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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.

Reviewing the Answer Signals

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.

Clustered Answer Choices

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.

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Posted on
17
Sep 2020

Which Is The Greatest – GMAT Problem

Today we’re going to look at a GMAT problem that screams for estimation but can really tie you in knots if you don’t have the right pivot question, the right perspective. Of the following which is greatest? And on its surface this would seem like a straightforward question except of course the GMAT being the GMAT they’re going to give you a bunch of numbers that are going to be hard to interpret. One part of this problem is simply training. The square root of 2, the square root of 3, the square root of 5. These are common, especially root 2 and root 3 because we see them a lot on triangle problems.

Get Familiar With Identities

And knowing these identities by heart as an estimate is really, really valuable just for being able to get a bearing whether you’re on a geometry problem and you’re trying to navigate or make sure that your answer seems correct or if you’re in a problem like this knowing these identities root 2 is 1.4, root 3 is 1.7, root 5 is 2.2 is useful as a touchstone.

Break Down The Problem

But this problem in general and the greater problem can be broken down not by saying oh well this is 1.4, this is 1.7, but by asking ourselves well logically which is bigger which is smaller. Remember it’s a multiple choice exam and they’re asking for the biggest or the smallest or whatever it is but these are opportunities to compare not nail down knowledge and this attitude is exceptionally vital for the data sufficiency but it crops up in problem solving a lot more than people might care to admit.

Especially if you’ve been there just trying to study and study and study and get to a precise answer on a lot of these things. So, let’s start just by taking a look at a few things. First square root of three square, root of two which one’s larger? If you said root three you are correct. How much larger? That might be a little bit more difficult to ascertain but if you say 1.7 versus 1.4 maybe 20 percent larger 3 is 50% larger than 2 so root 3 is going to be some smaller percentage larger than root two. But either way we know that root three is the bigger one it’s going to be the dominant value so the question becomes how much larger? Or which part of the answer drives the answer choice?

What Do We Know?

So we know that the integers 2 and 3 are more meaningful, larger than the square roots because the square roots are components of those integers. So between A and B, a drives the question that is the three drives the root two more than the two drives the root three. We can take a look at the following two and notice that both of them are around root three.

That is if we take apart the ugly part, which is the square root and take a look at the rest of it – four over five, five over four, these numbers are about one and compared to the two root three we have and the three root two which we’ve already decided is even stronger we don’t really need to entertain C and D all that much. Just to understand that oh they’re about a root three and that’s not going to be enough.

Looking At Answer Choice E

Finally, we have E. E is a little funky but we can ask ourselves how many times will root 3, will this 1.7 go into 7 and we get this answer that it’s a bit below 4. Compared with 3 root 2 which is 4.2 (3 times 1.4), we still have a driving the answer. You guys see how this is a marriage of doing a little bit of estimation but also really keeping your framing as is this greater or less than. Now we’ve included a bunch of other different answer choices here for you to take a look at play around with it and see if you can get yourself familiar with comparing these things because the GMAT is only going to come at you with things like square roots that are unfamiliar.

So it’s a fairly defined GMAT problem in that sense. I hope this helps, questions below, like us, subscribe, keep checking in and we’ll see you again real soon.

If you enjoyed this GMAT problem, try these problems next: Probability problem, and the Speed Distance problem.

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Posted on
06
Aug 2020

Probability GMAT Problem

Probability GMAT Problems can be super complex if you don’t frame it correctly. One of the keys to looking at probability problems, particularly conditional probability and independent probability problems, is breaking each part up into its own entity, and a lot of times this clarifies the problem.

1. Introduction To The XYZ Probability Problem

Let’s take a look at this ‘XYZ’ probability problem. Xavier, Yvonne, and Zelda are solving problems. We’re given the 3 probabilities for correct answers and we’re being asked what’s the probability of X being right and solving it, Y solving it, and Z not solving it.

The first thing we can look at is, say: “Well what’s the probability of Zelda not solving it?” And it’s just going to be the flip, the other side of 5/8 to bring us up to 1. If she solves it 5 out of 8 times, she’s not going to solve it the other 3 out of 8 times. So, we’re dealing with 1/4, 1/2, and 3/8.

2. Doing The Math May Seem Simple

The math here is straightforward, multiply them together. But that might not be readily apparent, or at the very least, just plugging it into that formula can get you into trouble. So, here’s where owning it conceptually and mapping it out with a visualization helps you take command of this problem. 

3. Xavier Getting It Correct

Since each probability is independent of the others we can look at them independently. What’s the probability of Xavier getting this correct? 1 out of 4 times. So, we can say in general, for every four attempts, he gets it correct once or 25%. If, and only if Xavier gets it correct can we move on to the next part – Yvonne.

4. Yvonne Getting It Correct

Xavier gets a correct 1 out 4 times then what are the chances that Yvonne gets a correct? 1 out of 2. So to have Xavier get it correct and then Yvonne get it correct it’s going to be 1 out of 8 times – 1/4 times 1/2.

It’s not that we can’t look at a Yvonne when Xavier gets it incorrect, it’s that it doesn’t matter. From a framing perspective, this is all about only looking at the probability for the outcome that we want and ignoring the rest.

5. Zelda Getting It Incorrect

Xavier: 1 out of 4, Yvonne: 1 out of 2, gets us to 1 out of 8. Then and only then, what are the chances that Zelda gets it incorrect? 1 out of 8 trials brings us to X and Y are correct, then we multiply it by the 3/8 that Zelda gets it incorrect. That gets us to 3/64. 3 out of every 64 attempts will end in ‘correct’, ‘correct’, ‘incorrect’.

This is one of those problems that may have to go through a few times but once you attach the explanation to it, you can’t mess up the math.

If you enjoyed this GMAT probability problem, try your hand at these other types of challenging problems: Combinatorics & Algebra

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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:

snack shop problem

1. Selecting A Solution Path

If they’re looking for a level of precision, the estimation solution path isn’t available to us. However, 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.

2. Solving the Snack Shop GMAT 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 that we already have is 460. Therefore, our answer is D.

3. Graphical Solution Path

snack shop graphic 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 “The Gas Mileage GMAT Problem” next.

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Posted on
19
May 2020

GMAT Scoring – Demystified

One of the most common questions asked by those who are new to the GMAT is how exactly does the computer adaptive test or CAT work? The long and short of it is that if you get a problem correct, they give you a harder one, if you get a problem incorrect, they give you an easier one. By doing this the GMAT is able to bounce up and down and calibrate to your skill level.

1. Should You Spend more time on the first 10 questions?

A few things come out of this including questions about how to spend your time. Whether certain questions are weighted more than others, whether your timing, that is the amount of time you spend on a problem, factors into the score.

To start, there’s a common misconception that you should spend more time on the first 10 questions because they tend to adjust your level for the computer adaptive test at a greater rate. While that’s true in the sense that the computer-adapted model on the GMAT does influence it more at the outset, whether you should spend more time is actually a more complex question. That’s because generally, the GMAT is going to give you problems that are about average and build up or down from that average.

2. Planning To Score An Elite GMAT Score

If you’re planning on performing at a top level, at an elite level, if your goal is 700 or even 600, you need to assume that those early problems – that are average level problems – you’re going to do well and in a timely manner anyway.

That is spending extra time to ensure you get them correct is a grandiose version of spending extra time to make sure that you’re getting two plus two correct. You wouldn’t check that because you’re confident enough in your skills and if you’re in the GMAT and you’re getting ready to shoot for a 700 you should already be confident enough in your skills not to have to spend extra time on average level problems. To take these problems on a problem-by-problem basis rather than with blanket statements.

3. Does The GMAT Test keep Track of Other Information?

A common question is whether or not the test keeps track of the type of problems you do. This can refer to:

    • subject matter
    • problem solving vs data sufficiency 
    • reading comprehension vs critical reasoning vs sentence correction

However, we can still go about it with the core rule: if you get it right you’re going to see something more challenging, get it wrong, less challenging. We tend to believe that they don’t keep a great track of that but really rely upon the bouncing up and down to calibrate you to your average performance level. You don’t want to sweat any single problem or worry about any single problem type in regards to the Computer Adaptive Test.

Certainly,  sometimes you’ll know that certain types of problems require more or less attention from you or that you make common errors on those problems. However, that’s not a CAT thing, that’s just a general GMAT thing. 

4. You are penalized for spending too much time on a problem but not in the way you think.

The other big question we hear a lot is whether or not the amount of time you take on a problem factors into the score. The answer here is subtle, it’s yes and no. No in the sense that the GMAT scoring algorithm does not track the amount of time that you spend on a problem. But, yes in the sense that the more time you spend on problems the less time you have for other problems. In particular, if you’re scoring above average, you’re on this ascendant curve so that the difficult problems at the end require more time than the less challenging problems at the beginning.

Therefore, if the GMAT kept track of your time and penalized you for spending longer on problems they would actually be penalizing you twice and this gets us into our timing decisions and the trade-off between time and score.

4. Time and Score Trade-off

When you’re armed with confidence and knowledge about how something works you don’t have to worry about how it works or how what you’re doing affects how it works and you can focus on the task at hand. 

The more that you can offload the burden of worrying about the scoring and the mechanisms by which the GMAT measures you, the more success you will find. As always, I hope this helps, and keep prepping!

If you enjoyed GMAT Scoring Demystified, watch The Effects Of Coffee On GMAT Performance.

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Posted on
21
Jun 2019

Number Theory Problem Form – Wedding Guest

Today, we’re going to be looking at what at first seems to be an allocation problem. But on further reflection, actually turns out to be a much simpler number theory problem. Let’s take a look at it: 

At a wedding, the bride’s side has 143 guests and the groom’s side has 77 guests. What is the largest number of identical tables that can be created if each table has to have an equal number of guests from the bride’s side and the groom’s side? An identical table is one where the number of guests from the bride’s side is the same at every table and the number of guests from the groom’s side is the same at every table.

A. 3
B. 5
C. 7
D. 11
E. 13

If we take a look at the problem stem these numbers 143 and 77. They stick out to us and they stick out not just because they don’t seem to have any relative association but also because they’re sort of odd-looking numbers, they don’t look like most the numbers were used to seeing. Say, 48 or 24 or 36 – something easily divisible clearly breakable into factors. Here, we’re given these two disparate numbers and we’re being asked to formulate not what the tables are made up of but how many tables there are.

Solving the Problem

So, we look at these two numbers and we examine first the 77 because it’s a simpler lower number. 77 breaks into factors of 7 and 11. This clues us in as to what to look for out of the 143. 143 must have a factor of 7 or 11. And in fact, 143 is evenly divisible by 11 and it gives us 13.

This means that the maximum number of tables is 11. Each one has 13 people from the bride’s side and 7 people from the groom’s side. 13 plus 7 there are 20 people at each table. Times the 11 tables is 220.

And, we can back check our math, 143 plus 77 is 220. We don’t need to go that far but that might help deliver some comfort to this method. So in reality this is a very creative clever way the GMAT is asking us for the greatest common factor.

Graphical Solution Path

Another way to think about this is that we need an equal number of groups from the bride and groom side. The number of people on the bride’s side doesn’t have to equal the number of people on the groom’s side. We just need them broken in into the same number of equal groups. Graphically, the illustration shows us how a certain number of different sized groups combined into this common table. So 13 and 7 and we have 11 groups of each.

Number Theory Problem Forming

This is a great problem to problem form. It will give you some additional mental math or common result experience by forcing you to figure out numbers that you can present that at first don’t look like they match but in fact do have a common factor. You’ll notice that if they had given you 16 people and 36 people finding that common factor might be easier.

So as you problem form this try and do it in a way that sort of obscures the common factor. Either try it maybe where they have multiple common factors and you tweak things like what is the greatest number what is the fewest number of tables. Or even do a perspective shift and take a look at say how many guests are represented at each table. Or on the bride’s side or on the groom’s side. Of course, there are conceptual shifts to this and you can make this story about anything. Once you control the story or rather the structure of the story this problem becomes very very straightforward.

Hope this helped, I look forward to seeing you guys soon.

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