Posted on
01
Sep 2021

Additional Voters – GMAT Quant Problem

Hey guys, today we’re going to look at a particularly challenging GMAT Quant problem that just about everyone resorts to an algebraic solution path on, but there’s a very elegant part solution path. When we take a look at this problem we observe immediately that the difficulty is that we have no baseline for the number of voters that we start with. That’s the confusing part here and this is one of the ways that the GMAT modulates difficulty; when they give us a problem without fixed numbers, and where we’re not free to run a scenario because there are add-on numbers that change the relative values.

Here they’re adding the 500 and the 600 which means there exist fixed values at the beginning, but we don’t know what they are. What we want to do here is remove ourselves a bit from the problem and let the ratios that they give us guide our way.

We start out with three parts Republicans, five parts Democrats. These eight parts constitute everything, but we don’t know how many voters are in each part – it could be one voter in each, or a hundred, or a thousand, and we can’t speculate yet. So, what we need to do is not worry about it, and this is where a lot of people get really uncomfortable. Let it go for a second, and notice that, after we add all the new voters, we end up with an extra part on the Republican side and the same number of parts on the Democrat side.

What does this mean? Well, the parts are obviously getting bigger from the before to the after. But because we have an overall equivalence between the number of parts we can actually reverse engineer the solution out of this.

Reverse Engineering the Solution

We’re adding 500 Democrats and we’re maintaining five parts from the before to the after. This means that each part is getting an extra 100 voters for the total of plus 500. On the Republican side, we’re adding 600 voters. We already know, from the Democratic side, that each part needs to increase by 100 to keep pace with all the other parts. So, 300 voters are used in the three republican parts, leaving 300 extra voters to constitute the entirety of the fourth part.

Now we know that each part after we add the voters equals 300 and therefore each part before we added the voters was 200. From there we get our answer choice. I forget what they were asking us at this point, and this is actually a really great moment because it’s very common on these complex problems to get so caught up, even if you’re doing it mentally, with a more conducive solution path, to forget what’s being asked. When you’re doing math on paper, which is something we really don’t recommend, it’s even easier to do so because you get so involved processing the numbers in front of you that you lose conceptual track of what the problem is about.

So, they’re asking for the difference between the Democratic and Republican voters after the voters are added. Now we know there’s one part difference and we know that after voters are added a part equals 300 voters so the answer choice is B, 300.

Something to Keep in Mind

This one is not easy to get your head around, but it’s easier than dealing with the mess of algebra that you’d otherwise have to do.
Review this one again. This is a GMAT Quant problem you may have to review several days in a row. It’s one where you might attain an understanding, and then when you revisit it four hours later or the next day, you lose it and you have to fight for it again. It’s in this process of dense contact and fighting that same fight over and over again that you will slowly internalize this way of looking at it, which is one that is unpracticed. The challenge in this problem isn’t that it’s so difficult. It’s that it utilizes solution pads and way of thinking that we weren’t taught in school and that is entirely unpracticed. So, much of what you see as less difficult on the GMAT is less difficult only because you’ve been practicing it in one form or another since you were eight years old. So, don’t worry if you have to review this again and I hope this was helpful.

Check out this link for another super challenging GMAT Quant problem.

Posted on
17
Aug 2021

GMAT Arithmetic 101- All You Need To Know

By: Apex GMAT
Date: 17 August 2021

While studying and preparing for the GMAT quant section, you might have come across some different types of GMAT arithmetic questions. These are actually quite common in the quantitative reasoning section and can be often intertwined with other GMAT algebra and GMAT geometry questions.

These usually come in 2 different formats: data sufficiency problems and problem-solving. The former have a very particular structure where you will have to determine whether the 2 statements are enough to come up with a solution. The latter type of problem requires you to actually solve the problem and derive a proper solution.

Arithmetic Concepts you need to revise

These are the arithmetic concepts you’ll need to know before you start practicing. Make sure to revise these fundamentals:

How to solve a GMAT arithmetic problem?

The number 1 thing you need to keep in mind when dealing with GMAT arithmetic problems is that the concepts that you’ll come across are fairly simple. You can easily revise these concepts because they are all things we study in high-school-level math. But here’s the kicker: the way these concepts are incorporated into the GMAT problems makes them more challenging, especially when the GMAT arithmetic problems are intertwined with GMAT algebra problems or even GMAT geometry problems. That is where things get tricky, as you need to apply your knowledge in a much more complicated setting that incorporates more than one concept. However, it all comes down to knowing the basics of arithmetics, which we can also refer to as the mechanics of the problem.

In order to help you better understand how to go about a GMAT arithmetic question, we will discuss an arithmetic problem and its solution and solution paths. In this GMAT problem, we are going to see how even the simplest mathematical concepts can become more challenging given the way the problem is formulated and structured.

Problem (GMAT Official Guide 2018)

When positive integer x is divided by positive integer y, the remainder is 9.
If x/y = 96.12, what is the value of y?

(A) 96
(B) 75
(C) 48
(D) 25
(E) 12

Solution:
In this case, you will have to revise the properties of numbers in order to properly find a solution to the problem.
When x is divided by y, the remainder is 9. So x=yq + 9 for a random positive integer q.
After dividing both sides by y, we get: x/y = q + 9/y.
But, x/y= 96.12 = 96 + 0.12.
Equating the two expressions for x/y gives q + 9/y= 96+0.12.
Thus:

q=96 and 9/y= 0.12
9=0.12y
y=9/0.12
y=75

Now that we went over the solution path for an arithmetic problem on the GMAT exam, you are ready to start your prep. Keep in mind that you should not overthink the questions. Some of them might really look challenging and complex. However, the solution paths can be fairly easy and it ultimately comes down to knowing the “mechanics” of the question.

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
04
Aug 2021

GMAT Abstract Data Sufficiency Problem

Abstract Data Sufficiency Problems & Scenarios

Hi guys! Abstract data sufficiency problems tend to really lend themselves to running scenarios – It doesn’t matter if it’s an abstract inequality or a number theory problem, really anytime you’ve got variables thrown into the question stimulus on a DS problem, scenarios is a good way to go. Now your scenarios can be discrete actual numbers that you throw in there, but you can also leverage rules and have more conceptual-level scenarios. We’re going to take a look at both in this problem.

Problem Introduction

We’re being asked here for the evenness or oddness of n which is an integer. At first blush, we’re going to say, “Well, if we have the evenness or oddness of any expression involving n and n alone, we should be able to backtrack it to n.” If you don’t see that then you might fall into the trap of having to go much more deeply into it and figure out “Well, what if n is this, what if n is that?” But notice here that because we’re dealing with evens and odds there are a set of identities that govern every possible addition, or multiplication, subtraction, or division of evens and odds. So, as long as there’s nothing complicating it the expression itself will be enough.

Statement 1

Taking a look at the introduced information, number one gives us n2 + 1 is odd that means that n2 is even. How do we know without numbers? If n2 + 1 is odd then adjusting it down by one, removing that one, means we’re definitely going to get to an even, because the number line is just even, odd, even, odd, even, odd all the way up. So, we have n2 is even, and only even times even gives us an even. Odd times odd doesn’t, odd times odd gives us an odd.

So, n must be even if the square of it leads us to an even. Notice again, that we don’t need to do any of that, it’s enough just to say we’ve got n in an expression, and we have its evenness and oddness.

Statement 2

Number two works the same way. 3n + 4 is even that’s enough, no more to do, but if we want to we can adjust that 3n – 4 as even down by 4 notches (odd, even, odd, even). So 3n is even and then we know that n divided by 3, that is what is an even divided by 3, will give us n. An even divided by an odd is going to always be an even, for the same reason even times an odd is always going to be an even.

Run some scenarios here, start out with an even number; let’s do 6, 50, and 120. Divide each by 3; 2 (6/3=2), 50 divided by 3 doesn’t work, 40 (120/3=40). So on the two that do work, we get to even numbers. 50 is not allowed to be used as a scenario because we’re told that n – 3 has to be an integer which means, that 3n must also be an integer; that is 3n is a multiple of 3. Since 50 is not a multiple of 3 it’s not a potential 3n. Take a minute with that one, because it’s kind of looking at everything in reverse.

So here we have two different expressions that both give us evenness and oddness, they both work independently. The answer choice is D – each alone is sufficient.

If you enjoyed this problem, try your hand at these Data Sufficiency Problems GMAT Trade Show Problem & Area of a Triangle Problem.

Posted on
28
Jul 2021

GMAT Trade Show Problem – Data Sufficiency

Today we’re going to take a look at the Trade Show Problem and this is a GMAT Data Sufficiency problem with averages as the focal point. But really the concept of average is distracting from this problem. So, if we take a look at the question stimulus, we want to figure out what we need, but we need to synthesize some of the information there to understand what we know.

We’re being asked whether or not it gets above a certain threshold an average of 90, and over six days that’s going to be over a total of 540 points. Notice how I did it mathematically, you can represent it graphically as a rectangle, but 90 times 6 is that 540 points. We know though that all of our days at a minimum are 80 which means we can build up from that piece of knowledge. We have 80 x 6 = 480 points and we want to know if we have more or less than 60 points above that minimum that we’re already working with that’s what we need.

Solving the GMAT Problem

Ways we might get it include any number of slices and dices for the performance of the rest of the days and the difficulty of this problem in large part will be dependent on how convoluted the GMAT gives us the introduced information on number one and two.

When we look at number one, we’re told that the final four days average out to a hundred. Once again, like with other average problems, each of the individual four days the performance doesn’t matter. We can just say each is exactly 100 and make that assumption, which means each is 20 over – we’re 80 points over the mean. Because we want to know whether we are more or less than 60 points, this knowledge that we’re 100 points tells us “Yes, definitively. We are over that average of 90, we’re over that surplus of 60 points.” So, number one is sufficient.

Number two gives us the opposite information, it talks about the minimum, and, in aggregate, that doesn’t let us know directly whether or not we make those 60 points. That is it’s possible but it’s also possible that we don’t, because we’re dealing with a minimum rather than a maximum or rather we’re dealing with information that can lie on either side of what we need. Therefore 2 is insufficient. Our answer here is A.

I hope that was useful. GMAT nation stay strong, keep averaging. You guys got this! I believe in you. If you want to test your GMAT Data Sufficiency skills, check out the Science Fair problem.

Posted on
14
Jan 2021

Averages Problem No.1 : Test Averages

Hey guys, today we’re going to take a look at the test averages problem. This is a very straightforward mathematically oriented average problem or at least it can be. But there are very strong graphic solution paths here and there’s also a really strong sort of intuitive running tally counting solution path here. We’re going to start out with the math though, just because that’s how a lot of people are familiar with this problem. Before we jump into the heavier duty quicker sort of stuff.

Doing the Math

So to solve this problem we want to take an average. But one of the components of our average is missing. So we have four things with an average of 78, and a fifth unknown. That means we can assume that each of the first four exams were 78. So we’ve got 4 times 78 plus X over 5. The total number of exams is going to give us our average of 80. Then through algebra, algebraic manipulation we multiply the 5 over, we get 400 equals 4 times 78 plus x. The 4 times 78 is 312. We subtract that off the 4 and that brings you to 88. Answer choice E.

Graphic Solution Path: Poker Chips

Let’s take a look at this a little differently. One of the ways I like looking at averages is imagining stacks of poker chips and you can have stacks of anything. I like poker chips because they fit together and you can make two stacks equal very easily so what we’re being told here is we have four stacks of 78 a fifth unknown stack but if we equalize them all that is if we take chips off of the unknown stack and distribute them all the stacks will be 80. That means that the fifth stack needs to be 80 and then it needs two poker chips for each of the other four stacks to bring those 78’s up. We can also envision this as just a rectangle our goal is 80 but we have 78, and our goal is five tests but we have four so we have 78 by four here. And then 80 by 5 here what’s missing is the full 80 and then 2 on each of four stacks of 48.

Running Tally Method: Intuitive Approach

The most powerful way to handle this problem though is probably by doing a running tally. Don’t even worry about the visualization but rather notice that, I’ve got 47 8s each of those are too short so I’m two, four, six. eight points short on the last test. I need to get the 80 that I want plus those eight points that I’m short bringing us to 88. And anybody who’s sweated like A+, B+, A- or a C+, B- has done this math. So if you characterize it like that a lot of times it becomes much more intuitive and once again allows you to cultivate confidence for a deeper treatment and more complex averages problems and mean problems check out the snack shop problem, check out the company production problem and there’s a great ds problem that we do the trade show problem you’ll find links to all of them just below and I hope this helped.

Enjoyed this Averages Problem ? Try another type of GMAT problem to get familiar with all question types on the exam: Remainder Number Theory Problem.

Posted on
03
Nov 2020

7 Tips To Improve Your GMAT Quant Score

By: Apex GMAT
Contributor: Altea Sulollari
Date: 3rd November 2020

If you’ve experienced the GMAT, you may have noticed that your score is higher on some sections than others. Some otherwise strong business school candidates struggle with their score on the quantitative section. The problem might derive from preparation style, in which case, you might consider professional GMAT tutoring, a service offered by a number of organizations including Apex GMAT. Until then, these tips will help kick start your prep process so you’re ready to ace the quant section.

What’s on the GMAT Quantitative section?

First, let’s talk about what exactly the GMAT quant section consists of. Test takers have 62 minutes to answer 31 math problems. This means that on average, each question should take two minutes. However, this isn’t a hard rule, so there’s no need to get nervous if one problem takes longer than others.

The questions are divided into two types: data sufficiency and problem-solving.

Data sufficiency questions ask test takers to analyze two given statements and determine whether the provided data tells readers enough to solve the problem. These questions are designed to evaluate quantitative fluency and critical thinking skills.

Problem-solving questions are multiple choice. They evaluate logical and analytical ability.

Keep in mind that both question types require only algebra, arithmetic, and geometry, so there’s no need to worry about trigonometry or calculus. Moreover, all of the problems can be solved using basic high school level math.

Why is the GMAT Quantitative section so difficult?

Based on the above description, you might think that the quant section won’t be too difficult. That isn’t exactly true. The GMAT is designed to confuse and restrict test takers in various ways. For example, each problem has a time limit and calculators aren’t allowed. Furthermore, problem solving and data sufficiency problems are in the same section, so test-takers must alternate between the two question types. These factors can cause stress.

The following tips will help you remain calm and collected as you prepare for the quant section.

1: Don’t overthink the math

First and foremost, don’t forget that the GMAT quant section consists of simple math problems. Use this to your advantage. Don’t do all of the calculations; rather, determine what makes a problem look more difficult than it actually is.

2: Start managing your time before the test

You can start saving time before you even pick up your pencil by practicing arithmetic. Limiting the time it takes to do simple equations means you can spend more time on the problems. Be sure to review exponent rules and brush up on decimals with fractions. And don’t forget about higher powers!

3: Use alternative strategies to find solutions

If you can’t solve a problem with simple math, try using an alternative path to the solution. There’s usually an easier way to solve quant problems–the GMAT is designed to test for efficient problem solving. Sometimes, straightforward logic or plugging in numbers will solve a problem faster. Keep in mind that a traditional approach might not be necessary for every problem.

4: Analyze each sentence step by step

During the GMAT preparation process, learn how to simplify each question. Some problems might seem daunting, but they can be broken into smaller steps that you can solve one-by-one. Trying to solve the whole problem at once can lead test takers to answer the wrong question. The more you break down the problem, the easier it will become. Don’t worry–you’ll actually save time by (re-)reading the questions.

Tip 5: Simplify the answer choices

In addition to simplifying the questions, the answer choices can also be simplified. For example, all data sufficiency questions use the same five answer choices:

1. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
2. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
3. Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
4. Each statement alone is sufficient to answer the question.

Seems wordy, doesn’t it? Fortunately, you can memorize these simpler versions:

1. only statement 1
2. only statement 2
3. both statements together
4. either statement
5. neither statement

Tip 6: Scratch paper is a must

Although scratch paper may seem unnecessary for quant problems, it can help you keep track of calculations and clarify your thought process. It might take a little extra time, but ultimately, avoidable mistakes are even more time consuming.

Tip 7: Plug in the answer choices

Another way to save time with alternative solution paths is to start by reading all of the answer choices and plugging them into the problem. If you don’t know which answer choices to start with, start from the middle.

Bonus tip

The most important tip of all is practice, practice, and practice! There are many different ways to prepare: memorizing rules and formulas, watching GMAT problem-solving videos (don’t forget to check out our YouTube channel), and enrolling in