GMAT Prep & Test Approaches to Score in the 650 - 700 range
Posted on
01
Jun 2021

GMAT Prep & Test Approaches to Score in the 650 to 700 Range

By: Andrej Ivanovski
Date: 1st June 2021

Getting a good GMAT score is no walk in the park. A lot of test takers struggle with hitting the minimum score to get into their desired graduate program, and they find themselves taking the GMAT multiple times before achieving their score goal. But, what is a good GMAT score? The answer is, as you might have guessed, it depends. Different business schools have different expectations. What might be considered an excellent score at one school, could be viewed as acceptable but not stellar at another.

Therefore, it is safe to say that a good GMAT score is one that gets you into the graduate program of your choice. However, one thing to keep in mind is that sometimes achieving the minimum scoring requirement may not be enough. Generally speaking, it is better to aim for the average class GMAT score, or higher. A score in the 650 to 700 range is very likely to secure you a spot at some great business schools (given that you satisfy the other admission requirements), but at the end of the day, it all depends on the specific program that you are applying to. In this article, we are going to look at some of the most important GMAT prep and test approaches which can help you score in the 650 to 700 range.

4 Tips to Score in the 650 – 760 Range

Practice your pacing

Wouldn’t the GMAT be a whole lot easier if you did not have to think about timing? Timing is a huge issue and often curtails test takers from attaining their desired score. If you distribute the given time equally, you only have around two minutes per question. Planning your time accordingly is integral to success, spending less time on easier questions allows you to spend more time on more challenging ones. Different questions have different difficulty levels, so it is normal that some questions might take longer than others. Our advice is to forget about the timing aspect of your GMAT prep altogether, and instead focus on mastering the skills you need to answer the questions correctly. In this way you will find that timing issues take care of themselves. If you want to learn more pacing techniques, make sure to check out our video on time management.

Learn how to skim

This one might seem obvious – and you might even say: “Of course I know how to skim”. But do you really? A lot of people think that they are skimming a passage, when in fact they are skipping it. The difference between skimming and skipping is that skimming includes paying attention to the author’s tone and point of view, but without actually reading the passage word for word. When you find yourself being able to take away the important pieces of information from the passage, and understand what the author is trying to say, then it is safe to say that you have learned how to skim. Mastering the art of skimming can help you do well on the Verbal section, which can ultimately lead you to a 650 – 700 GMAT score.

Pay attention to transition words

We definitely do not mean to sound like your middle school English teacher, but paying attention to transition words could save you a whole lot of time on the GMAT. Transition words are used to show the relationship between sentences (or parts of sentences). For instance, if the author is using transition words such as “however”, “nevertheless”, “in spite of”, “on one hand” or “on the contrary”, then you would know that the author is trying to express a contrasting point. Even though you can understand that by reading the whole passage, paying attention to transition words can save you a lot of time.

Use an appropriate strategy to solve quant problems

No matter how well prepared you are, there are always going to be questions whose answers you are not entirely sure of. Of course, it should be your goal to reduce the chances of that happening, but the GMAT is not designed to be that easy. When you find yourself struggling to answer a question, at first it might seem like all of the answers make sense. For that reason, it is good to have multiple strategies to tackle all types of GMAT problem types.

  • Elimination: write down ABCDE on the scratch board, and work on eliminating the answers that do not make much sense. When you are left with 2 or 3 answers to pick from, the chances of getting the right one are much higher (you do the math).
  • Guessing: leaving questions unanswered on the GMAT is not a good practice, as it is not favored by the grading algorithm. That is why it is important that you answer all of the questions from a given section, even if that means guessing the answer to some questions that you are not sure about.
  • Graphical solution path: sometimes it is easier to solve a problem graphically, rather than taking the standard, mathematical approach. Our instructor, and director of curriculum development, Mike Diamond, talks about the graphical solution path in his videos. If you want to find out more about this approach, see how he solves the Snack Shop problem and the Rope problem using a graphical solution path.
  • Story telling: some problems on the GMAT might require you to put yourself in the story and retell it from your perspective. This is especially useful when you are given information about two or more entities relative to each other. For instance, For some questions like, John was three years older than Tim was 5 years ago. Tim will be 23 two years from now. How old is John now? Here putting yourself in the story and retelling it can help you make the information easy to follow

Which schools can a 650 – 700 GMAT score get you into?

A GMAT score in the 650 – 700 can definitely get you into some of the highest ranked MBA programs in the world, and our clients are proof of that.

Kyle

kyle scored a 650 after working with Apex and got accepted to Georgetown university
Kyle scored 650 on the GMAT and he was able to get into the McDonough School of Business at Georgetown University. In his words:  I wouldn’t be in business school if I hadn’t gone through this process with an Apex tutor, not only from a scoring standpoint but also from a mental preparation standpoint.

Amy

amy scored a 690 on her GMAT and went to dukeAmy got into the Fuqua School of Business at Duke University with a GMAT score of 690. She says: After working with Apex I could look at a problem and know exactly what they were testing me on and the steps that I needed to take to get to the desired solution. They were always there to help and offered multiple solution paths in case the first one did not resonate.

Lohe

lohe scored a 690on her gmat and got into columbiaA GMAT score of 680 was able to help Lohe get into Columbia University. She says: When I started working with Apex we mostly focused on improving my stress and anxiety. So we worked on different kinds of breathing exercises and on different problem solving techniques that were not the usual math solutions. Once I was able to get comfortable with these techniques my speed and score increased a lot. It was a good mix of stress management and thinking out of the box.

 

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Posted on
13
May 2021

GMAT Factors Problem – 700 Level GMAT Question

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.

Important Notes About Factors

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.

 

 

 

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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
14
Apr 2021

GMAT Percentage Problem – Unemployment Rate -Multiple Solution Paths

GMAT Percentage Problems

Hey guys, GMAT Percentage problem/s are commonplace on the GMAT and today we’re going to take a look at one that is straightforward but could very easily get you caught up with the math. In this problem, notice that there’s the word “approximately.” That always means there’s an Estimation Solution Path. We’ll take a look at that first but then we’re going to look at a Scenario Solution Path, which for many people is a lot more natural. In addition to seeing that word approximately you can see that there’s this massive spread within the answer choices. Once again pushing us towards an Estimation Solution Path.

Estimation Solution Path

So let’s dive in: The unemployment rate is dropping from 16% to 9% and your quick synthesis there should be: okay it’s being cut about in half or a little less than half. And monitoring that directionality is important. Additionally, the number of workers is increasing. So we have lower unemployment but a greater number of workers. So we have two things, two forces working against one another. If the number of workers were remaining equal then our answer would be about a 50% decrease or just under a 50% decrease, so like 45% or something like that. But because we’re increasing the number of workers, our decrease in unemployment is lower. That is we have more workers, so we have a larger number of unemployed so we’re not losing as many actual unemployed people and therefore our answer is B: 30% decrease.

Scenario Solution Path

If we want to take a look at this via Scenario, we can always throw up an easy number like 100. We begin with 100 workers and 16% are unemployed so 16 are unemployed. Our workers go from 100 to 120. 9% of 120 is 9 plus 0.9 plus 0.9 = 10.8% or 11%. What’s the percentage decrease from 16 to 11? Well it’s not 50, that’s too big. It’s not 15, that’s too small. It’s about 30 and the math will bear us out there.

So thanks for watching guys! Check out the links below for other GMAT percentage problem/s and we look forward to seeing you again real real soon.

Another GMAT percentage problem

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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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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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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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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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