Posted on
18
Aug 2021

## GMAT Prime Factors Problem – GMAT Quant

Hey guys, check out this problem. This is an example of a problem that requires daisy-chaining together or linking together several key algebraic insights in order to answer it. ###### GMAT Prime Factors Problem – Applied Math Solution Path

Notice there’s an applied math solution path. We want prime factors of 3⁸ - 2⁸, and it’s just reasonable enough that we can do the math here. And the GMAT will do this a lot, they’ll give us math that’s time-consuming, but not unreasonably time-consuming in order to just draw us into an applied math solution path. We’ll take a look at this really quickly.

3⁸ is the same as 9⁴.
3⁸ = 3²*⁴= (3²)= 9
9 = (9 * 9)² = 81²
81 * 81 = 6,561

9 * 9 is 81² – about 6,400 or if we want to get exact, which we do need to do here because we’re dealing with factors, 81 * 81 is 6,561. Don’t expect you to know that, it can be done in 20 seconds on a piece of paper or mentally. And then 2⁸, that one you should know, is 256. And then, 6,561 – 256 = 6,305.

So now we need to break down 6,305 into prime factors. You know how to do that using a factor tree, so I’m going to zoom us right into a better solution path because I don’t want to give away the answer.

###### GMAT Prime Factors Problem – Another Solution Path

Notice that 3⁸  and 2⁸ are both perfect squares so we have the opportunity to factor this into (3– 2) * (3 + 2). Once again, the first term is a difference of two squares, the second term we can’t do anything with. So we break down that term, and lo and behold, (3² – 2²) * (3² + 2²) * (3 + 2), and once again we can factor that first term out into (3 + 2), (3 – 2), and so on. We work these out mathematically, and they’re much easier and more accessible mathematically, and we get 3 – 2 = 1 which obviously is a factor of everything. 3 + 2 = 5, 3² + 2² = 9 + 4 = 13, and then 3 + 2⁴ = 81 + 16 = 97.

So now we’ve eliminated everything, except B and C, 65 and 35. This is where the other piece of knowledge comes in. Since we have factors of 5 and 13. 65 must also be a factor because it’s comprised of a 5 and a 13. 35 requires a 7. We don’t have a 7 anywhere, so the correct answer choice is C, 35.

###### GMAT Prime Factors Problem – Takeaways

So the big takeaways here are, that, when provided with some sort of algebraic expression like this, look for a factoring pattern. And, when it comes to prime factorization, remember, that if you break it down into the basic prime factor building blocks, anything that is a product of those building blocks also exists as a factor.

Hope this helped and good luck!

Found it helpful? Try your hand at this GMAT problem, GMAT Prime Factorization (Anatomy of a Problem).

Posted on
11
Aug 2021

## GMAT Markup Problem – GMAT Data Sufficiency

Hey guys, today we’re going to take a look at a typically characteristic data sufficiency problem that gives us a relationship, and then asks us if we have enough to compute the final value of that relationship. There’s an algebraic solution path here, where they give us the equation and we need to see if we have all but one of the variables, that final variable being the one that they’re asking for. We can also do this via parts, scenario, and graphically, and we’ll take a look at all those as well.

###### GMAT Markup Problem Introduction This problem describes to us the relationship between the selling price, the cost, and the markup. And notice that, while we’re going to sketch it out here, the actual relationship doesn’t matter to us – all that matters is that if they’re asking for one term in terms of the rest if we have the other terms, that’ll be enough.

Algebraically we have selling price S equals the cost C plus the markup M. So this is giving us the markup in, let’s say dollar terms, whereas we might also set this up as selling price equals cost times one plus the markup percentage. And here we just have that notational shift. So, what we’re looking for, if we want to know the markup relative to the selling price, is an understanding of it either relative to the selling price or relative to the cost. That is, these two things are associated and the markup, when associated with the cost, gives us a ratio. Where the markup, when associated with the selling price, is a fraction. And if you’ll remember notationally these things are expressed differently, but conceptually there’s the same math behind it.

###### Statement 1

Number one gives us in percentage terms the mark up compared to the cost. So, here we can see it as 25% more and this is where it ties into that second version of the algebraic one we just looked at. The cost we can break up into four parts of 25% so that when we add the markup that’s a fifth part. Therefore, the markup comprises one-fifth or 20% of the selling price.

###### Statement 2

Number two provides us a concrete selling price but doesn’t tell us anything about the markup or the mix of cost versus markup as a percentage of the total selling price. Two is insufficient on its own, and as we’ve seen in many other data sufficiency problems, what they’re trying to do here is fool us into thinking we need a specific price, a discrete value to get sufficiency. When the question stem is asking us only for a relative value and when we’re being asked for a relative value, a percentage, a fraction, a ratio be on the lookout for fooling yourself into thinking that you need an anchor point a specific discrete value.

I hope this helps. If you enjoyed this GMAT Markup Problem, try your hand at this Triangle DS Problem.

Posted on
19
May 2021

## GMAT Algebra Problem – Parts – Hotdogs & Donuts

#### GMAT Algebra Problem Introduction

Hi guys. Today I’m here with a classic GMAT Algebra problem, what we call a parts problem. And if you take a look at this problem you’re going to realize that it just looks like a bunch of algebra. But the key here is in how you frame it. We’ve got this diner or whatnot selling hot dogs and then after that point, so imagine like a timeline, they start selling donuts. Then they give us a piece of information about hot dogs to donuts over that course of secondary time but then give us this overarching total number of food products sold.

#### Distill The Ration

So what we need to do are two steps: the first one is fairly straightforward. We see that we have to get rid of the hot dogs that were sold in advance in order to distill the ratio but then the ratio can seem very, very complex, especially because it just tells us seven times and a lot of times the GMAT will do this as a way to throw us off the scent. So when we have seven times, what that means is we have eight parts. That is it’s saying for every one of these we have one, two, three, four, five, six, seven of these. Meaning in total there are eight. So while seven is kind of a scary number, eight is a number we can divide by easily. You always want to look for that when you’re given a ratio of one thing to another especially when they say something times as many.

#### Solving the GMAT Problem

We take that thirty thousand two hundred knock off the fifty four hundred and get to twenty four thousand eight hundred and lo and behold that’s divisible by eight meaning each part is going to be 3100. Notice there’s no complex division there, 24 divided by 8, 800 divided by 8 and that’s the sort of mental math we can expect from the GMAT always. Which as you’ve seen before: if you’re doing that you’re doing something wrong.

Each part is 3100 and we’re concerned with the seven parts so we can either scale that 3100 up by seven into 21700, again the math works out super smoothly or we can take the 24800 knock off 3100 and get to that 21700. Notice in the answer choices there’s a few things to address sort of common errors that might be made.

On one of the answer choices what you’re looking at is dividing the total, the 30 200 by eight and multiplying by seven that is seven eighths of it without getting rid of those first 5400. Another answer is close to our 21700 correct answer and this is also a fairly reliable signal from the GMAT.

When they give you a range of answers but two of them are kind of tightly clustered together a lot of times it’s going to be one of the two and that second one there is to prevent you from too roughly estimating. But at the same time if you’re short on time or just in general you want to hone down and understand what you’re supposed to do that serves as a really strong signal. And then one of the answer choices is the 1/8 of it rather than the 7/8.

I want to speak a little more deeply about that signal about those two tightly clustered answer choices because as I said it can help you narrow to a very quick 50/50 when you’re constrained for time or this problem is just one that’s really not up your alley but it also can be leveraged in a really, really neat way.

If we assume that one or the other is the answer choice we can differentiate these two different answer choices by what they’re divisible by and so notice the 21700 is very clearly, with strong mental math is divisible by seven. Where the other one is not. Also neither of them are divisible by eight. We can look at these two say okay one of them is probably right, one of them is divisible by seven, the other one is not, so there’s our right answer and we can move on to the next problem. So I hope this helps. Write your comments and questions below. Subscribe to our channel at Apex GMAT here and give us a call if we can ever help you.

To work on similar GMAT algebra problem/s see this link: Work Rate Problem.

Posted on
28
Apr 2021

## Advanced Work Rate GMAT Problem

#### Work Rate Problem Introduction &Challenges

Hi guys! Today we’re going to look at a super challenging work rate problem. This is one of those keystone problems, where if you have this problem really, really down then it indicates that you won’t have a problem with any work rate problem, speed-distance problem whatsoever.

The challenges in this problem are several. First off, you don’t have any base number to work with. That is, it’s all done in percentages and while a lot of times this can be an asset for running a scenario, here the scenario can really trip us up, as we’ll see. We also are being given different movements that are happening in different directions and it’s not entirely clear from the language in this problem that they are happening in different directions. Finally, there’s a notational issue that both the problem and the answer choices are in percentage and yet with work-rate, speed-distance, many times it’s best to work with fractions. So we have the option to notationally shift over to fractions and back. So let’s dive in.

#### Machine Efficiency (& Inverse)

On its surface, this is a textbook GMAT problem and what we’re being asked for is relatively straightforward. That is, there’s not a large interpretive part to understanding what we’re being asked for. The challenge here is how we’re going to get it. What would be the  best way to approach this, in my opinion, for most people is to break apart the two different changes that are happening in the problem: the machine efficiency and the length of the production process and understand what each of these two tweaks is doing to your overall problem. Let’s begin with the production time.

The length of the production is decreasing by 25. So the pivot question is how much time is this saving us? And you’re right, it’s on the surface, it’s 25%. But we want to take the inverse of this because we don’t care about the time that it’s saving us, even though the question’s asking that. Rather, what we need to do is figure out how much total time we’re taking at the start versus with these tweaks and see how that’s affected so we’re going to have to invert everything and instead of saying: okay I’m saving 25% of my time, it’s taking only 75% of the time. If we do this in fractions we’re saving 1/4 so it takes us 3/4’s as long to do the same thing. Let’s take that three quarters put it to the side for a second.

#### Machine Speed

The second part is a little more tricky! Our speed is increasing by 1/3 but that’s the inverse that is when we go faster the time we’re going to spend decreases. I’ll say that once more: the faster we’re going the less time we’re spending. So what does increasing our speed by a third do for us? Well instead of making 3 things, in the same amount of time we can make 4 things. We start out with a unit and we’re adding another third. Three parts, three, four parts.

So once again we are taking only 3/4s of the time to do the same thing due to the increased speed so we only have to spend 3/4s of the amount of time for the increased efficiency and only three quarters of the amount of time for the speed. We put those together multiplicatively and we find that it’s going to take us 9/16 of the time that we used to spend doing in order. The flip of that where we invert, is that we’re saving 7/16 of our time or a little under half. You’ll see from the answer choices that if you’re attuned, you’re limited to the 56.25% and/or 62.5%.

And if you’re familiar with your eighths being 50 and 62.5 as two of the of the eighths, then it’s got to be that 56 number. So there’s a bit of known numbers feeding into this but ultimately the challenge is doing these inversions and recognizing that these problems are built for fractions. Not just this one but just about every work-rate problem.

#### Deal With Work Rate Problems Fractionally

You want to deal with it fractionally because it’s these ratios of time, the numerator to the denominator that allow us to do things flexibly and to flip stuff around. 4/3s to 3/4s as we saw in this problem. Notice here that running a scenario, especially if you choose a generic number like: Okay well let’s say I make 100 widgets is going to get you into a ton of problems because it’s going to be extraordinarily complex from a calculation standpoint.

You can think about it in advance and choose really good numbers but in doing so you’ll have circumvented the solution path and logically push yourself into saying well wait this is going to be 16ths of something. So for just about everyone out there I would say put it into fractions think carefully and deeply about what each of these two switches does and then put it all together the way you would any other problem. Post your questions below. Subscribe to our channel! And come visit us anytime at www.apexgmat.com. I’ll look forward to seeing you guys again soon.

For another gmat work rate problem, try this Car Problem.

Posted on
23
Apr 2021

## Standard Deviation – Clustering (Birds) Problem

Hey guys! Today we’re going to take a look at a DS problem that is a skills problem, focused on GMAT standard deviation.

#### Standard Deviation & Variance

What they’re asking here is do we have enough information to compute a standard deviation? It’s useful to think of standard deviation as clustering. If we have a whole series of points we can define how clustered or un-clustered the group of points is. That’s all that’s standard deviation, that’s all that variance is. So if we have all the points that works. What we should be on the lookout here for are parametric measurements. Especially things like the average number is, because while the average can be used to compute standard deviation, we need to know how each of the points differs from the average. But if we have each of the points we always get the average. That is, we can compute the average. So the average is a nice looking piece of information that actually has little to no value here. So let’s jump into the introduced information.

#### Statement 1

Number 1 BOOM – tells us that the average number of eggs is 4 and that’s great except that it doesn’t tell us about the clustering. If we run some scenarios here we could have every nest have 4 eggs or we could have 5 nests have 0, 5 nests have 8, or 9 nests have 0, 1 nest has 40. These are all different clusterings and we could end up with anything in between those extremes as well. So number 1 is insufficient.

#### Statement 2

Number 2: tells us that each of the 10 bird’s nests has exactly 4 eggs. What does this mean? We have all 10 points. They happen to all be on the average, which means the standard deviation is 0. that is there’s no clustering whatsoever. But 2 gives us all the information we need so B – 2 alone is sufficient is the answer here.

Hope this was useful guys, check out the links below for a video about how to compute standard deviation as a refresher, as well as other problems related to this one. Thanks for watching we’ll see you again real soon

If you enjoyed this GMAT problem, try another one next: Normative Distribution

Posted on
10
Mar 2021

## GMAT Ratio Problem – Mr. Smiths Class

### GMAT Ratio DS Problem

#### Expressing Different Notations

Hey guys!

Expressing different notations is often challenging when you’re first starting out on the GMAT and by different notations mean percentages fractions decimals ratios. We learn all these separately and we tend to of them as separate systems of math when in fact they’re all different expressions of the same math. One half is no different from 0.5 is no different from 50 percent there are different ways of the same thing.

#### Breaking Down The Problem

In this problem all their testing is our ability to shift notations. We’re being asked what the ratio, keyword ratio, is between boys and girls in the or what do we need is just that a ratio it’s fairly straightforward. So they’re probably going to come to us with weird information that doesn’t quite look like a ratio. The big thing to note before we dive in is that when we’re being asked for a ratio. In fact, when we’re being asked for any sort of relative notation, fractions, percentages, anything that needs a base that is compared to a whole. We don’t need precise numbers.

#### Possible ways to solve this problem

So this leaves us open either to run scenarios if we want to or to deal entirely in the relative. So we’re looking for an expression of that ratio in a non-ratio sort of language. Number one tells us there are three times as many boys and girls. We can run a scenario with 3 boys, 1 girl, 75 boys, 25 girls, but we’re being given that ratio. It’s being expressed in language rather than with the term ratio or with the two dots : in between but it’s still a ratio. So it’s sufficient!

#### What Did You Miss?

Correction!! Number one states there are three times as many girls as there are boys. Why do we leave that error in? To point out that here it doesn’t matter. We’re not looking to determine whether the ratio is 1 boy to 3 girls or 3 girls to 1 boy or 3 boys to 1 girl. The only thing that matters, the threshold issue on this problem, is getting to a single specific ratio. What that is or in this case even reversing the boys and girls doesn’t matter because it’s a referendum on the type of information that we have. The moment we have a quantitative comparison of boys and girls coming from number one we know that number one is sufficient. Being able to have flexibility and even focus on the more abstract thing you’re looking for sometimes leads to careless errors on the details though and this is important. Many times those careless errors don’t matter, freeing yourself up to make those and understanding that you don’t have to manage the nitty-gritty once you have the big abstract understanding is very important.

#### Looking at Statement No. 2

Number two goes fractional, telling us that 1/4 of the total class is boys. We can break that into a ratio by understanding that a ratio compares parts to parts whereas a fraction is part of a whole so one out of four has a ratio of one to three. If this isn’t immediately obvious, imagine a pizza and cut it into four slices. One slice is one quarter of the total pizza the comparison of the one slice to the other three slices is the ratio one to three so if you get one slice and your friends get the other ones. The ratio of your slice to the others is 1:3. You have 1/4 of the total so two is also sufficient. Therefore, the answer choice here is D.

Hope this helped guys! Practice this skill of going in between these different notations because it’s one that pays off in dividends. Check out the links below for other problems and we’ll see you again real soon.

If you enjoyed this GMAT Ratio DS Problem, try your hand at this

Posted on
07
Jul 2020

## GMAT Problem – Speed Distance Problem

Speed and distance problems are among the most complained about problems on the GMAT. Numerous clients come to us and say they have difficulty with speed and distance problems, word problems, or work rate problems. So we’re going to look at a particularly difficult one and see just how easy it can be with the right approach.

#### The Two Cars Problem

In this problem we have two cars – car ‘A’ and ‘B’. Car ‘A’ begins 20 miles behind car ‘B’ and needs to catch up. Our immediate DSM (Default Solving Mechanism) is to dive in and create an equation for this and that’s exactly what we don’t want to do.

These types of problems are notorious for being algebraically complex, while conceptually simple. If you hold on to the algebra, rather than getting rid of it, you’re going to have a hard time.

#### Solution Paths

In this problem we’re going to build up solution paths. We’re gonna skip the algebra entirely. We’re going to take a look at an iterative way to get to the answer and then do a conceptual scenario, where we literally put ourselves in the driver’s seat to understand how this problem works. So if we want to take the iterative process we can simply drive the process hour-by-hour until we get to the answer.

#### Iterative solution path

We can imagine this on a number line or just do it in a chart with numbers. ‘A’ starts 20 miles behind ‘B’ so let’s say ‘A’ starts at mile marker zero. ‘B’ starts at 20. After one hour ‘A’ is at 58, ‘B’ is at 70 and the differential is now -12 and not -20. After the second hour ‘A’ is at 116, ‘B’ is at 120. ‘A’ is just four behind ‘B’. After the third hour ‘A’ has caught up! Now it’s 4 miles ahead. At the fourth hour it’s not only caught up but it’s actually +12, so we’ve gone too far. We can see that the correct answer is between three and four and our answer is three and a half.

Now let’s take a look at this at a higher level. If we take a look at what we’ve just done we can notice a pattern with the catching up: -20 to -12 to -4 to +4. We’re catching up by 8 miles per hour. And if you’re self-prepping and don’t know what to do with this information, this is exactly the pattern that you want to hinge on in order to find a better solution path.

You can also observe (and this is how you want to do it on the exam) that if ‘A’ is going 8 miles an hour faster than ‘B’, then it’s catching up by 8 miles per hour. What we care about here is the rate of catching up, not the actual speed. The 50 and 58 are no different than 20 and 28 or a million and a million and eight. That is, the speed doesn’t matter. Only the relative distance between the cars and that it changes at 8 miles per hour.

Now the question becomes starkly simple. We want to catch up 20 miles and then exceed 8 miles, so we want to have a 28 mile shift and we’re doing so at 8 miles an hour. 28 divided by 8 is 3.5.

#### Conceptual scenario solution path

You might ask yourself what to do if you are unable to see those details. The hallmark of good scenarios is making them personal. Imagine you’re driving and your friend is in the car in front of you. He’s 20 miles away. You guys are both driving and you’re trying to catch up. If you drive at the same speed as him you’re never going to get there. If you drive one mile per hour faster than him you’ll catch up by a mile each hour. It would take you 20 hours to catch up. This framework of imagining yourself driving and your friend in the other car, or even two people walking down the street, is all it takes to demystify this problem. Make it personal and the scenarios will take you there.

Thanks for the time! For other solutions to GMAT problems and general advice for the exam check out the links below. Hope this helped and good luck!

Found it helpful? Try your hand at some other GMAT problems: Profit & Loss Problem.

Posted on
11
Jun 2020

## Snack Shop GMAT Problem

The Snack shop GMAT problem is an average or a mean problem. A characteristic of many average problems is that one big takeaway right at the outset is that the answer choices are clustered tightly together. We want to refrain from making any calculations.

The problem is below: #### Selecting A Solution Path

If they’re looking for a level of precision, the estimation solution path isn’t available to us. If we dive into the problem, right from the first sentence we have sort of a conclusion that we can create via either a graphic or accounting solution path.

If you were the business owner immediately you’d say to yourself: Well for 10 days and an average of \$400 a day I made \$4000.

This is how we want to think about averages. Many times they’ll tell us a parameter about a length of time or over a certain universe of instances and here we want to treat them all as equal.

#### Solving the Problem

It doesn’t matter if one day we made 420 and another day we made 380. We can treat them in aggregate as all equal and start out with that assumption. That’s a very useful assumption to make on average problems. So, we start out knowing that we made 4,000.

What I want us to do is do a little pivot and notice from a running count standpoint how much above or below we are on a given day. So we’re told that for the first six days we averaged \$360 which means each of those six days we’re short \$40 from our average. That means in aggregate we’re short \$240. 6 days times \$40 –  and this has to be made up in the last 4 days.

Notice how we’re driving this problem with the story rather than with an equation. In the last four days we need to outperform our 400 by 240. 240 divided by 4 is 60. 60 on top of the 400 target

#### Graphical Solution Path

If we are more comfortable with graphic solution paths, imagine this in terms of 10 bars each representing \$400. Lowering six of those bars down by 40 and taking the amount that we push those first six down and distributing it among the last four bars gives us our \$460 total per day.

#### If you enjoyed this Snack Shop GMAT Problem, watch next.

Posted on
28
May 2020

## Gas Mileage GMAT Problem

The Gas Mileage problem is a classic example of the GMAT triggering one of our DSM’s: Our Default Solving Mechanisms for applied math. Yet there are three higher level solution paths that we can engage instead. So we are going to skip the math entirely on this one. In reading the question stimulus, there’s a signal that estimation is going to be a very strong and viable solution path and in fact for most folks estimation is the dominant solution path for this problem.

#### What to Take Note Of

Notice in the first sentence here that we are given the relationship between the efficiency for Car X and the efficiency for Car Y. When comparing 25 to 11.9, 11.9 is a little bit less than half. Whenever we have a relationship that is a little less or a little more than a factor, that’s a clear signal that the GMAT wants us to estimate.

Now, we have an inverse relationship here, between the efficiency of Cars X and Y and the amount of gas they use. So if Car Y is using a little half or rather if Car Y has a little less than half efficiency it’s going to use a little more than double the amount of gas. Managing the directionality of estimation is essential to make full use of this solution path.

#### Estimation Solution Path

Right off the bat, we have a sense that Car Y is going to use a little bit more than double the amount of gas. Now, all we need to do is figure out how much Car X will use. This is an exercise in mental math. Instead of dividing the 12,000 miles by 25 we want to build up from the 25 to 12,000.

Ask ourselves, in a scenario type of way, how many 25’s go into 100 – The answer is 4. 4 quarters to a \$1. Then we can scale it up just by throwing some zeros on. So, 40 25’s are 1,000. How do we get from 1,000 to 12,000? We multiply by 12. So 40 times 12, 480 25’s gives us our 12,000 miles. Car X uses 480 gallons.

Therefore, Car Y is going to use a little more than double this and we point to answer C because we just need to answer the amount Y uses in addition to X. SO there is a bit of verbal play there that we also have to recognize. That’s the estimation solution path.

#### Graphical Solution Path

We can see this via the graphic solution path by imaging a rectangle, where we have the efficiency of the engine on one side and the amount of gallons on the other. With Car X, 25 miles per gallon time 480 gallons is going to give us the area of 12,000 miles. That is we’ve driven the 12,000 miles in that rectangle. If we are cutting it in half on efficiency, or a little more than half, we end up with two strips and if we lay them side by side we see that we’re doubling of going a little more than double on the amount of gas that we use to maintain that 12,000 mile area.

#### Logical Solution Path

Finally, we can look at this from a logical solution path which overlaps a bit with the estimation. But the moment we know that Y uses a little more than double the amount of gas of X, we can also look at and not manage that directionality and just say it uses about double. The only answer choice among our answer choices that is close but not exactly, is C – 520. 480 is our exact number and the A answer is way too low. It’s not close enough to 480 to be viable. So here is an example where, while best practices have us managing the directionality, we don’t even need to do that.

#### Similar Problems

For similar problems like this take a look at the Wholesale Tool problem, The Glucose Solution Problem and for a really good treatment of the graphic solution path check out Don’s Repair Job. There should be links to all three right below and I hope that this helps you guys on your way to achieving success on the GMAT.

If you enjoyed this Gas Mileage Problem but would like to watch more videos about Meta strategy, try “How coffee affects your GMAT performance“.

Posted on
22
May 2020

## Percentage GMAT Problem

Mike is here with your Apex GMAT problem of the day. Today we are going to look at a percentage problem and we are going to break it down based upon a few characteristics. This is a very typical GMAT percentage problem.

#### Approximately

So, first things first, the thing that you should hone in on immediately in this problem is this term “approximately”. Whenever you see the term you know that they’re not going to give you a precise answer, and so you are not on a hook for the precise answer. It should scream estimation to you!

#### Questions Tricks

If you take a look at the problem itself you see that they offer you two numbers that you will be comparing. But one of the interesting features is that they give you the more complicated, more ugly number, less round number, first and the other number, the 28,000, second. And this is designed to focus you towards the more exacting approach. When in fact, your optimal solution path is recognizing that the 28,000 is your base and instead of computing the differential, super math style, of you know 36,700 minus 28,000 and then putting it over the 28,000, the original number.

#### What If?

Instead we want to play a “What If” and say okay, 28,000 is my base so what if I took 10% of it? That’s going to be 2,800. What if I took 20% of it? 5,600. What if I took 30% of it? And there’s your number right there. So, what we can see if it’s not immediately apparent from a scale perspective is that this big ugly number here is 30% higher. Even if we had that from the scale perspective. Even if we’ve recognized it’s about a one-third higher.

Notice there are two answer choices that are tightly clustered around that 30 percent. There is the 30% that’s our correct answer. Because the real number is somewhere around 31 percent and change. But there’s also that 28%, and so we need to get to some exacting level.  And we do this by playing that “What If?” and saying: Okay, we can fit three blocks of 2,800 in and that gets us just below the target number that they give us in the problem.

This is a great problem to problem form. And you can play around with your mental map as well on it. Also, there’s a signal. It’s more of a subtle one and a little less reliable in the answer choices. On the one hand, you have the cluster of 28 and 30. And so, you can reasonably suggest that because these two numbers are close together and because we’re looking at estimation as a solution path.

The GMAT is testing our differentiation and our estimation skills. And that hones us into, or narrows us down to a B vs. C situation. Other clusters that are here, that are less meaningful is the difference between A and C which is a factor of ten. But given that, and given our B vs. C once again, we are pointed towards a C answer. Now we have two different clusters that share C in common.

The GMAT does this a lot more often than you might think. And while it’s not always 100% reliable, it can be a very valuable tool. Especially when you’re short on time or need to make a decision on a problem where you don’t have a lot of uncertainty.

So, thanks for watching guys! Check out the links for other GMAT Quant & Verbal problems below and I’ll see you guys again soon.

If you enjoyed this Percentage GMAT Problem, try out others: Combinatorics Problem