Posted on
07
Sep 2021

## How-to GMAT: No Calculator? Use These Mental Math Tips Instead

The GMAT is an exam largely focused on numbers and numerical data. And while doing math on the GMAT should be avoided sometimes it is inevitable. True, the test-taker is given a calculator for the duration of the Integrated Reasoning section but the same cannot be said for the Quantitative Reasoning Section.

###### The Basics

Before explaining any methods for dividing and multiplying with ease, let’s make sure we have revised a few simple rules:

• Numbers with an even last digit are divisible by 2 – 576 is and 943 is not;
• Numbers with a sum of digits divisible by 3 are also divisible by 3 – 3,465 for example (3+4+6+5=18);
• If the last 2 digits of a number a divisible by 4, the number itself is divisible by 4 – 5,624 for example (because 24/4=6);
• Numbers with last digit 0 or 5 are divisible by 5;
• Numbers that can be divided by both 2 and 3 can be divided by 6;
• Similar to numbers divisible by 3, numbers divisible by 9 must have a sum of digits divisible by 9 – 6,453 for example;
• If the last digit of a number is 0 it is divisible by 10;

With that out of the way, we can move onto some more advanced mental math techniques.

###### Avoid division at all costs

Don’t divide unless there is no other option. And that is especially true with long division. The reason why long division is so perilous is that it is very easy to make a careless mistake as there are usually several steps included in the calculation, it takes too much time, and to be honest, few people are comfortable doing it.

Fortunately, the GMAT doesn’t test the candidates’ human-calculator skills but rather their capacity to think outside the box and show creativity in their solution paths, especially when under pressure – exactly what business schools look for.

However, sometimes you cannot avoid division, and when that is the case remember: Factoring is your best friend. Always simplify fractions especially if you’ll need to turn them into decimals. For example, if you have 234/26 don’t start immediately trying to calculate the result. Instead, factor them little by little until you receive something like 18/2 which is a lot easier to calculate.

A tip for factoring is to always start with smaller numbers as they are easier to use (2 is easier to use compared to 4, 6, or 8) and also look for nearby round numbers.

If you have to calculate 256/4 it would be far less tedious and time-consuming to represent 256 as 240+16 and calculate 240/4+16/4=60+4=64. Another example is 441/3. If we express it like 450-9 it is far easier to calculate 450/3-9/3=150-3=147.

###### Dividing and Multiplying by 5

Sometimes when you have to divide and multiply by 5 (you’ll have to do it a lot) it would be easier to substitute the number with 10/2. It might not always be suitable for your situation but more often than not it can be utilized in order to save some time.

###### Using 9s

With most problems, you could safely substitute 9 with 10-1. For example, if you have to calculate 46(9) you can express it as 46(10 – 1) which is a lot more straightforward to compute as 46(10) – 46(1) = 460 – 46 = 414

You can also use the same method for other numbers such as 11, 8, 15, 100, etc:

18(11) = 18(10 + 1) = 180 + 18 = 198

28(8) = 28(10 – 2) = 280 – 56 = 224

22(15) = 22(10 + 5) = 220 + 110 = 330

26(99) = 26(100 – 1) = 2600 – 26 = 2574

###### Dividing by 7

The easiest way to check if a number is divisible by 7 is to find the nearest number you know is divisible by 7. For instance, if you want to check if you can divide 98 by 7 you should look for the nearest multiple of 7. In this instance either 70, 77, or 84. Start adding 7 until you reach the number: 70 + 7 = 77 + 7 = 84 + 7 = 91 + 7 = 98. The answer is yes, 98 is divisible by 7 and it equals 14

###### Squaring

When you have to find the square of a double-digit number it might be easier to break the number into components. For example, 22^2 would be calculated like this:

22^2
= (20 + 2)(20 + 2)
= 400 + 40 + 40 + 4
= 484

Similarly, if you have to find the square of 39 instead of calculating (30 + 9)(30 +9) you could express it like this:

39^2
= (40 – 1)(40 – 1)
= 1600 – 40 – 40 + 1
= 1521

You can use the same approach when multiplying almost any double-digit numbers, not only squaring. For example 37 times 73:

(40 – 3)(70 + 3)
= 2800 + 120 – 210 – 9
= 2701

###### Conclusion

This ends the list of mental math tips and tricks you can utilize to make the Quant section a bit less laborious. Keep in mind that no strategy or shortcut would be able to compensate for the lack of proper prep so it all comes down not only to practicing but doing so the right way.

For more information regarding the GMAT Calculator, GMAT Calculator & Mental Math – All You Need To Know, is a very insightful article to read.

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
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
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
05
Aug 2021

## Why is your GMAT Score Important for Prospective Jobs?

By: Apex GMAT
Date: 5th August 2021

Taking the GMAT and getting a 700+ score is not only going to help you pursue your MBA career, it will also facilitate additional professional benefits. Indeed, the GMAT requires far more skills than just the math or verbal skills that are tested, and success can be evidence of an array of capabilities. Read on to find out what GMAT score use in employment is and why more employers are taking candidates’ GMAT scores into account in hiring decisions.

Of course, a high GMAT score primarily makes one stand out from other job applicants. Moreover, it is also a clear and objective indicator of your integrated reasoning abilities, as well as your analytical, verbal, and quantitative reasoning skills. Particularly for those interested in applying for finance, investment, or business-related employment, an excellent GMAT score can be proof of expertise in the aforementioned categories.

At the surface level, a high score in the quant section demonstrates that a candidate can solve and interpret numerical problems. More significantly, it also implies that the applicant can be trusted with complex calculations, extensive financial reports, and other major related tasks. Furthermore, a candidate’s integrated reasoning skills will be seen to be of great professional value, especially when working with a large amount of data from multiple sources. Extrapolating the right takeaways and decision-making points from this wide array of data is a skill highly sought after by employers.

The GMAT’s testing of analytical writing and verbal reasoning skills have implications for a candidate’s professional capabilities. Scores in these sections speak to the applicant’s capacity for critical thinking as well as how clearly and precisely they can express their ideas in written form.

Ultimately, the GMAT score helps employers select their hires based on information gleaned from standardized testing, and not just personal characteristics or experience. This allows for a selection process that is much more comprehensive.

Since the GMAT is a requirement for MBA admission, a high score also indicates that the candidate has been admitted to a prestigious and academically rigorous university. Potential employers perceive such individuals as having a high-quality education from top-notch professors. Many of whom have worked in their industry.

Finally, a candidate with a high GMAT score is also better placed to perform well during a job interview than someone who has never prepared for such a test. By putting his/her critical thinking and verbal reasoning skills into practice, a job candidate with a 700+ score is more likely to excel at answering questions that require the application of analytical and logical skills. Moreover, having taken the GMAT, prospective hires enjoy minimal interview anxiety or stress, because they were trained to manage such issues while preparing for the test. Additionally, they may be exempt from taking company interview tasks due to their performance on the GMAT.

For all these reasons, employers will always value individuals with high GMAT scores, giving them preference over the job seekers with low or no GMAT scores. For more information regarding the GMAT Scoring, GMAT Scoring Demystified is a very insightful article to read.

Posted on
22
Jul 2021

## GMAT Quant Syllabus 2021-2022

Author: Apex GMAT
Contributor: Altea Sollulari
Date: 22 July, 2021

We know what you’re thinking: math is a scary subject and not everyone can excel at it. And now with the GMAT the stakes are much higher, especially because there is a whole section dedicated to math that you need to prepare for in order to guarantee a good score. There is good news though, the GMAT is not actually testing your math skills, but rather your creative problem solving skills through math questions. Furthermore, the GMAT only requires that you have sound knowledge of high school level mathematics. So, you just need to practice your fundamentals and learn how to use them to solve specific GMAT problems and find solution paths that work to your advantage.

The Quantitative Reasoning section on the GMAT contains a total of 31 questions, and you are given 62 minutes to complete all of them. This gives you just 2 minutes to solve each question, so in most cases, the regular way of solving math equations that you were taught in high school will not cut it. So finding the optimal problem solving process for each question type is going to be pivotal to your success in this section. This can seem a daunting start, so our expert Apex GMAT instructors recommend that you start your quant section prep with a review of the types of GMAT questions asked in the test and math fundamentals if you have not been using high school math in your day to day life.

## What types of questions will you find in the GMAT quant?

There are 2 main types of questions you should look out for when preparing to take the GMAT exam:

### Data Sufficiency Questions

For this type of GMAT question, you don’t generally need to do calculations. However, you will have to determine whether the information that is provided to you is sufficient to answer the question. These questions aim to evaluate your critical thinking skills.

They generally contain a question, 2 statements, and 5 answer choices that are the same in all GMAT data sufficiency questions.

Here’s an example of a number theory data sufficiency problem video, where Mike explains the best way to go about solving such a question.

### Problem Solving Questions

This question type is pretty self-explanatory: you’ll have to solve the question and come up with a solution. However, you’ll be given 5 answer choices to choose from. Generally, the majority of questions in the quant section of the GMAT will be problem-solving questions as they clearly show your abilities to use mathematical concepts to solve problems.

Make sure to check out this video where Mike shows you how to solve a Probability question.

## The main concepts you should focus on

The one thing that you need to keep in mind when starting your GMAT prep is the level of math you need to know before going in for the Quant section. All you’ll need to master is high-school level math. That being said, once you have revised and mastered these math fundamentals, your final step is learning how to apply this knowledge to actual GMAT problems and you should be good to go. This is the more challenging side of things but doing this helps you tackle all the other problem areas you may be facing such as time management, confidence levels, and test anxiety

Here are the 4 main groups of questions on the quant section of the GMAT and the concepts that you should focus on for each:

### Algebra

• Algebraic expressions
• Equations
• Functions
• Polynomials
• Permutations and combinations
• Inequalities
• Exponents

### Geometry

• Lines
• Angles
• Triangles
• Circles
• Polygons
• Surface area
• Volume
• Coordinate geometry

### Word problems

• Profit
• Sets
• Rate
• Interest
• Percentage
• Ratio
• Mixtures

Check out this Profit and Loss question.

### Arithmetic

• Number theory
• Percentages
• Basic statistics
• Power and root
• Integer properties
• Decimals
• Fractions
• Probability
• Real numbers

Make sure to try your hand at this GMAT probability problem.

## 5 tips to improve your GMAT quant skills?

1. Master the fundamentals! This is your first step towards acing this section of the GMAT. As this section only contains math that you have already studied thoroughly in high-school, you’ll only need to revise what you have already learned and you’ll be ready to start practicing some real GMAT problems.
2. Practice time management! This is a crucial step as every single question is timed and you won’t get more than 2 minutes to spend on each question. That is why you should start timing yourself early on in your GMAT prep, so you get used to the time pressure.
3. Know the question types! This is something that you will learn once you get enough practice with some actual GMAT questions. That way, you’ll be able to easily recognize different question types and you’ll be able to use your preferred solution path without losing time.
4. Memorize the answer choices for the data sufficiency questions! These answers are always the same and their order never changes. Memorizing them will help you save precious time that you can spend elsewhere. To help you better memorize them, we are sharing an easier and less wordy way to think of them:
5. Make use of your scrap paper! There is a reason why you’re provided with scrap paper, so make sure to take advantage of it. You will definitely need it to take notes and make calculations, especially for the problem-solving questions that you will come across in this GMAT question.
• Only statement 1
• Only statement 2
• Both statements together
• Either statement
• Neither statement
Posted on
21
Jul 2021

## GMAT 3D Geometry Problem

In this problem we’re going to take a look at 3D objects and in particular a special problem type on the GMAT that measures the longest distance within a three-dimensional object. Typically, they give you rectangular solids, but they can also give you cylinders and other such objects. The key thing to remember about problems like this one is that effectively we’re stacking Pythagorean theorems to solve it – we’re finding triangles and then triangles within triangles that define the longest distance.

This type of problem is testing your spatial skills and a graphic or visual aid is often helpful though strictly not necessary. Let’s take a look at how to solve this problem and because it’s testing these skills the approach is generally mathematical that is there is some processing because it’s secondary to what they’re actually testing.

#### GMAT 3D Geometry Problem Introduction

So, we have this rectangular solid and it doesn’t matter which way we turn it – the longest distance is going to be between any two opposite corners and you can take that to the bank as a rule: On a rectangular solid the opposite corners will always be the longest distance. Here we don’t have any way to process this central distance so, what we need to do is make a triangle out of it.

Notice that the distance that we’re looking for along with the height of 5 and the hypotenuse of the 10 by 10 base will give us a right triangle. We can apply Pythagoras here if we have the hypotenuse of the base. We’re working backwards from what we need to what we can make rather than building up. Once you’re comfortable with this you can do it in either direction.

#### Solving the Problem

In this case we’ve got a 10 by 10 base. It’s a 45-45-90 because any square cut in half is a 45-45-90 which means we can immediately engage the identity of times root two. So, 10, 10, 10 root 2. 10 root 2 and 5 makes the two sides. We apply Pythagoras again. Here it’s a little more complicated mathematically and because you’re going in and out of taking square roots and adding and multiplying, you want to be very careful not to make a processing error here.

Careless errors abound particularly when we’re distracted from the math and yet we need to do some processing. So, this is a point where you just want to say “Okay, I’ve got all the pieces, let me make sure I do this right.” 10 root 2 squared is 200 (10 times 10 is 100, root 2 times root 2 is 2, 2 times 100 is 200). 5 squared is 25. Add them together 225. And then take the square root and that’s going to give us our answer. The square root of 225 is one of those numbers we should know. It’s 15, answer choice A.

Okay guys for another 3D and Geometry problem check out GMAT 680 Level Geometry Problem – No Math Needed! We will see you next time.

Posted on
08
Jul 2021

## 7 Daily Practices For GMAT Success

By: Apex GMAT
Contributor: Ruzanna Mirzoyan
Date: 8th July 2021

## 7 Things You Need To Do Daily When Preparing For The GMAT (GMAT Guide)

1. Visualize success and the value you will get in the end
2. Review a the GMAT sections
3. Set a time limit for each day
4. Do not forget to reward yourself
5. Forget about the target score only focus on improvement
6. Give yourself a pep talk
7. Evaluate Yourself Honestly

Achieving a great score on the GMAT exam is not an easy task. The overall preparation process is daunting for a majority of test takers, especially for non-native English speakers. It requires diligent work and a daily checklist that you need to follow. So how do you come up with a plan that works? This article covers seven tips for successful GMAT prep which will guide you throughout the entire process. Even though every individual taking the exam has different expectations, experiences and may be approaching the test in a different way, sticking to a daily routine is an integral part of test success; the most difficult thing is adhering to it, avoiding procrastination and maintaining motivation. Therefore, after learning all the exam basics, such as the timing, the sections, and the preparation materials, it is worth creating a checklist to help keep you on track.

#### Visualize success and the value you will get in the end

The thought of success can create happiness! Once we attain something that seemed difficult initially, the suspense wears off, and the excitement rapidly grows. By taking time every day to imagine achieving your goal you can stay motivated and on the right path. When we experience happiness our brain releases serotonin, the hormone responsible for happiness. By keeping the picture of accomplishment in our mind, this happiness never fades. Hence, if every day contains even a tiny bit of happiness, even the most complex struggles seem simpler to overcome. Whether the GMAT exam is a struggle or not, happiness and motivation are something that one undoubtedly always lacks. Do your best to look at the bigger picture and think of the steps that will expedite reaching the top.

#### Review the GMAT exam sections

Whether you have a private GMAT tutor or are studying on your own, be sure to review difficult parts of the overall format of the exam every day before going through your study materials, for example the data sufficiency answer choices. You may do a short quiz on quantitative, verbal, or integrated reasoning to keep pace with timing and question types. You can consider this form of revision as stretching your brain muscles before the main exercise. Doing a simple GMAT quiz each time will make you more cautious about time management and remind you about the type of questions that you may have already mastered in previous study sessions.

#### Set a study time limit for each day

As it is said, time is the only non-redeemable commodity, so proper allocation is a fundamental key to success. We recommend you have a specific time allocation for GMAT prep each day. That can be some time for weekday preparation and extension on the weekends. Ensure the limit you set for yourself is reasonable because procrastinating one day and doubling the hours the next day does not work out. It does not matter how many months you have on your hands; the significant thing is precise allocation. If you want to get a decent score, you must spend approximately 100-120 hours reviewing the materials and practicing. However, top scorers usually  spend 120+ hours studying. Whether you belong to the former or the latter category, remember that time is the most expensive investment you are making. At the same time keep in mind that your study-life balance should be of utmost importance.

#### Do not forget to reward yourself

It is not a secret that the GMAT is burdensome and overwhelming, and preparing for it can be stressful and oftentimes disheartening. Not having small rewards to look forward to can lead to demotivation. Rewards are things that rejuvenate your broken concentration. Try something like the Pomodoro Technique. This technique helps break down time into intervals with short breaks. Instead of breaks, you can think of something ‘non-GMAT related’ that will make you regain focus. For example, by grabbing a quick snack, meditating, or walking around the house or even watching a short YouTube video. Whichever works best for you, make use of it; even brief respites retain your stamina. Finally, never forget about the bigger reward; your final score.

#### Forget about the target score, only focus on improvement

GMAT preparation practices do generate plight both in physical and mental states. It is crucial to remind oneself of the improvement phases. We agree that everything you are going through is for the final score. But focusing on the final score too much can frustrate you if you are not making big leaps towards it, which in turn can be counter productive. All successful practices dictate that you should focus on one thing at a time, which improves every day until the exam day. When the exam day comes, you will utilize all the knowledge and effort to get the highest GMAT score possible. Keeping daily track of your improvements relieves some of the burden on your shoulders. Even the tiniest advantage acquired can be a game changer. For instance, finishing each section a minute earlier than before will eventually contribute to achieving more significant results on the exam day, or perfecting a solution path which has you approaching a host of GMAT problems in a more efficient manner. These small wins can be the fuel to keep you going.

#### Give yourself a pep talk

I am sure you receive a lot of support from the people surrounding you. However, self-encouragement is of the utmost importance. Look around, see what others are doing at your age and inspire yourself. Choose wisely between the tradeoffs. Such as choosing to study instead of partying. Giving yourself a daily pep talk will make you more enthusiastic about reaching your objectives. A recent scientific study has shown that talking to yourself dwindles anxiety and stress while boosting performance. This is no less true for GMAT test preparation. Give yourself motivational and instructional pep talks. This method promotes positivity as motivational talks cheer you up and keep up the eagerness to study and strive for more, while a self-instructional talk directs detail-orientation and accentuates what exactly you need to do for that particular day. For example, start every day by loudly stating what should be done for the day. It helps with thinking about the mechanisms of every individual task and visualizing methods to complete them correspondingly.

#### Evaluate Yourself Honestly

Of course, you need all the encouragement and self-support to reach your goals, but especially during GMAT exam preparation, you need to be hard on yourself if required. If you need a 650+ GMAT score, you should be aware that it will not be a piece of cake. Give yourself credit for what you are doing right, but also consider aspects of the GMAT problems that you need to elaborate on and master additional skills. The dominant thing is separating the action from the person because you are evaluating your actions and not you as a person; you should not upset yourself but rather detect the triggers of low performance and challenges and make yourself accountable for such actions with a plan to move forward from them successfully. Ultimately, the ability to discern your flaws and work on personal evolution is an inherent quality for capacitating your abilities and aptitudes and pulling it off in life.

We hope that adding these practical and mindful aspects to your daily preparation will be helpful as when you are preparing for an exam like the GMAT, being in the right mind frame can be as important as doing the quant or verbal practice. Whether you have a GMAT private tutor or not, it is on you to maintain motivation during the entire process. We suggest you develop a GMAT test strategy along with these seven tips to attain greater productivity and manifest superb performance. Make studying for the GMAT a daily habit and success will follow.

Posted on
24
Jun 2021

## The Basics of GMAT Combinatorics

By: Apex GMAT
Contributor: Svetozara Saykova
Date: 24th June 2021

Combinatorics can seem like one of the most difficult types of questions to come across on the GMAT. Luckily there are not many of them within the exam. Still these questions make up the top level of scoring on the test and therefore it is best if you are well equipped to solve them successfully, especially if you are aiming for a 700+ score. The most important rule to follow when considering this question type is the “Fundamental Counting Principle” also known as the “Counting Rule.” This rule is used to calculate the total number of outcomes given by a probability problem.

The most basic rule in Combinatorics is “The Fundamental Counting Principle”. It states that for any given situation the number of overall outcomes is equal to the product of the number of each discrete outcome.

Let’s say you have 4 dresses and 3 pairs of shoes, this would mean that you have 3 x 4 = 12 outfits. The Fundamental Counting Principle also applies for more than 2 options. For example, you are at the ice cream shop and you have a variety of 5 flavors, 3 types of cones and 4 choices for toppings. That means you have 5 x 3 x 4 = 60 different combinations of single-scoop ice creams.

The Fundamental Counting Principle applies only for choices that are independent of one another. Meaning that any option can be paired with any other option and there are no exceptions. Going back to the example, there is no policy against putting sprinkles on strawberry vanilla ice cream because it is superb on its own. If there were, that would mean that this basic principle of Combinatorics would not apply because the combinations (outcomes) are dependent. You could still resort to a reasoning solution path or even a graphical solution path since the numbers are not so high.

Let’s Level Up a Notch

The next topic in Combinatorics is essential to a proper GMAT prep is  permutations. A permutation is a possible order in which you put a set of objects.

Permutations

There are two subtypes of permutations and they are determined by whether repetition is allowed or not.

• Permutations with repetition allowed

When there are n options and r number of slots to fill, we have n x n x …. (r times) = nr permutations. In other words, there are n possibilities for the first slot, n possibilities for the second and so on and so forth up until n possibilities for position number r.

The essential mathematical knowledge for these types of questions is that of exponents

To exemplify this let’s take your high school locker. You probably had to memorize a 3 digit combination in order to unlock it. So you have 10 options (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) for 3 available slots. The total number of locker passwords you can have is 103 = 1,000.

• Permutation without repetition allowed

When repetition is restricted in the given GMAT problem, we would have to reduce the number of available choices for each position.

Let’s take the previous example and add a restriction to the password options – you cannot have repeating numbers in your locker password. Following the “we reduce the options available each time we move to the next slot” rule, we get 10x9x8 = 720 options for a locker combination (or mathematically speaking permutation).

To be more mathematically precise and derive a formula we use the factorial function (n!). In our case we will take all the possible options 10! for if we had 10 positions available  and divide them by 7!, which are the slots we do not have.

10! =  10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

7! =  7 x 6 x 5 x 4 x 3 x 2 x 1

And when we divide them (7 x 6 x 5 x 4 x 3 x 2 x 1) cancels and we are left with 10 x 9 x 8 = 720.

Pro tip: Taking problems and deeply examining them by running different scenarios, and changing some of the conditions or numbers is a great way to train for the GMAT. This technique will allow you to not only deeply understand the problem but also the idea behind it, and make you alert for what language and piece of information stands for which particular concept.

So those are the fundamentals, folks. Learning to recognize whether order matters and whether repetition is allowed is essential when it comes to Combinatorics on the GMAT. Another vital point is that if you end up with an endless equation which confuses you more than helps, remember doing math on the GMAT Quant section is not the most efficient tactic. In fact, most of the time visualizing the data by putting it into a graph or running a scenario following your reasoning are far more efficient solution paths.

Feeling confident and want to test you GMAT Combinatorics skills? Check out this GMAT problem and try solving it. Let us know how it goes!

Posted on
13
May 2021

## GMAT Factors Problem

Hey guys! Today we’re going to take a look at one of my favorite problems. It’s abstract, it’s oddly phrased and in fact the hardest part for many folks on this problem is simply understanding what’s being asked for. The difficulty is that it’s written in math speak. It’s written in that very abstract, clinical language that if you haven’t studied advanced math might be new to you.

How this breaks down is they’re giving us this product from 1 to 30, which is the same as 30!. 30*29*28 all the way down the line. Or you can build it up 1*2*3*……*29*30.

#### The Most Difficult Part of The GMAT Problem

And then they’re asking this crazy thing about how many k such that three to the k. What they’re asking here is how many factors of three are embedded in this massive product. That’s the hard part! Figuring out how many there are once you have an algorithm or system for it is fairly straightforward. If we lay out all our numbers from 1 to 30. And we don’t want to sit there and write them all, but just imagine that number line in your head. 1 is not divisible by 3. 2 is not divisible by 3, 3 is. 4 isn’t. 5 isn’t. 6 is. In fact, the only numbers in this product that concern us are those divisible by 3. 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.

Here it’s important to note that each of these components except the three alone has multiple prime factors. The three is just a three. The six is three and a two. The nine notice has a second factor of three. Three times three is nine and because we’re looking at the prime factors it has two. It’s difficult to get your head around but there are not three factors of three in nine when you’re counting prime factors.

Three factors of three would be 3 by 3 by 3 = 27. So notice that 3 and 6 have a single factor. 9 has a double factor. Every number divisible by 3 has one factor. Those divisible by 9 like 9, 18 and 27 are going to have a second factor and those divisible by 27, that is 3 cubed, are going to have a third factor. If we lay it out like this we see ten numbers have a single factor. Another of those three provide a second bringing us to thirteen. Finally, one has a third bringing us to fourteen. Answer choice: C.

#### GMAT Problem Form

So let’s take a look at this problem by writing a new one just to reinforce the algorithm. For the number 100 factorial. How many factors of seven are there? So first we ask ourselves out of the 100 numbers which ones even play? 7, 14… 21 so on and so forth. 100 divided by 7 equals 13. So there are 13 numbers divisible by 7 from 1 to 100. Of those how many have more than one factor of 7? Well we know that 7 squared is 49. So only those numbers divisible by 49 have a second factor. 49 and 98. There are none that have three factors of 7 because 7 cubed is 343. If you don’t know it that’s an identity you should know. So here our answer is 13 plus 2 = 15.

Try a few more on your own. This one’s great to do as a problem form and take a look at the links below for other abstract number theory, counting prime type problems as well as a selection of other really fun ones. Thanks for watching guys and we’ll see you soon.

If you enjoyed this GMAT factors problem, here is an additional number theory type problem to try next: Wedding Guest Problem.