turned around.

Naturally that brings us to how do we how do we set this one up the right way so we want to increase an unknown amount by 15% and then set that equal to 207.

So our equation is going to look something like 115 over 100 times P equals to 07 and then we can solve from there and everything's going to work out great as long as we don't make a mistake but that first step is absolutely pivotal for almost one third of us which is again I know I've said this in many times but like imagine 100 future MBAs like the brightest folks in your generation standing in a room and 30 of them go down the wrong path on this question that's way too much.

So there are some stumbling blocks with with the computation because it's not the easiest and there are some other incorrect answers that apparently do get picked to go to mount but that first mistake is yeah I mean that's just this is huge.

So if you find yourself struggling with that kind of setup then a good tip for that is the percent change formula can really help.

And if you're not familiar with that formula it's just new value minus old value that difference divided by the old value and then that whole fraction times 100 that'll equal percent change not going to go in depth on that right now because I've detailed it just to an absurd degree in past episodes and I feel like I already am so repetitive on on these pods but repetition is the father of learning and the mother of skill and so we do need it but I just trying to do the right amount of repetition and not not over do it.

But quickly the way that the percent change formula could work here is again new minus old over old times 100 so it would be 207 which is the new value minus P.

The old value divided by P times 100 and then that equals 15 that's the percent increase that we're looking for and if we execute the math there we're going to get the right answer so.

That will get you the same result without you having to struggle with the setup if you tend to struggle with setting up percent increase or decrease questions there's plenty more in the previous episodes in this series so definitely check those out if you want a little bit more practice with the percent change technique.

For now let's assume that we could all get to 115 over 100 times P equals 207 let's just say that we can get there from there we want to solve for P which is the original price before the gratuity and then that's going to allow us to answer the question.

So I'm just going to run through the math here like I always say you don't need to mimic the exact steps that I'm using here is just an example of how the computation could be done correctly but pretty much anyway that you want to compute things works as long as the setups right and that's why I've been.

Spending so much time talking about the setup here so let's divide both sides of our equation by 115 over 100 that's the same as multiplying by 100 over 115 from there we get P equals 207 over one I think I've said in the past I like to write my whole numbers as fractions over one when I'm doing fraction multiplication I find visually makes me a lot less error prone again not essential but helpful 207 over one times 100 over 115 from there we can start canceling 207 is probably.

A pretty unfamiliar number for most of us so let's start by reducing 100 over 115 first you might be able to tell that both of those numbers are divisible by five quick tip all integers that end in zero or five are divisible by five check out the math basics lesson on divisibility below if you're not sure what I mean by integer or if it's been a minute.

And don't fear doing some long division if if you need to figure out what happens when you divide both from by five there's also math basics episodes on long division like below if you need that.

If you execute properly there you would get 20 over 23 100 over 115 reduces down to 20 over 23 now at that point most of us are thinking that maybe this isn't going to go so well because I've got 207 over one times 20 over 23 and that's a little bit gnarly.

But that's okay a good tip there is because there's no calculator on the GMAT Quant section it's safe to assume that numbers will often work out as integers meaning like they'll divide or multiply evenly now you can't say that 100% of the time that goes back to what I was talking about at the top of the episodes few things work 100% of the time but there are a lot of bets that you can make that are going to be like 80 90% bets and this is one of them so it's a pretty safe bet to at least try doing long division of 207 by 23 like it's it's highly likely that that's going to work.

And that's a good move because if you do that you get 9 9 times 23 is 207 207 divided by 23 is 9 basically it works out cleanly there even though it's a little scary sometimes when you look at the numbers so we'll circle back in a moment to a technique you can use if you're struggling with that kind of thing because it's not always easy but for now let's say we just arrive there and our equation would then be 9 over one times 20 over one so we get that fraction canceling right so I'm just going to tie off the solution and then we'll double that.

Back on the extra technique so if we do the math correctly there we get the original price is 180 dollars before the gratuity which is correct and then we want to the average cost per person for 15 person groups we just need to divide 180 by 15 that gets us 12 and that is our correct answer which is option B as in beta.

Okay so that's what a correct solution path could look like again reach out any time if you have questions let's talk about what you can do if you struggle to simplify the fractions 207 over one times 100 over 115 a great move in those kinds of situations where you're unsure of what's divisible by what or you're not sure if you can cancel is to prime factor as many numbers as possible prime factoring is really really helpful we've discussed prime factoring before.

But as a brief refresher when you are prime factoring you just keep dividing by prime numbers until you can't divide by prime numbers anymore and if you need help with primes and understanding what those are.

We got a math basics I would like 40 below so let's start with prime factoring 100 because that ends in zero we know it's even which is another way of saying we know it's divisible by two so if we divide that by two we would get 50 lot of people like to make a little factor trees when they're prime factoring so they have 100 on the top then they have.

Two little like branches going down from 101 with two at the end one with 50 at the end and then 50 also end in zero so we can branch that one as well divide by two again to get 25 and then 25 we can branch again to get five times five and you just stop each branch at each prime number and then that that shows you the end of each branches what's called the complete prime factorization of the number if you multiplied all those primes together you would get back to the original number it's kind of like the DNA of an integer every integer has a unique.

Prime factorization side note but kind of interesting so if we if we do that tree chart and we get our prime factorization.

And we do that for all the numbers it just it makes it a little bit easier to see what's going to cancel where so like you'll have some twos in the top and bottom you'll have some fives in the top and bottom if you prime factor 115 you'll get 23 if you prime factor 207 you'll get the 23.

It's just like a nice bridge to figuring out what's divisible by what it's really really helpful on divisibility questions in general I wouldn't call this question a divisibility question it just happens to have some division involved in it.

But prime factoring is is really really helpful in those kinds of situations so I wasn't going to go deep on that but figure I'd mention it because I have talked with a lot of people who really struggle with that kind of stuff and I struggled with a lot actually because my divisibility instruction as a kid was was not the greatest.

And I had to re skill with that when studying for the GMAT myself back in the day and the prime factor thing really really really helped out.

Okay, so if we execute all that then we get to our answer and then we are good to go.

So you might not need the prime factor anything but again if you struggled I think it's a good tip so as usual I recommend pausing here and just making any notes to self that you want to remember from this question and then we'll finish off with with one more.

Alright feel free to pause I'm just going to jump forward this is problem number 124 it says according to a car dealers sales report.

One third of the cars sold during a certain period were sedans and one fifth of the other cars sold were station wagons.

If N meaning the letter N used as a variable if N station wagons were sold during that period how many sedans in terms of N were sold.

I'll read that again.

According to a car dealer sales report one third of the cars sold during a certain period were sedans and one fifth of the other cars sold were station wagons.

If N station wagons were sold during that period how many sedans in terms of N were sold.

Option A says 2 times N divided by 15.

Option B says 3 times N divided by 5.

Option C says 5 times N divided by 3.

Option D 5 times N divided by 2.

Option E 15 times N divided by 2.

Option D 5 times N divided by 3.

Alright feel free to pause and work more on this one.

Really interesting problem actually with a lot of potential strategies what I think is going to be the most beneficial to focus on here because we talked about quite a bit in this lesson and in past versions of this series is let's just focus on the phrase in terms of and make sure that we really clarify that for everybody because we've got 30% of us missing this question as well.

Again much higher than expected part of the reason I chose it for this lesson it seems like a decent number of those misses center around a genuine misunderstanding of the whole in terms of phrase.

And again it's just one of those things that comes up a lot when I'm talking to people in the community about what's holding them back or about struggles are having with questions and it's just one of those little things that seems to make big problems so let's fix that.

First of all the phrase in terms of means use a specific element or style to express something else that's like literally what it means.

It means use a specific element or style to express something else for example if I ask you to explain geometry to me in terms that a five year old would understand then what I'm asking you is to use only five year old language to explain geometry.

Explain or represent X in terms of why means use only why to explain X and we can replace whatever we want with X and Y.

Another example if I ask you to describe your job in terms that someone outside your industry would understand.

Then I'm asking you to explain your work without using industry jargon no acronyms all that stuff I'm asking you to describe it using every day language that someone who does not work in your industry would be able to comprehend.

So when a GMAT question ask you to express the value of something in terms of N it's asking you to use the variable N only only use N to describe the thing and another way of saying that is you'll want to solve for whatever's being asked with only N on the other side of the equals sign and that's what we're going to do in our solution in a minute okay that's what in terms of means.

You can see that reflected in the answer options you'll notice that N is the only variable that appears in the answers even though there are multiple variables in the question and that's going to be the case with all in terms of questions whatever comes after in terms of is going to be the only stuff in the answer options or the only variables I should say obviously there's other numbers in there but I think you understand what I'm saying.

So the reason for that is you're being asked to solve using only those terms that's what in terms of means.

So definitely reach out if you're unsure how to handle that or if you have additional questions but hopefully that at least helps with understanding that phrase I've come across it a lot again it's a big pain point for a lot of people very understandable especially if you didn't have strong math instruction as a kid or up until this point in your life but we're getting all that resolved today.

Like we've discussed so many times in this series a good approach to a problem like this is usually going to involve just writing what's given and asked really clearly and carefully that's true for virtually all GMAT questions but particularly word problems and word translations questions if you've been listening for a while hopefully I've already demonstrated the value of that.

So let's say that that we do that the question asks us to solve for sedans but in terms of and meaning using only the variable and on the other side of the equation when we solve for sedans so we're solving for sedans but we have to do it only in terms of and then the question tells us that one third of the total cars are sedans.

Yes, let's pretend we're writing all this it also tells us one fifth of the other cars sold our station wagons and that's that's really important one fifth of the other cars is different than just one fifth of the cars and now that we have that basically the land we can start to formulate our solution.

I think a good solution to a problem like this is probably going to start with a placeholder for the total number of cars sold since all the quantities we care about in the problem are fractions of that total.

There are a few different ways that we can approach that total including making up a number and using a variable like like a T to represent the total.

So both approaches have a lot of merit and they're worth exploring but just for the sake of simplicity and to really drive the point home about the whole in terms of thing I'm going to use a variable for the total and I'm going to solve with algebra but the whole like created number for the total thing super, super viable and worth exploring if you want.

So I'm just going to make a T equal the total and I'm going to write that down.

Always write what your variables represent I know I've said that a bunch in the past I'll probably say it again before this lessons over just super important small stuff like I was talking about earlier.

I can start by setting up an expression for sedans which would be one third times T equals D or some other variable to represent sedans I'll use D equals sedans T equals total cars.

Once we have that expression for sedans let's see if we can create an expression for the other given information the problem were also told again one fifth of the other cars are station wagons.

And if you if you miss that other piece by the way if you just do one fifth of the total is station wagons then you're going to get that get the wrong answer really really fast that's not good that's not good a large percentage of us about 20% of us are doing that.

So please read read carefully and I'll have a good tip for you for preventing that kind of thing in in a moment even if the reading piece is tough so the correct expression would be one fifth times two thirds times T.

So remember one third of the cars are sedans one fifth of the other cars so the other cars is two thirds of the total and then one fifth of that two thirds that station wagons.

Okay so really really important point to make there easy to miss and that's how that's how we get our correct expression there so I'm going to use W to represent station wagons so one fifth of two thirds of T equals W.

All right we are told at the end that N the variable N represents the number of station wagons sold so instead of W I'm just going to swap out N and we'll replace that.

So the question is asking us to solve for the number of sedans I chose the variable D for that and you might notice there's a wide variety of ways that I can solve for D that would include T that would include N or some combination of those variables and again we don't want that that's why the in terms of N phrases so important.

And once you do understand that it can actually help you be a much better strategist on this question because we've got three variables here D T and N we want to solve for D that's what the question is asking for but we only want N on the other side of the equation when we do that so that what that means is we want to make T disappear.

And if we can get an equation with D and N but without T we're going to be happy campers.

It's a key inflection point in the problem without that you can do a bunch of correct math and still not get the right answer that's a big bummer let's keep that from happening so I'm going to avoid a broad overview of substitution in general because that's why we made the math basics episode for you and it's down at the description of the content if you want it but to get the right answer we can use substitution to make T.

That's the beauty of substitution is it can eliminate certain variables so let's do that let's do that with our equation with N because we want an equation with just in N if we replace the T in one third T equals D was something that as N instead we will have accomplished our objective here so with our one fifth times two thirds times T equals N equation let's do the fraction math one fifth times two thirds that's two over 15 so we would have two over 15 times T equals N.

Let's isolate T and then we'll substitute in for T in the other expression that'll make T disappear so we're going to multiply both sides by 15 over two to get T equals 15 over two times N and then we're going to substitute that in for T in the other expression so instead of one third T equals D I'm going to have one third times in parentheses 15 over two times N equals D.

And that's also because now we've got our equation with just N and D and that's what we wanted so we'll solve for D here.

Fortunately that's already isolated so we just need to do the fraction math one over three times 15 over two gets us five over two and gets us five over two so we would have five over two and which is the same as option D as in delta that's our correct answer five times N divided by two.

Okay, hopefully you can see why clarifying the in terms of N piece is super super helpful there and how if you're confused about that piece the problem gets much much more difficult.

Real quick let's double back on the wrong answer and what happens if you're doing one fifth T equals station wagons again super understandable mistake it looks like people are just reading the problem as one third of the cars are sedans and one fifth of the cars are station wagons.

If you set up the problem like that it quickly leads to see as in Charlie which is the wrong answer so if that's what happened for you here a good little tip on that is always double check whatever you transcribe from a word problem really from any problem actually let's just say always double check what you transcribe from the problem so the problems going to be on the computer screen on test day but all your scratch work is going to happen on on the scrap paper or whiteboard whatever you're using.

And so transcription is really really key because if you copy down the wrong thing perhaps obviously you do a bunch of correct math and still get the question wrong so.

If you wrote down X Y and Z just do a quick reread of the problem text and make sure that what you wrote down is accurate that's all I mean by double check your transcriptions simple simple tip extremely powerful I use it all the time.

Pretty much any time I translate something on a GMAT problem I look back up the computer screen look back at what I wrote did I transcribe everything quickly usually saves me one to two questions per exam it's really really valuable so if you found yourself falling into that that's a good way to prevent that from happening.

It's a really innocent mistake so it's tempting to sweep it under the rug like when it happens and be like it's not a big deal I won't do that again but I'm just going to tell you like person person is a really big deal it's a huge huge deal for the vast majority of people like I was saying at the top of the call sorry top of the episode you know a lot of you are going to know the material really really well very soon and then those process oriented things can just they can just undercut you and it's so frustrating that's that's what happened to me for sure took me way too long.

It took me way too long to figure it out so hopefully doing you a solid here everybody if you think about it if you're not getting credit for what you know on the exam it's technically impossible for you to get a score that accurately reflects your skills and the effort that you've invested and your candidacy for these programs so again might be annoying to deal with these kinds of things I find it super annoying to double check my transcriptions 100% of the time but it's just so valuable that it's worth it it's worth transcending that annoyance and.

Just getting out of the 30% of us who are missing this question definitely no need for that.

One final time I'll just recommend pausing and make any note to self that you want to remember you can text yourself email yourself add something to a note make a flash card and feel free to pause while you do.

And we will be back very soon with more strategies more questions to go through more potential pitfalls to hopefully get you ahead of and keep you from falling into on test day.

In the meantime if you would like more help and more strategies and more tips for increasing your score on the GMAT then please head to our website the GMATStrategy.com which is linked in the description of this content and check out our free video on how you can reach your dream GMAT score and half the normal time I know that sounds crazy like a crazy bold claim but.

Even the simple simple simple advice that I talk through in the video and some of the case studies that I show you should really help you.

Not fall into the major pitfalls that I fell into some of the stuff that we talked about today I mean basically like we could we could almost say this entire.

Podcast is just a combination of many of the mistakes that I made in the process obviously it's a lot of what I've learned from helping out so many people at this point in the process.

But that that video is really a distillation of the main main key things that cost me the most time and caused the most frustration and like self doubt and like lack of belief in myself that I was going to be able to make it happen all that stuff.

So highly highly recommend checking that out in the meantime though this is a regular show so please subscribe and please stay positive and stay consistent with your studies no matter how difficult it gets it's totally worth it I promise you have so much to offer the business community in the world at large.

Business leadership in general is one of the most powerful influences on everybody's human life worldwide and so this really really matters what you're up to here and we myself and everyone at TGS behind the scenes really wants to support you as much as we can.

So please stay consistent and stay positive talk to you all soon.