GMAT Most Asked Questions
Posted on
03
May 2022

GMAT Most Asked Questions 2022

If you’re thinking about taking the GMAT or have already registered for a testing date, you undoubtedly have a ton of questions swirling around in your mind. In this blog post, we’ll answer some of the GMAT FAQs in 2022.

1. What does GMAT stand for?

The GMAT stands for General Management Admission Test. The GMAT is a standardized test that measures your analytical, writing, quantitative, and verbal skills. The GMAT is used by business schools to help decide which applicants to admit into their programs.

2. Who conducts the GMAT exam?

The administrator of the GMAT is the General Management Admission Council (GMAC).

3. Why is the GMAT exam required for MBA?

The exam is considered to be a predictor of academic success for MBA programs and business careers. The GMAT tests reasoning and problem-solving skills, and critical thinking. It is also a measure of verbal, mathematical, and analytical writing skills.

4. When can I register for the GMAT 2022?

You can register for the GMAT between 6 months to 24 hours before the exam. However, we recommend you register 3 months in advance. 

5. How do I register for the GMAT 2022?

To register online you will need to:

    • Create an account on the mba.com website.
    • Verify your email.
    • Book a date.
    • Pay the application fee of $250.

You can also register through fax, phone, or mailThe registration process can take 15 to 30 minutes. 

6. How much does the GMAT cost?

The GMAT costs $250, approximately 230 euros and 190 pounds. The price may differ by country.

7. Where to take the GMAT?

You can find the nearest testing center on the mba.com website or take the exam online. 

8. Can the GMAT exam be taken online?

Yes, the GMAT exam can be taken online. The GMAC has decided to make the online GMAT a permanent option, after it was introduced at the beginning of the pandemic, along with in-person exams. 

9. When is the GMAT exam held in 2022?

GMAT is available almost all year round. Testing dates are available 6 months in advance. You can book an available slot in the nearest testing center, appointments are usually available 6 days a week in most countries. If you are taking the GMAT online, you can take the exam 7 days a week.

We recommend registering 3 months in advance or no more than 3 weeks ahead.

10. How to reschedule my GMAT exam?

You can reschedule your GMAT online or by phone up to 24 hours prior to the exam. Note that if you cancel by phone, you will be charged an additional fee of $10. A rescheduling fee applies if you decide to reschedule your exam:

    • 14 days to 24 hours prior to the exam: $150
    • 15 to 60 days prior to the exam: $100
    • 60 days prior to the exam: $50

11. How often can I take the GMAT?

You can take the GMAT 5 times in a 12-months period. However, you can’t take it more than once in a 16-day period. However, we recommend not to retake the exam in less than 3 months. It’s unlikely that your score would improve drastically in a short period of time.

12. Are GMAT and GRE similar?

The main difference between GMAT and GRE is that the GMAT is designed specifically for business schools, while the GRE is accepted by a series of master’s programs. The GRE keeps your options open in case you haven’t made up your mind about your master’s degree. However, keep in mind that not all business schools accept GRE. Also, make sure you contact your admissions office and check which exam they prefer.

13. How long should I study for the GMAT?

There is no one-size-fits-all answer to this question. The GMAT journey is unique to everyone, and you’re the only one to know what’s right for you. However, on average candidates spend 3-6 months preparing for the GMAT. We recommend a 3-month GMAT study plan, which can be shrunk or stretched according to your schedule.

14. Can GMAT be cracked without a private tutor?

When you start preparing for the GMAT, you need to establish some goals and a study plan. Achieving the score you’re aiming for is not an easy mission. The GMAT prep requires perfect preparation and continuous motivation and dedication. If you find yourself falling behind and you aren’t anywhere near where you planned to be, you might consider hiring a GMAT tutor. Having someone by your side step-by-step can make the prep journey easier on academic and social aspects.

Before hiring a GMAT tutor do your research to find the best tutor for you. At Apex we offer personalized tutoring according to each candidate’s needs. We provide a free complimentary consultation call for your questions about GMAT private tutoring.

15. Can I use a calculator on the GMAT?

You are not allowed to bring in your own calculator. However, you will be provided with a calculator only during the Integrated Reasoning section. During the Quantitative section, you won’t be able to use a calculator, but you will be given a note board and markers to do calculations.

16. Can I skip questions on the GMAT exam?

No, you need to provide an answer before moving to the next questions. The GMAT is a computer-adaptive test (CAT) which means that the questions’ difficulty adapts to your skill level. As you progress, the difficulty of the next question is based on your performance on the previous one. Therefore, you can’t skip a question.

17. Are GMAT questions repeated?

Yes, and no. GMAT questions don’t repeat but the concepts and the patterns do. Often elements of some questions will be reused to formulate a new one, but not the same question.

18. How does the GMAT scoring work?

The way GMAT scoring works can be complicated since it’s a CAT. The GMAT is scored on a scale from 200 to 800, with 800 being a perfect score. Each section of the GMAT is scored individually.

The overall 800-score is done by a confidential algorithm by the GMAC.

19. Are the GMAT results instant?

Right after the exam, you will have an unofficial report with the scores of your Quant, Verbal and Integrated Reasoning section. You have up to two minutes to accept or cancel them. If you don’t make a decision your score will be automatically canceled.

In case you accept the results, you and the schools you have chosen to send the reports to will receive an official report up to 20 days after the exam. The official report will also include the Analytical Assessment score and your GMAT percentile ranking. 

In case you cancel your results, they won’t show up on your score report.

20. What GMAT score do I need?

There is no “passing” score on the GMAT. To know what score you’re aiming for, you need to check the class profile and the admission requirements of the programs you’re looking at. Your score goal may differ depending on your school(s) needs.  

21. Can I cancel my GMAT score?

You can cancel your GMAT score immediately after the exam at no cost. The score can be canceled up to 72 hours after the exam for a fee. If you cancel your score, it will not be shown on your score reports. If you cancel your score and want to reinstate it, you can do so online or by phone for a fee of $50. An additional $10 fee applies if you cancel by phone.

22. For how many years is the GMAT valid?

Your GMAT score is valid for 5 years after you take the exam.

23. Can the GMAT be waived?

Few schools in the US have policies for waving the GMAT, those are usually significant professional work experience, degrees, or high achievements. The applications are reviewed on a case-by-case basis. Other schools accept the GRE instead of the GMAT.

 

If you have questions that we haven’t answered, book a 30-minute complimentary consultation call with one of our top GMAT instructors or check our article on GMAT Test Days FAQs.

 

Contributor: Cynthia Addoumieh

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2 Types Of GMAT Videos That You Should Include In Your Prep
Posted on
14
Oct 2021

2 Types Of GMAT Videos That You Should Include In Your Prep

As everything is shifted online due to the recent global events, students have had to find ways to prepare for the online GMAT exam from the comfort of their own homes. The good news is that they no longer need to sit down and read books and guides to excel at the GMAT. Times have changed and there are now so many handy sources that can help you succeed. And now more than ever, people are including GMAT videos in their preparation strategy and are relying on them as sources for information and different solution paths.

GMAT Prep Videos

GMAT prep videos are especially important for visual learners who tend to learn better by looking at the information presented to them. Watching videos as part of the learning process has proven to be a good approach that definitely improves the learning experience for most students. Videos are also more time-effective as you get to access and absorb information in a shorter period of time. However, one thing to be mindful of is not to focus only on videos while preparing for the exam, as other mediums can offer just as much information as a video does.

GMAT prep videos can prove to be very helpful if they are utilized in a moderate way and are a great way to give you insights on what to expect on the exam day. They usually come in 2 main types and we will tell you more about how to utilize them in this guide: 

Problem Videos

The first type of GMAT prep video is the problem video. These usually include solved examples and problem-solving strategies. They aim to show you concrete examples and clear illustrations of how best to look at the problem and solve it in an efficient manner. If you are struggling with probability or combinatorics problem types, videos explaining these will aid you in the problem-solving process.

One such example is this video where Mike, our Head of Curriculum, explains in detail the solution path for a Percentage Problem commonly found in the GMAT exam. He goes into detail about the process of coming up with a solution to the problem and discusses every single answer choice in order to give you a better understanding of how to tackle the problem and how to get to the correct answer.

Another GMAT video to look out for is the Strategies video where you’re presented with different strategies and some best practices that you can use to go about a certain type of problem on the GMAT exam. These videos can really come in handy, especially because they are more generalized and you can easily use the approach shown on the video for a lot of problems you come across. Here’s an example of a strategy video, where Mike explains the best ways to approach a Data Sufficiency problem in the GMAT.

GMAT Advice

The second type of GMAT prep video that you can utilize to help you with your preparation are GMAT advice videos.

Generally, experience videos give you a better perspective of what to expect on exam day. Here’s an experience video where you are given more information about the online GMAT and how to go about taking it.

Another type of GMAT advice video to watch out for is the testimonial videos. These include actual test-takers’ testimonials and you’ll get to hear more about other people’s experience with certain aspects/sections of the exam. That way, you can definitely find ones that you can relate to and use to your own advantage. This is David’s testimonial where he discusses working with ApexGMAT and how that improved his score immensely. 

Key Takeaways

It is clear now how essential GMAT prep videos can be when it comes to your preparation. 

But there is one last thing to keep in mind: do NOT use these GMAT videos as your only source to help you with your prep. They can be especially helpful as they cover different topics in a short amount of time, but they can never replace detailed guides and actual practice.

 

Contributor: Altea Sulollari

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GMAT Probability Problems
Posted on
12
Aug 2021

GMAT Probability Problems – How to Tackle Them & What Mistakes to Avoid

By: Apex GMAT
Contributor: Ilia Dobrev
Date: August 12, 2021

The concept of probability questions is often pretty straightforward to understand, but when it comes to its application in the GMAT test it may trip even the strongest mathematicians.

Naturally, the place to find such types of problems is the Quantitative section of the exam, which is regarded as the best predictor of academic and career success by many of the most prestigious business schools out there – Stanford, Wharton, Harvard, Yale, INSEAD, Kellogg, and more. The simple concept of probability problems can be a rather challenging one because such questions appear more frequently as high-difficulty questions instead of low- or even medium-difficulty questions. This is why this article is designed to help test-takers who are pursuing a competitive GMAT score tackle the hazardous pitfalls that GMAT probability problems often create.

GMAT Probability – Fundamental Rules & Formulas

It is not a secret that the Quantitative section of the GMAT test requires you to know just the basic, high-school-level probability rules to carry out each operation of the practical solution path. The main prerequisite for success is mastering the Probability formula:
Probability = number of desired outcomes / total number of possible outcomes

Probability = number of desired outcomes
total number of possible outcomes

We can take one fair coin to demonstrate a simple example. Imagine you would like to find the probability of getting a tail. Flipping the coin can get you two possible comes – a tail or a head. However, you desire a specific result – getting only a tail – which can happen only one time. Therefore, the probability of getting a tail is the number of desired outcomes divided by the number of total possible outcomes, which is ½. Developing a good sense of the fundamental logic of how probability works is central to managing more events occurring in a more complex context.

Alternatively, as all probabilities add up to 1, the probability of an event not happening is 1 minus the probability of this event occurring. For example, 1 – ½ equals the chance of not flipping a tail.

Dependent  Events vs. Independent Events

On the GMAT exam, you will often be asked to find the probability of several events that happen either simultaneously or at different points in time. A distinction you must take under consideration is exactly what type of event you are exploring.

Dependent events or, in other words, disjoint events, are two or more events with a probability of simultaneous occurrence equalling zero. That is, it is absolutely impossible to have them both happen at the same time. The events of flipping either a tail or a head out of one single fair coin are disjoint.

If you are asked to find a common probability of two or more disjoint events, then you should consider the following formula:

Probability P of events A and B   =    (Probability of A) + (Probability of B)

Therefore, the probability of flipping one coin twice and getting two tails is ½ + ½.

If events A and B are not disjointed, meaning that the desired result can be in a combination between A and B, then we have to subtract the intersect part between the events in order to not count it twice:

Probability P of events A and B   =    P(A) + P(B) – Probability (A and B)

Independent events or discrete events are two or more events that do not have any effect on each other. In other words, knowing about the outcome of one event gives absolutely no information about how the other event will turn out. For example, if you roll not one but two coins, then the outcome of each event is independent of the other one. The formula, in this case, is the following:

Probability P of events A and B   =    (Probability of A) x (Probability of B)
How to approach GMAT probability problems

In the GMAT quantitative section, you will see probability incorporated into data sufficiency questions and even problems that do not have any numbers in their context. This can make it challenging for the test taker to determine what type of events he or she is presented with.
One trick you can use to approach such GMAT problems is to search for “buzzwords” that will signal out this valuable information.

  • OR | If the question uses the word “or” to distinguish between the probabilities of two events, then they are dependent – meaning that they cannot happen independently of one another. In this scenario, you will need to find the sum of the two (or more) probabilities.
  • AND | If the question uses the word “and” to distinguish between the probabilities of two events, then they are independent – meaning their occurrences have no influence on one another. In this case, you need to multiply the probabilities of the individual events to find the answer.

Additionally, you can draw visual representations of the events to help you determine if you should include or exclude the intersect. This is especially useful in GMAT questions asking about greatest probability and minimum probability.

If you experience difficulties while prepping, keep in mind that Apex’s GMAT instructors have not only mastered all probability and quantitative concepts, but also have vast experience tutoring clients from all over the world to 700+ scores on the exam. Private GMAT tutoring and tailored customized GMAT curriculum are ideal for gaining more test confidence and understanding the underlying purpose of each question, which might be the bridge between your future GMAT score and your desired business school admissions.

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Posted on
28
Jul 2021

GMAT Trade Show Problem – Data Sufficiency

GMAT Trade Show Problem Introduction

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

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

Solving the GMAT Problem

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

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

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

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

 

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Posted on
21
Jul 2021

GMAT 3D Geometry Problem – GMAT Math – Quant Section

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 question

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.

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Posted on
15
Jul 2021

10 Things To Consider Before You Begin Your GMAT Prep

1. Get Comfortable With The GMAT Structure

Before doing anything else, you need to familiarise yourself with the GMAT structure.

     1- Analytical Writing Assessment (AWA section)

This section concentrates on critical analysis and idea communication. You will be presented with an argument where a strong analysis of the reasoning behind the given argument should be provided. (30 minutes, 1 question)

     2- Integrated Reasoning (IR section)

The second part of the exam evaluates the ability to assess information and interpret data displayed in different formats. (30 minutes, 12 questions) 

    3- Quantitative Reasoning (Quant section)

This section measures the ability to solve mathematical and quantitative problems as well as the ability to interpret data. There are two types of questions in the Quantitative Section – Problem Solving and Data Sufficiency. Both types of questions require some knowledge of arithmetic, elementary algebra, and commonly known geometry concepts. Since there are 31 questions in Quantitative Reasoning, about 15 of them will be data sufficiency questions which are quite confusing and unique. (62 minutes, 31 questions)

     4-Verbal Reasoning (Verbal section)

This is the final section, which evaluates reading comprehension skills, editing abilities, and whether you can make sense of written arguments. (65 minutes, 36 questions)

2. GMAT Scores are Valid for Five Years

You will receive your official GMAT score within 20 days of taking the exam. Your GMAT test score is valid for five years. Before taking or preparing for the GMAT, it is essential to know when to take the exam. If you already have a particular school or program in mind then you have to schedule your test based on the deadlines the school has specified. Nevertheless, it is good to keep in mind how long GMAT scores are valid for if you are uncertain about when you will apply to schools.

3. Two Sections of the GMAT are Computer-Adaptive

The GMAT is a Computer Adaptive exam. Two sections of GMAT, the Quantitative and Verbal Reasoning sections are Computer-adaptive. So, what does it mean? If you answered a hard level question correctly the next question will be more complex. If you answered a question wrong then the other question will be easier. In these sections, the difficulty of the questions take into consideration the number of questions that you previously answered correctly or incorrectly.  

4. Take a Practice Test Before Starting Preparation for the GMAT Exam

Before starting the preparation for the GMAT exam, take a GMAT practice test to find out your baseline, how well prepared you are, and how far off you are from your target score. In this way, you will get familiar with the question types and style and understand the time frame. Via this method, you can compare your starting point versus the ending when you take the actual GMAT exam.  

5. Familiarize Yourself with the Style and Format of the Exam

The GMAT exam is different from other exams such as SAT, TOEFL, ACT. You need to become familiar with the format of the questions so that during the exam, you won’t allocate too much time to understanding the questions. Some GMAT sections have unique question types that might confuse the test-takers, such as the quantitative (data sufficiency) and integrated reasoning sections where some questions will require more than one response. You will save time and feel comfortable with the questions if you know them beforehand—especially the data sufficiency questions from the quantitative section. 

6. Practice Without a Calculator

The GMAT exam doesn’t allow calculators on the Quant section. This may sound tough, but in actuality, it is for the best since you need to train your mind and mental math to solve the problems. It may also indicate that the problems aren’t that complex and that you can solve them without using a calculator. However, working without a calculator is challenging since you need to carefully check your calculations after every step to ensure you don’t have errors. Therefore, to prepare yourself for this challenge, try practicing from the beginning without a calculator. Instead, become familiar with what it feels like and gain experience using the math problems by hand. Another trick that can help you during this process is familiarizing yourself with the GMAT tips you can use while solving the GMAT questions.

10 gmat tips7. Define your Strengths and Weaknesses

This analysis will help you know what you are good at and what you need to improve. First of all, plan your strategy about how you are going to analyze your weaknesses and strengths. It can be by taking the GMAT practice exam once and then figuring out which areas you felt particularly weak or strong in. Another option is to maintain a notebook for a week and mark down the weaknesses and strengths you encounter during your initial studying. Via this analysis, you might get a sense of whether you are good at time management, what your speed is, and much more. During the analysis, try to identify which question types are the most challenging for you in each section. Figure out what soft skills you have that might help you during the exam and pinpoint the ones that need improvement. After that, conclude and start working on developing new skills and overcoming weaknesses. Always keep in mind having an achievable goal for the final target as a score. Scoring a 700 or higher on the GMAT isn’t always easy! 

8. Design a Study Plan

After acknowledging your strengths and weaknesses, design a personalized study plan to guide you throughout your preparation, decide what sources and courses you need, whether you are going to prepare only with tests, or go step by step through topics and sections. Schedule your learning format and decide which strategy fits the best with your prep level. You might also consider taking courses with a GMAT private tutor, with which you will get a lot of help and guidance in your GMAT preparation creed.

9. Keep Track of Time

When preparing for the GMAT exam try to keep track of your time to allocate it equally to each section. However, do this step after you have identified what concepts are complicated for you in order to allocate more time on those topics and train yourself to solve those problems. Practice pacing because GMAT time management is critical in order to complete the exam. The worst scenario in the GMAT exam is that sometimes the test takers run out of time towards the end. This is because some of the test takers do not stick with the time and fall behind. Thus, set and stick to certain time milestones to finish the exam on time.

10. Keep Going, Do Not Get Stuck on a Question

It is also essential to remember that you don’t need to answer every question correctly and that completing the exam is most important. This is because your score will decrease if you do not complete the sections of the GMAT. 2 minutes is more than enough for each question. So, if you are stuck, make an educated guess and move on to another question. 

Conclusion

In conclusion, before preparing for the GMAT exam, first, know about the GMAT exam structure and familiarize yourself with the format and style, then take a practice test to find out your score as well as your weaknesses and strengths. After that, design your study plan and hit the green light! Of course, while practicing for the GMAT exam, try not to use a calculator, keep track of time and concentrate on learning rather than answering all the questions correctly. Finally, consider having a GMAT tutor along the way, should you think having a professional guiding you throughout the process is an effective way for you to succeed. 

 

Contributor: Simona Mkhitaryan

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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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When Probability Meets Combinatorics: One Problem, Two Approaches article
Posted on
16
Mar 2021

When Probability Meets Combinatorics: One Problem, Two Approaches

By: Rich Zwelling, Apex GMAT Instructor
Date: 16th March, 2021

Now, we’d like to take a look at an Official GMAT Probability problem to pull everything together. The following is a good example for two reasons:

 1. It illustrates a quirky case that is difficult more conceptually than mathematically, and thus is better for the GMAT.

 2. It can be tackled either through straight probability or through a combination of probability and combinatorics.

Here’s the question:

Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter, she prepared an envelope with its correct address. If the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address?

A) 1/24
B)
1/8
C) 1/4
D) 1/3
E) 3/8

First, as always, give the problem a shot before reading on for the explanation. If possible, see if you can tackle it with both methods (pure probability and probability w/ combinatorics). 

Explanation #1:

First, we’ll tackle pure probability. Let’s label the letters A, B, C, and D, and let’s say that A is the letter we wish to match with its correct envelope. The other three will be matched with incorrect envelopes. We now must examine the individual probabilities of the following events happening (green for correct, red for incorrect):

_A_   _B_   _C_   _D_

For the above, each slot represents a letter matched with an envelope. There are four envelopes and only one is correct for letter A. That means Tanya has a 1/4 chance of placing letter A in its correct envelope:

_1/4__   _B_   _C_   _D_

We now desire letter B to be placed in an incorrect envelope. Two of the remaining three envelopes display incorrect addresses, so there is a 2/3 chance of that happening:

_1/4__   _2/3_   _C_   _D_

We then desire letter C to also be placed in an incorrect envelope. Only one of the remaining two envelopes displays an incorrect address, so there is a 1/2 chance of that happening:

_1/4__   _2/3_   _1/2_   _D_

At that point, the only remaining option is to place the last remaining letter in the last remaining envelope (i.e. a 100% chance, so we place a 1 in the final slot):

_1/4__   _2/3_   _1/2_   _1_

Multiplying the fractions, we can hopefully see that some cancelling will occur:

¼ x ⅔ x ½ x 1

= 1 x 2 x 1
   ———–
   4 x 3 x 2

= 1/12

But lo and behold, 1/12 is not in our answer choices. Did you figure out why?

We can’t treat letter A as the only possible correct letter. Any of the four letters could possibly be the correct one. However, the good news is that in any of the four cases, the math will be exactly the same. So all we have to do is take the original 1/12 we just calculated and multiply it by 4 to get the final answer: 4 x 1/12 = 4/12 = 1/3. The correct answer is D.

Explanation #2:

So what about a combinatorics approach?

As we’ve discussed in our previous GMAT probability posts, all probability can be boiled down to Desired Outcomes / Total Possible Outcomes. And as we discussed in our posts on GMAT combinatorics, we can use factorials to figure out the total possible outcomes in a situation such as this, which is actually a simple PERMUTATION. There are four envelopes, so for the denominator of our fraction (total possible outcomes), we can create a slot for each envelope and place a number representing the letters in each slot to get:

_4_  _3_  _2_  _1_  =  4! = 24  possible outcomes

This lets us know that if we were to put the four letters into the four envelopes at random, as the problem says, there would be 24 permutations, giving us the denominator of our fraction (total possible outcomes). 

So what about the desired outcomes? How many of those 24 involve exactly one correctly placed letter? Well, let’s again treat letter A as the correctly placed letter. Once it’s placed, there are three slots (envelopes) left: 

___  ___  ___ 

But the catch is: the next envelope has only two letters that could go into it. Remember, one of the letters correctly matches the envelope in address, and we want a mismatch:

_2_  ___  ___ 

Likewise, that would leave two letters available for the next envelope, but only one of them would have the wrong address:

_2_  _1_  ___ 

And finally, there would be only one choice left for the final envelope:

_2_  _1_  _1_ 

That would mean for the correctly-placed A letter, there are only two permutations in which each of the other letters is placed incorrectly:

_2_ x  _1_ x  _1_ = 2 possible outcomes.

But as before, we must consider that any of the four letters could be the correct letter, not just letter A. So we must multiply the 2 possible outcomes by four to get 8 desired outcomes involving exactly one letter being placed in its correct envelope. That gives us our numerator of Desired Outcomes. Our denominator, remember, was 24 total possible outcomes. So our final answer, once again, is 8/24 = 1/3.

This is a great example of how GMAT combinatorics can intersect with probability.

To tide you over until next time, give this Official GMAT problem a try. It will also give a nice segue into Number Theory, which we’ll begin to talk more about going forward. Explanation next time…

If x is to be chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7}, what is the probability that xy will be even?

A) 1/6
B) 1/3
C) 1/2
D) 2/3
E) 5/6

 

Permutations and Combinations Intro
A Continuation of Permutation Math
An Intro To Combination Math
Permutations With Repeat Elements
Permutations With Restrictions
Combinations with Restrictions
Independent vs Dependent Probability
GMAT Probability Math – The Undesired Approach
GMAT Probability Meets Combinatorics: One Problem, Two Approaches

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An “Undesired” Approach to GMAT Probability gmat article
Posted on
11
Mar 2021

An “Undesired” Approach to GMAT Probability

By: Rich Zwelling, Apex GMAT Instructor
Date: 11th March, 2021

In our last post, we discussed a solution for the following question, which is a twist on an Official Guide GMAT probability problem:

Xavier, Yvonne, and Zelda individual probabilities for success on a certain problem are 1/4, 1/2 and 5/8, respectively. Xavier will attempt the problem first. If he solves it, Yvonne and Zelda will not attempt it. If Xavier cannot solve it, Yvonne will attempt it next. If she solves it, Zelda will not attempt it. If Yvonne cannot solve it, Zelda will then attempt it. What is the probability that Zelda does not get to attempt the problem?

A) 3/16
B)
5/8
C) 3/8
D) 5/64
E) 3/64

We also mentioned that there was an alternate way to solve it. Did you find it? In truth, it relates to something we discussed in a previous post we did on GMAT Combinatorics, specifically Combinations with Restrictions. In that post, we discussed the idea of considering combinations in which you’re not interested. It might seem counterintuitive, but if you subtract those out from the total number of combinations possible, you’re left with the number of combinations in which you are interested:

You can actually do something similar with probability. Take the following basic example:

Suppose I told you to flip a fair coin five times, “fair” meaning that it has an equal chance of landing heads-up or tails-up. I then wanted to know the probability that I flip at least one head. Now, when you think about it, the language “at least one” involves so many desired possibilities here. It could be 1 head, 2 heads, …, all the way up to 5 heads. I’d have to calculate each of those probabilities individually and add them up.

Or…

I could consider what is not desired, since the possibilities are so much fewer:

0 heads   |   1 head      2 heads      3 heads      4 heads      5 heads

All of the above must add to 100% or 1, meaning all possible outcomes. So why not figure out the probability that I get 0 heads (or all tails), and then subtract it from 100% or 1 (depending on whether I’m using a percentage or decimal/fraction)? I’ll then be left with all the possibilities in which I’m actually interested, without the need to do any more calculations.

Each time I flip the coin, there is a ½ chance that I flip a tail. This is the same each of the five times I flip the coin. I then multiply all of the probabilities together:

½ x ½ x ½ x ½ x ½ = 1 / 25  = 1 / 32

Another way to view this is through combinatorics. Remember, probability is always Desired outcomes / Total possible outcomes. If we start with the denominator, there are two outcomes each time we flip the coin. That means for five flips, we have 25 or 32 possible outcomes, as illustrated here with our slot method:

_2_  _2_  _2_  _2_  _2_ = 32

Out of those 32 outcomes, how many involve our (not) desired outcome of all tails? Well, there’s only one possible way to do that: 

_T_  _T_  _T_  _T_  _T_    ← Only 1 outcome possible

It really is that straightforward: with one outcome possible out of 32 total, the probability is 1/32 that we flip all tails. 

Now remember, that is our, not desired. Our desired is the probability of getting at least one head

0 heads   |   1 head      2 heads      3 heads      4 heads      5 heads

So, since the probability of getting 0 heads (all tails) is 1/32, we simply need to subtract that from 1 (or 32/32) to get our final result. The probability that we flip at least one head if we flip a fair coin five times is 31/32.

Application to problem from previous post

So now, how do we work that into the problem we did last time? Well, in the previous post, we took a more straightforward approach in which we considered the outcomes we desired. But can we use the above example and consider not desired instead? Think about it and give it a shot before reading the explanation:

Xavier, Yvonne, and Zelda individual probabilities for success on a certain problem are 1/4, 1/2 and 5/8, respectively. Xavier will attempt the problem first. If he solves it, Yvonne and Zelda will not attempt it. If Xavier cannot solve it, Yvonne will attempt it next. If she solves it, Zelda will not attempt it. If Yvonne cannot solve it, Zelda will then attempt it. What is the probability that Zelda does not get to attempt the problem?

A) 3/16
B) 5/8
C) 3/8
D) 5/64
E) 3/64

Explanation

In this question, our desired case is that Zelda does not attempt the problem. That means, quite simply, that our not desired case is that Zelda does get to attempt it. This requires us analytically to consider how such a case would arise. Let’s map out the possibilities with probabilities:

An “Undesired” Approach to GMAT Probability treeNotice that two complementary probabilities are presented for each box. For example, since there is a 1/4 chance Xavier solves the problem (left arrow), we include the 3/4 probability that he does not solve the problem (right arrow). 

If Zelda does get to attempt it, it’s clear from the above that first Xavier and Yvonne must each not solve it. There is a 3/4 and a 1/2 chance, respectively, of that happening. This is also a dependent situation. Xavier must not solve AND Yvonne must not solve. Therefore, we will multiply the two probabilities together to get ¾ x ½ = ⅜. So there is a 3/8 chance of getting our not desired outcome of Zelda attempting the problem.

So, we can finally subtract this number from 1 (or 8/8) and see that there is a 5/8 chance of Zelda not getting to attempt the problem. The correct answer is B.

Next time, we’ll discuss how GMAT Probability and Combinatorics can combine to form some interesting problems…

Permutations and Combinations Intro
A Continuation of Permutation Math
An Intro To Combination Math
Permutations With Repeat Elements
Permutations With Restrictions
Combinations with Restrictions
Independent vs Dependent Probability
GMAT Probability Math – The Undesired Approach
GMAT Probability Meets Combinatorics: One Problem, Two Approaches

Read more
Independent vs Dependent Probability article for the GMAT
Posted on
09
Mar 2021

Independent vs. Dependent Probability

By: Rich Zwelling, Apex GMAT Instructor
Date: 8th March, 2021

Independent vs. Dependent Probability

As promised last time, we’ll return to some strict GMAT probability today. Specifically, we’ll discuss the difference between independent and dependent probability. This simply refers to whether or not the events involved are dependent on one another. For example, let’s take a look at the following Official Guide problem:

Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4, 1/2 and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?

A) 11/8
B)
7/8
C) 9/64
D) 5/64
E) 3/64

In this case, we are dealing with independent events, because none of the probabilities affect the others. In other words, what Xavier does doesn’t affect Yvonne’s chances. We can treat each of the given probabilities as they are. 

So mathematically, we would multiply, the probabilities involved. (Incidentally, the word “and” is often a good indication that multiplication is involved. We want Xavier AND Yvonne AND not Zelda to solve the problem.) And if Zelda has a chance of solving the problem, that means she has a chance of not solving it. 

The answer would therefore be ¼ x ½ x ⅜  = 3/64 or answer choice E. 

What if, however, we changed the problem to look like this:

Xavier, Yvonne, and Zelda individual probabilities for success on a certain problem are 1/4, 1/2 and 5/8, respectively. Xavier will attempt the problem first. If he solves it, Yvonne and Zelda will not attempt it. If Xavier cannot solve it, Yvonne will attempt it next. If she solves it, Zelda will not attempt it. If Yvonne cannot solve it, Zelda will then attempt it. What is the probability that Zelda does not get to attempt the problem?

A) 3/16
B)
5/8
C) 3/8
D) 5/64
E) 3/64

As you can see, the problem got much more complicated much more quickly, because now, the question stem is dependent upon a very specific series of events. Now, the events affect one another. Xavier will attempt the problem, but what happens at this stage affects what happens next. If he solves it, everything stops. But if he doesn’t, the problem moves to Yvonne. So in effect, there’s a ¼ chance that he’s the only person to attempt the problem, and there’s a ¾ chance the problem moves to Yvonne.

This is most likely how the GMAT will force you to think about probability: not in terms of formulas or complicated mathematical concepts, but rather in terms of narrative within a new problem with straightforward numbers. 

That brings us to consideration of the question stem itself. What would have to happen for Zelda not to attempt the problem? Well, there are a couple of possibilities:

 1. Xavier solves the problem

If Xavier solves the problem, the sequence ends, and Zelda does not see the problem. This is one case we’re interested in, and there’s a ¼ chance of that happening. 

 2. Xavier does not solve, but then Yvonne solves

There’s a ½ chance of Yvonne solving, but her seeing the problem is dependent upon the ¾ chance that Xavier does not solve. So in reality, we must multiply the two numbers together to acknowledge that the situation we want is “Xavier does not solve AND Yvonne does solve.” This results in ¾ x ½ = ⅜ 

The two above cases constitute two independent situations that we now must add together. For Zelda not to see the problem, either Xavier must solve it OR Yvonne must solve it. (The word “or” is often a good indication that addition will be used).

This leads us to our final probability of ¼ + ⅜ = that Zelda does not get to attempt the problem.

There is an alternative way to solve this problem, which we’ll talk about next time. It will segue nicely into the next topic, which we’ve already hinted at in our posts on GMAT combinatorics. Until then…

Permutations and Combinations Intro
A Continuation of Permutation Math
An Intro To Combination Math
Permutations With Repeat Elements
Permutations With Restrictions
Combinations with Restrictions
Independent vs Dependent Probability
GMAT Probability Math – The Undesired Approach
GMAT Probability Meets Combinatorics: One Problem, Two Approaches

Read more