4 Best Practices to help you master the GMAT AWA section
Posted on
27
Apr 2021

4 Best Practices to Help You Master the GMAT AWA Section

By: Apex GMAT
Contributor: Altea Sulollari
Date: 27th April 2021

When preparing for the GMAT most people neglect the GMAT AWA section, and even though this section is scored separately, it is important that you spend some time focusing on performing well on it.

The section is specifically designed to test your ability to impartially analyze an argument and to state your ideas with precision – skills that will be invaluable in your future career.

Another reason to pay attention to this section of the GMAT is the fact that the schools you apply to will get to see your essays, and impressing them with your writing skill can only help your application.

In the upcoming sections, we’ll go over all you need to know about:

  • The GMAT AWA (Analytical Writing Assessment)
  • How the AWA is scored
  • Five best practices to follow when preparing for the AWA section

The GMAT AWA Explained

When it comes to the AWA, keep in mind that this section is not as important as the others as it does not contribute to the all important 800 score. That being said, your essay is sent to the schools that you are applying to and the recruiters will get to see how you structure an argument. Even though the GMAT AWA section is not the most important, it still showcases your writing skills and that is a good enough reason to put some effort into it.

The section is a timed 30-minute essay writing task. You will be presented with a passage and your task will be to analyze the author’s argument to the best of your abilities. You will be expected to provide a thorough analysis of the strong points as well as to point out the weaknesses of the argument. Similar to the critical reasoning section, you will have to speak about an argument construction using abstract language and to show how it can potentially be weakened or strengthened. Your ability to successfully express your ideas in a precise manner will be crucial in this process. A good way to do this is to constantly ask yourself the question: “What if?”, to show you the methods that an argument can be strengthened and weakened. 

The GMAT AWA Scoring System

Now that you know what this section is all about, let’s focus on the scoring system for this part of the GMAT.

Your analysis will be scored separately from the other sections of the GMAT and the score you get will not count towards your final combined score, which ranges from 200 to a maximum of 800. Rather the AWA score range is from 0 to 6 in half point increments, where 6 is the maximum score for a well-structured analysis.

The second thing you’ll need to keep in mind is that your essay will be checked twice: once by a human reader and once by a computer algorithm. The scores from both are taken into consideration and your final score will be the average of those two. However, if the scores from the human reader and the computer algorithm differ from one another significantly, another human reader has to check your argument analysis.

This information is important because although you do not have an idea about how the human reader will check your essay, the computer algorithm uses certain criteria to base its final decision on, and this criteria includes keywords related to the topic, grammar, punctuation, structure, etc. This is useful insight into what is asked of you and where you should focus when preparing for the section in order to succeed. 

What’s a good GMAT AWA score?

Consider the AWA to be pass/fail, where the task in question is whether you can construct a coherent argument, as compared to your peers. In this light, a passing grade would be a 4.5 or greater.  While it is always good to aim high, it’s important to keep in mind that once you’ve achieved a 4.5, there’s very little use of worrying about obtaining a higher score, and you’d do better focusing on the other parts of your application to distinguish yourself.

Pro tip: There is a simpler way to improve your GMAT AWA score without putting too much effort into preparing for this specific section: master the GMAT Verbal section! Both the Verbal section and the AWA section require you to have good critical reasoning skills and for you to be able to analyze arguments impartially. As both of these sections require the same set of skills, you won’t have to work harder, only smarter!

4 Best Practices to Help You Ace the GMAT AWA Section

Now that you’re familiar with the GMAT AWA section and its scoring system, here are some best practices to follow that will assure you master this section.

Remember that you are dealing with an analysis! 

Do what is asked of you and do not deviate from that. You’ll need to focus on analyzing the arguments that are presented to you in the passage. Concentrate on identifying the strong points as well as the weaknesses of the argument. This is not, however, an opportunity to express your own opinion on the matter or topic, so be careful not to cross that line and risk losing points. Also, try to stir away from personal views and irrelevant outside information that can potentially affect the way you structure and phrase your analysis. Instead, try to focus on the logic of the argument and stick to that.

Do NOT focus too much on the word count!

The number of words you use does not matter as much as the structure and quality of your work. However, there’s a catch! The computer algorithm that checks your essay is more likely to give you a higher score if you write a longer essay with more complex sentence structure. Ultimately, you’ll have to make sure that you have a clearly laid out argument in an easy-to-follow structure, and if you do so well, generally the length will be sufficient and you won’t have any problems regarding word count. Bottom line: if your essay is a bit short, there’s probably something you’ve missed, so go back and look for additional features of the argument to deconstruct. 

Pro tip: Mind your grammar and punctuation! Grammar and punctuation are just as important as structure. A well-written essay should not have grammatical mistakes or sentences that are out of place or do not make sense. Use your Sentence Correction skills! 

Practice is key!

Practice makes perfect. Writing a few practice essays is particularly important when it comes to acing the AWA section of the GMAT as it familiarizes you with the process of writing an analysis of argument under a time constraint. Reading many arguments in different formats and on varying subjects will certainly help you improve your overall skills and make you ready for any argument presented come test day.

That being said, do not overdo it. If you graduated from University in an English speaking country with a liberal arts or social sciences degree under your belt, this should be enough for you to make the 4.5 mark in the AWA without much further preparation.

Finally, make good use of ready-made templates to structure your essay. There are plenty of templates that you can download for free so make sure to take advantage of that.

Don’t stress it too much!

There is nothing worse than stressing out on exam day as it can affect your overall performance on the exam. Working on the GMAT AWA section can be especially stressful and overwhelming because you have to come up with your own explanations rather than rely on provided answers. Try to take it easy and remember that the AWA’s role on the GMAT is as much about grinding down your stamina as it is about writing. You’ve practiced a lot and are prepared to ace this section and the exam as a whole, so don’t worry about it.

Now that we went over everything, you’ve got an ace up your sleeve and you’ll be able to tackle the GMAT AWA with confidence.

Good luck with your exam! 

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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

 

 

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taking the gmat prep journey. On our own or with peers?
Posted on
22
Apr 2021

Taking the GMAT Prep Journey: On your own or with peers?

By: Apex GMAT
Contributor: Arin Agich
Date: 22nd April 2021

 If you aim to apply for your dream MBA program or you want to reach the next level in your career, attending business school is a step that you should be considering. If so, you will need to take the GMAT exam. Before starting to prepare for your GMAT journey you have to decide which learning style suits you best. This depends on the amount of available time you have, your score goal, and your budget. In this article we are going to look at the two most common methods to prepare for the GMAT: One on one GMAT prep and Group prep.

What are the differences between one-on-one and group-based GMAT preparation?

Before deciding which one of these methods will work best for you it is important to review the main differences between them.

 Do you study best alone or with peers?

One of the biggest differences between these two learning styles is the presence or absence of others. Being surrounded with others going through the same journey might be encouraging, knowing that the others are sharing similar challenges on their GMAT journey will help you see that you are not alone.  Whereas, being on your own can lead to higher success rates since you can move forward with your own pace without waiting for your peers.

Time Management

A bulk of your GMAT preparation will include a vast majority of practice problems so you will need to manage your time successfully and make sure that you are using this time productively to avoid preparing for the test for extended periods of time. Apex tutors suggest spending between 3-4 months studying for the exam. Managing your preparation schedule and discipline is all up to you if you decide to prepare for the exam on your own. On the other hand, being under a one-on-one prep program will give you plenty of flexibility, but make sure that you keep up to your self-built schedule!

Individual Workload vs Group Projects/Home-works

Irrespective of any type of GMAT preparation method you will need to spend numerous hours doing homework or self prep at home to get comfortable using the skills that you have learnt. If you are part of a group-based prep program you will be able to ask for help and advice from your classmates and even work in groups. For some this sounds time-consuming, whereas for others it is a great socializing opportunity during GMAT prep time. However, as an individual student, your home works can be personalized and built according to your needs. This will help you to focus more on your weaknesses and move forward faster with the topics that you have already developed. 

 Efficiency

Regardless of which method you decide to go for, in the end it comes to efficiency. Keeping in mind that you have a limited period of time until the big GMAT test day, being efficient throughout your preparatory period is the key. To be able to answer this it is important to know the benefits of each method. In the following section we wrote down some of the benefits both for one on one and group based GMAT prep.

Benefits of One-on-one GMAT Preparation

 Personalized Sessions: Curriculum Flexibility

One of the biggest benefits of one-on-one GMAT preparation is that the sessions are personalized according to your needs. After your first session with your tutor, where you can openly talk about your challenges that you want to work on and strengths you want to build on, you will be given a personalized curriculum that will help you tackle all your problems.

 Student-Tutor Bond

Preparing for your GMAT test can be overwhelming. This is where the student-tutor bond comes into play. Knowing that you have your tutor’s full attention and support will help you get over your anxiety and reduce your stress. Getting support during such long journeys is crucial. This will help you to refocus when required, rest when needed, and move forward faster when you are ready.

Alex who scored 730 on his GMAT test after working with Apex said this about his one on one GMAT prep experience:

“I felt like Apex was in my camp and in my corner, really making sure that I was putting my best foot forward and that I was going to get the best possible score that I could. The support system that was in place was great and the experience was seamless”.

 Two-way Feedback

For anyone going through GMAT preparation, having feedback on your work is highly important. This helps you to check in with how far you have come. However, it is also important to give feedback to your tutor, too. This will help her/him to understand your needs better. If you are part of a one-on-one tutoring program the feedback can go both ways, at any given time. Feedback can take different forms, some of the examples are: test taking strategies and advice, specific questions type strategies, habits for success, stress reducing advice, etc. 

 Progress at your own pace

Preparing with one-on-one tutoring for your GMAT means that you will have a personalized curriculum by your tutor. This means that, following this curriculum, you can also progress at your own pace. Working more on questions that you have a hard time with or going forward much faster with the ones that you have mastered, without having to wait for your peers. 

Benefits of group-based GMAT Preparation

 Sharing the Same GMAT Journey

Being part of a group-based GMAT prep program will give you the sense of belonging with fellow future GMAT takers. This will help you to share your struggles and anxieties, and also celebrate your success with your peers. Having a social group throughout GMAT’s many hours of practice questions and tests is supportive. Being surrounded with like minded people with similar goals will keep you motivated. 

Besides sharing your GMAT process during your preparation period, the weekly meetings during mutual classes will give you the opportunity to engage with your peers. Sharing tips, advice, and notes or simply: making new friends!

Study Dates 

Next to your individual tasks and homework, within your GMAT group you can also find study buddies and work on your questions together. This will help you to partner up with one of your peers who might have similar challenges and try to tackle the questions together or this person will be able to help you with the topics you have trouble going forward with. 

 Structured Schedule 

Group-based GMAT preparation courses are highly structured programs. If you are a person who functions easier and is more productive under a ready made structured schedule, working in a group is for you. It will have a routine that you can always count on. 

Developing additional skills

Next to developing your GMAT skills, being part of a group will help you develop additional skills, such as: social and communication skills which are highly acquired skills in MBA programs. Next to developing your personal and social skills, being part of a group will also give you the chance to be part of a team work. This will help you develop your leadership skills and the importance of cooperation with the others. 

Which GMAT prep strategy is the best for you?

Finding the most efficient way for reaching a high score on your GMAT test is important. After reviewing the benefits and differences of the two learning methods you can prioritize your needs, consult with previous GMAT takers and tutors and decide which method would work best for you!

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Intro to GMAT data sufficiency article
Posted on
20
Apr 2021

Intro to GMAT Data Sufficiency- All you’ll need to know

By: Apex GMAT
Contributor: Altea Sulollari
Date: 20th April 2021

As a GMAT test-taker, you are probably familiar with data sufficiency problems. These are one of the two question types that you will come across in the GMAT quant section, and you will find up to 10 of them on the exam. The rest of the 31 questions will be problem-solving questions.

The one thing that all GMAT data-sufficiency questions have in common is their structure. That is what essentially sets them apart from the problem-solving questions. 

Keep on reading to find out more about these questions’ particular structures and the topics that they cover:

The question structure:

The GMAT data sufficiency problems have a very particular structure that they follow and that never changes. You are presented with a question and 2 different statements. You will also be given 5 answer choices that remain the same across all data sufficiency problems on the GMAT exam. These answer questions are the following:

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.

Your job would be to determine whether the 2 statements that you are provided with are sufficient to answer the question.

What topics are covered?

Some of the math topics that you will see in this type of question are concepts from high school arithmetic, geometry and algebra.

Below, you’ll find a list of all concepts you need to know for each math topic:

Geometry

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

Algebra

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

Arithmetic

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

Word problems

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

Common mistakes people make when dealing with this question type

Actually solving the question

This is the #1 mistake most test-takers make with these problems. These problems are not meant to be solved. Instead, you will only need to set up the problem and not execute it. That is also more time-efficient for you and will give you some extra minutes that you can use to solve other questions. 

Over-calculating

This relates to the first point we made. This question type requires you to determine whether the data you have is sufficient to solve the problem. In that case, calculating won’t help you determine that. On the contrary, over-calculating will eat up your precious minutes.

Rushing

This is yet another common mistake that almost everyone is guilty of. You will have to spend just enough time reading through the question in order to come up with a solution. Rushing through it won’t help you do that, and you will probably miss out on essential details that would otherwise make your life easier. 

Not understanding the facts

What most test-takers fail to consider is that the fact lies in the 2 statements that are included in the questions. Those are the only facts that you have to consider as true and use in your question-solving process. 

3 tips to master this question type:

Review the fundamentals

That is the first step you need to go through before going in for actual practice tests. Knowing that you will encounter these high school math fundamentals in every single quant problem, is enough to convince anyone to review and revise everything beforehand.

Memorize the answer choices

This might sound a bit intimidating at first as most answer choices are very long sentences that tend to be similar to each other in content. However, there is a way to make this easier for you. What you need to do is synthesize the answer choices into simpler and more manageable options. That way, they will be easier to remember. This is what we suggest:

A) Only statement 1
B)
Only statement 2
C) Both statements together
D) Either statement
E) Neither statement

Examine each statement separately

That is definitely the way to go with this GMAT question. You will need to determine whether one of the statements, both, either, or neither is sufficient, and you cannot do that unless you look at each of them separately first.

Now that you have read the article and are well-aware of the best ways to solve data sufficiency problems on the GMAT, try your hand at this question: Number Theory: Data Sufficiency

 

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Posted on
08
Apr 2021

GMAT Factorial Problem Explained | Estimation & Scenario Solution Path

GMAT Factorial Introduction

Factorials and divisibility, together. Two mathematical kids from opposite sides of the tracks, they come together and fall in love and they create this problem. Here we’re asked what numbers might divide some new number 20 factorial plus 17. As a refresher, a factorial is simply the number times each integer below it. So in this case, 20! is equal to 20 x 19 x 18 …. x 3 x 2 x 1. It’s a huge number. And it’s not at all possible to process in GMAT time. What we want to notice about any factorial is that it has as factors every number that it contains. So 20! is divisible by 17, it’s divisible by 15, it’s divisible by 13, 9, 2, what have you and any combination of them as well.

What The GMAT is Counting On You Not Knowing

When we’re adding the 17 though, the GMAT is counting on the idea that we don’t know what to do with it and in fact that’s the entire difficulty of this problem. So I want you to imagine 20! as a level and we’re going to take a look at this graphically. So 20! can be comprised by stacking a whole bunch of 15’s up. Blocks of 15. How many will there be? Well 20 x 19 x 18 x 17 x 16 x 14 times all the way down the line. There will be that many 15’s. But 20! will be divisible by 15. Similarly, by 17, by 19, by any number. They will all stack and they all stack up precisely to 20! because 20! is divisible by any of them.

Answer

So when we’re adding 17 to our number all we need to see is that, hey, 15 doesn’t go into 17, it’s not going to get all the way up there. 17 fits perfectly. 19? guess what? It’s too big and we’re going to have a remainder. So our answer here is B, only 17.

For other problems like this, other factorials, and what have you, please check out the links below and we will see you next time. If you enjoyed this GMAT problem, try your hand at this Science Fair Problem.

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GMAT Prime Factorization Article
Posted on
01
Apr 2021

GMAT Prime Factorization (Anatomy of a Problem)

By: Rich Zwelling (Apex GMAT Instructor)
Date: 1st April 2021

First, if you’d prefer to go straight to the explanation for the solution to the problem given in the last post, continue to the end of this post. But we’ll start with the following Official Guide GMAT problem as a way to talk about GMAT Prime Factorization. Give the problem a shot, if you can:

How many prime numbers between 1 and 100 are factors of 7,150?

A) One
B) Two
C) Three
D) Four
E) Five

One of the things you’ll notice is the linguistic setup of the problem, which is designed to confuse you immediately (a common theme on GMAT problems). They get you panicking right away with mention of a large range (between 1 and 100), and then they compound your frustration by giving you a rather large value (7,150). 

Don’t let that convince you that you can’t do the problem. Because remember, the GMAT is not interested in large calculations, memorization involving large numbers, or weird arcana. Chances are, if you find yourself thinking about a complicated way to do a problem, you’re taking the wrong approach, and there’s a simpler way.

Try to pick out the most operative signal words, which let you know how to address the problem. We are dealing with prime numbers and also the topic of finding factors. The language of the problem may make you nervous, thinking that we must consider a slew of prime numbers up to 100. But the only primes we are really interested in are those that are actually factors of 7,150. 

So let’s focus our attention there. And we can do so with a prime factor tree. Does this bring back memories? 

Now, in the case of 7,150, we don’t have to break it down into prime numbers immediately. Split the number up into factors that are easy to recognize. In this case, the number ends in a zero, which means it is a multiple of 10, so we can start our tree like this:

prime factorization on the GMATNotice that the advantage here is two-fold: It’s easier to divide by 10 and the two resulting numbers are both much more manageable. 

Splitting up 10 into it’s prime factorization is straightforward enough (2 and 5). However, how do we approach 715? Well, it’s since it ends in a 5, we know it must be divisible by 5. At that point, you could divide 715 by 5 using long or short division… 

…or you could get sneaky and use a NARRATIVE approach with nearby multiples:

750 is nearby, and since 75/5 = 15, that must mean that 750/5 = 150. Now, 750 is 35 greater than 715. And since 35/5 = 7, that means that 715 is seven multiples of 5 away from 750. So we can take the 150, subtract 7, and get 143

Mathematically, you can also see this as: 

715/5 = (750-35)/5 = 750/5 – 35/5 = 150 – 7 = 143

So as stands, here’s our GMAT prime factorization:

prime factorization GMAT articleNow, there’s just the 143 to deal with, and this is where things get a bit interesting. There are divisibility rules that help make factoring easier, but an alternative you can always use is finding nearby multiples of the factor in question. 

For example, is 143 divisible by 3? There is a rule for divisibility by 3, but you could also compare 143 against 150. 150 is a multiple of 3, and 143 is a distance of 7 away. 7 is not a multiple of 3, and therefore 143 is not a multiple of 3.

This rule applies for any factor, not just 3. 

Now we can test the other prime numbers. (Don’t test 4 and 6, for example. We know 143 is not even, so it’s not divisible by 2. And if it’s not divisible by 2, it can’t be divisible by 4. Likewise, it’s not divisible by 3, so it can’t be divisible by 6, which is a multiple of 3.)

143 is not divisible by 5, since it doesn’t end in a 5 or 0. It’s not divisible by 7, since 140 is divisible by 7, and 143 is only 3 away. 

What about 11? Here you have two options: 

  1. Think of 143 as 110+33, which is 11*10 + 11*3 → 11*(10+3) → 11*13
  2. If you know your perfect squares well, you could think of 143 as 121+22 

→ 11*11 + 11*2 → 11*(11+2) → 11*13

Either way, you should arrive at the same prime factorization:

GMAT prime factorization QuestionNotice that I’ve marked all prime numbers in blue. This result shouldn’t be a surprise, because notice that everything comes relatively clean: there are only a few prime numbers, they are relatively small, and there is just one slight complication in solving the problem (the factorization of 143). 

So what is the answer? Be very careful that you don’t do all the hard work and falter at the last second. There are five ends to branches in the above diagram, which could lead you prematurely to pick answer choice E. But two of these branches have the same number (5). There are actually only four distinct primes (2, 5, 11, 13). The correct answer is D.

And again, notice that the range given in the question stem (1 to 100) is really a linguistic distraction to throw you off track. We don’t even go beyond 13. 

Next time, we’ll talk about the fascinating topic of twin primes and how they connect to divisibility.

Find other GMAT Number Theory topics here:
Odds and Ends (…or Evens)
Consecutive Integers (plus more on Odds and Evens)
Consecutive Integers and Data Sufficiency (Avoiding Algebra)
GMAT Prime Factorization (Anatomy of a Problem)
A Primer on Primes

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Posted on
31
Mar 2021

Ace GMAT Data Sufficiency Questions with this Science Fair Problem

Data Sufficiency Problem Video Transcript

Introduction to Data Sufficiency

Hey guys! Today we’re looking at the Science Fair Problem. In this Data Sufficiency, we’re being asked how many, discrete number, of the 900 students at the school attended all three days. And we can surmise that they’re going to come at us by giving us different breakdowns of how different groups of students behaved and so most likely we’re going to need more than one piece of information to come together in order to give us the precise amount. The only way, typically, that we would have a single piece of information be sufficient is if they gave us the inverse and told us how many, or what percentage, or what fraction of students didn’t attend on all three days. Where we could then compute the opposite.

Statement 1

Let’s take a look: Number 1 is telling us that 30% or 270 of the students attended two or more days. If we break this up into a chart, we see this block that’s undefined but we know that 270 attended either two days or three days. Some mix of them, but we don’t know that mix. Therefore, this doesn’t give us what we need from the box and it’s insufficient. However, we could use it possibly with other information that distinguishes between the two day visitors and the three day visitors.

Statement 2

Number 2 gives us relative information based upon some other number: 10% of those that attended at least one day. That means of all those that attended at all, for one day, for two days, for three days, 10% of those belong in the three-day box. However, we don’t know how many students that is. So 2 is insufficient. When we try and combine them notice that the information from 2 slices and dices a piece of information that 1 doesn’t give us. There’s no way to reconcile the 10% from that big group into the group that just attended two days or three days. Therefore, we don’t have enough information.

Answer

The answer choice is E: both together are still insufficient. Hope this helped. Guys thanks for watching! For other examples of DS problems where you can make charts to fill in the blanks and find the square you need check out the links below and we’ll see you again soon.

If you enjoyed this Data Sufficiency problem video try this Standard Deviation Problem

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GMAT Prime numbers article with questions
Posted on
29
Mar 2021

A Primer on Primes

By: Rich Zwelling (Apex GMAT Instructor)
Date: 30th March 2021

As I said in my previous post, GMAT Prime Numbers are my favorite topic. This is because not only are they inherently interesting mathematically but they show up in unexpected circumstances on GMAT problems, even when the term “prime” is not explicitly mentioned.

But before we get to that, I thought it would help to review a basic definition:

If you’ve gone through school, you’ve likely heard the definition of a prime as “any number that can be divided only by 1 and itself.” Or put differently, “any number that has only 1 and itself as factors.”  For example, 3 is a prime number, because 1 and 3 are the only numbers that are factors of 3.

However, there is something slightly problematic here. I always then ask my students: “Okay, well then, is 1 prime? 1 is divisible by only 1 and itself.” Many people are under the misconception that 1 is a prime number, but in truth 1 is not prime

There is a better way to think about prime number definitionally:

*A prime number is any number that has EXACTLY TWO FACTORS*

By that definition, 1 is not prime, as it has only one factor

But then, what is the smallest prime number? Prime numbers are also by definition always positive, so we need not worry about negative numbers. It’s tempting to then consider 3, but don’t overlook 2. 

Even though 2 is even, it has exactly two factors, namely 1 and 2, and it is therefore prime. It is also the only even prime number. Take a moment to think critically about why that is before reading the next paragraph…

Any other even number must have more than two factors, because apart from 1 and the number itself, 2 must also be a factor. For example, the number 4 will have 1 and 4 as factors, of course, but it will also have 2, since it is even. No even number besides 2, therefore, will have exactly two factors. 

Another way to read this, then, is that every prime number other than 2 is odd

You can see already how prime numbers feed into other number properties so readily, and we’ll talk much more about that going forward. But another question people often ask is about memorization: do I have to memorize a certain number of prime values? 

It’s good to know up to a certain value. but unnecessary to go beyond that into conspicuously larger numbers, because the GMAT as a test is less interested in your ability to memorize large and weird primes and more interested in your reasoning skills and your ability to draw conclusions about novel problems on the fly. If you know the following, you should be set (with some optional values thrown in at the end):

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, (41, 43)

Thankfully, you’ll notice the list is actually pretty manageable. 

(And an interesting note that many people forget that 27 is actually not prime. But don’t beat yourself up if this happens to you: Terence Tao, one of the world’s leading mathematicians and an expert on prime numbers, actually slipped briefly on national television once and said 27 was prime before catching himself. And he’s one of the best in the world. So even the best of the best make these mistakes.)

Now, here’s an Official Guide problem that takes the basics of Prime Numbers and forces you to do a little reasoning. As usual, give it shot before reading the explanation:

The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ?

A) 109
B) 108
C) 107
D) 106
E) 105

Explanation

For this one, you have a little hint going in, as we’ve provided you with the necessary list of primes you’ll use to find the product.

And the language given (“closest to”) is a huge hint that you can estimate:

2*3*5*7*11*13*17*19 ~= ??

Since powers of 10 are involved, let’s try to group the numbers to get 10s as much as possible. The following is just one of many ways you could do this, but the universal easiest place to start is the 2 and the 5, so let’s multiply those. We’ll mark numbers we’ve accounted for in red:

(2*5)*3*7*11*13*17*19 ~= ??

10*3*7*11*13*17*19 ~= ??

Next, we can look at the 19 and label it as roughly 20, or 2*10:

10*3*7*11*13*17*19 ~= ??

10*3*7*11*13*17*20 ~= ??

10*3*7*11*13*17*2*10 ~= ??

We could also take the 11 and estimate it as another 10:

10*3*7*11*13*17*2*10 ~= ??

10*3*7*10*13*17*2*10 ~= ??

At this point, we should be able to eyeball this. Remember, it’s estimation. We may not know 17*3 and 13*7 offhand. But we know that they’re both around or less than 100 or 102. And a look at the answer choices lets us know that each answer is a factor of 10 apart, so the range is huge. (In other words, estimation error is not likely to play a factor.)

So it’s not unreasonable in the context of this problem to label those remaining products as two values of 102:

10*3*7*10*13*17*2*10 ~= ??

10*(102)*10*(102)*2*10 ~= ??

And at this point, the 2 is negligible, since that won’t be enough to raise the entire number to a higher power of 10. What do we have left?

101*(102)*101*(102)*101 ~= 107 

The correct answer is C. 

Next time, we’ll get into Prime Factorizations, which you can do with any positive integer.

Find other GMAT Number Theory topics here:
Odds and Ends (…or Evens)
Consecutive Integers (plus more on Odds and Evens)
Consecutive Integers and Data Sufficiency (Avoiding Algebra)
GMAT Prime Factorization (Anatomy of a Problem)
A Primer on Primes

 

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Consecutive Integers and Data Sufficiency (Avoiding Algebra) Article
Posted on
25
Mar 2021

Consecutive Integers and Data Sufficiency (Avoiding Algebra)

By: Rich Zwelling (Apex GMAT Instructor)
Date: 25 March 2021

Last time, we left off with the following GMAT Official Guide problem, which tackles the Number Theory property of consecutive integers. Try the problem out, if you haven’t already, then we’ll get into the explanation:

The sum of 4 different odd integers is 64. What is the value of the greatest of these integers?
(1) The integers are consecutive odd numbers
(2) Of these integers, the greatest is 6 more than the least.

Explanation (NARRATIVE or GRAPHIC APPROACHES):

Remember that we talked about avoiding algebra if possible, and instead taking a narrative approach or graphic approach if possible. By that we meant to look at the relationships between the numbers and think critically about them, rather than simply defaulting to mechanically setting up equations.

(This is especially helpful on GMAT Data Sufficiency questions, on which you are more interested in the ability to solve than in actually solving. In this case, once you’ve determined that it’s possible to determine the greatest of the four integers, you don’t have to actually figure out what that integer is. You know you have sufficiency.)

Statement (1) tells us that the integers are consecutive odd numbers. Again, it may be tempting to assign variables or something similarly algebraic (e.g. x, x+2, x+4, etc). But instead, how about we take a NARRATIVE and/or GRAPHIC approach? Paint a visual, not unlike the slot method we were using for GMAT combinatorics problems:

___ + ___ +  ___ + ___  =  64

Because these four integers are consecutive odd numbers, we know they are equally spaced. They also add up to a definite sum.

This is where the NARRATIVE approach pays off: if we think about it, there’s only one set of numbers that could fit that description. We don’t even need to calculate them to know this is the case.

You can use a scenario-driven approach with simple numbers to see this. Suppose we use the first four positive odd integers and find the sum:

_1_ + _3_ +  _5_ + _7_  =  16

This will be the only set of four consecutive odd integers that adds up to 16. 

Likewise, let’s consider the next example:

_3_ + _5_ +  _7_ + _9_  =  24

This will be the only set of four consecutive odd integers that adds up to 24. 

It’s straightforward from here to see that for any set of four consecutive odd integers, there will be a unique sum. (In truth, this principle holds for any set of equally spaced integers of any number.) This essentially tells us [for Statement (1)] that once we know that the sum is set at 64 and that the integers are equally spaced, we can figure out exactly what each integer is. Statement (1) is sufficient.

(And notice that I’m not even going to bother finding the integers. All I care about is that I can find them.)

Similarly, let’s take a graphic/narrative approach with Statement (2) by lining the integers up in ascending order:

_ + __ +  ___ + ____  =  64

But very important to note that we must not take Statement (1) into account when considering Statement (2) by itself initially, so we can’t say that the integers are consecutive. 

Here, we clearly represent the smallest integer by the smallest slot, and so forth. We’re also told the largest integer is six greater than the smallest. Now, again, try to resist the urge to go algebraic and instead think narratively. Create a number line with the smallest (S) and largest (L) integers six apart:

S—————|—————|—————|—————|—————|—————L

Narratively, where does that leave us? Well, we know that the other two numbers must be between these two numbers. We also know that each of the four numbers is odd. Every other integer is odd, so there are only two other integers on this line that are odd, and those must be our missing two integers (marked with X’s here):

S—————|—————X—————|—————X—————|—————L

Notice anything interesting? Visually, it’s straightforward to see now that we definitely have consecutive odd integers. Statement (2) actually gives us the same information as Statement (1). Therefore, Statement (2) is also sufficient. The correct answer is D

And again, notice how little actual math we did. Instead, we focused on graphic and narrative approaches to help us focus more on sufficiency, rather than actually solving anything, which isn’t necessary.

Next time, we’ll make a shift to my personal favorite GMAT Number Theory topic: Prime Numbers…

Find other GMAT Number Theory topics here:
Odds and Ends (…or Evens)
Consecutive Integers (plus more on Odds and Evens)
Consecutive Integers and Data Sufficiency (Avoiding Algebra)
GMAT Prime Factorization (Anatomy of a Problem)
A Primer on Primes

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Posted on
24
Mar 2021

Standard Deviation Problem On The GMAT (Normative Distribution)

Standard Deviation 700+ Tips

Hey guys! Today, we’re going to take a look at a standard deviation problem. And standard deviation is a concept that only comes up infrequently on the GMAT. So it’s more important to have a basic understanding of the concepts associated with it than to go really deep. This is true largely for much of the statistics, probability, and combinatorics problems. They show up infrequently until you get to the higher levels and even when you’re at the higher levels, relative to the algebra, arithmetic and even the geometry problems, they play such a small role.

And yet there’s so much math there that it’s very easy to get caught up in spending a lot of time prepping on problems or on these types of math that offer very little in return relative to spending your prep time really mastering the things that come up frequently. I’m not saying don’t learn this stuff I’m saying balance it according to its proportionality on the GMAT. As a general rule you can assume that stat, combinatorics and probability, all that advanced math, constitutes maybe 10 to 15% of what you’ll see on the GMAT. So keep that in mind as you prep.

Problem Language

In this problem the first step is to figure out what the heck we’re actually being asked for and it’s not entirely clear. This one’s written a little bit in math speak. So we have a normal distribution which doesn’t really matter for this problem but if you studied statistics it just means the typical distribution with a mean m in the middle and a standard deviation of d which they tell us is a single standard deviation. So they’re really just telling us one standard deviation but they’re saying it in a very tricky way and they’re using a letter d. If it helps you can represent this graphically.

Graphical Representation

Notice that they tell you something that you may already know: that one standard deviation to either side of the mean is 68 in a normal distribution. This breaks up to 34, 34. But they’re asking for everything below. The +1 side of the distribution. Since the m, the mean is the halfway point, we need to count the entire lower half and the 34 points that are in between the mean and the +d, the +1 standard deviation. This brings us to 84 which is answer choice D. This is primarily a skills problem, that is, you just need to know how this stuff works. There’s no hidden solution path and the differentiation done by the GMAT here is based upon your familiarity with the concept. Rather than heavy-duty creative lifting as we see on so many other problems that have more familiar math, that everyone kind of knows.

I hope this was helpful. Check out below for other stat and cool problem links and we’ll see you guys next time. If you enjoyed this GMAT Standard Deviation problem, try this Data Sufficiency problem next.

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