EA Exam 2022
Posted on
04
May 2022

EA Exam 2022 – Everything You Need To Know In 5 Minutes

Table of Contents

  • About the EA Exam
    • What is EA used for?
  • EA Structure, Sections, Timing, & Scoring
    • EA Scoring & Validity
    • What is a Good Score?
  • How, When, & Where can I take the EA? 
    • EA Exam Day FAQs
  • How Much Does The EA Exam Cost?
    • Rescheduling & Cancellation of your EA appointment
    • Additional Costs Worth Considering 
  • EA History & Background
    • EA Changes Over Years
    • Online EA Test in the face of COVID-19

About The EA Exam

The Executive Assessment (EA) is considered a trusted predictor of business school readiness for busy professionals wishing to earn an MBA or EMBA. The exam is crafted and administered by the General Management Admissions Council (GMAC) to measure a candidate’s higher order reasoning, critical thinking, analysis, and problem solving skills. You can also register for the EA through their official portal or browse through some EA prep sources here and find free EA prep questions here

The EA test is a multiple-choice, computer adaptive test (CAT) – this means that an algorithm selects each following question based on the test taker’s ability level and performance on previous questions. If you are new to this concept, the most important feature to understand is that, when you answer a question correctly, the following question will be even more challenging. Conversely, if you answer a question incorrectly, it will give you an easier one next.

What Is The EA Exam Used For?

The Executive Assessment is primarily used for admissions to nearly 100 institutions, universities, and MBA and EMBA programs worldwide which offer business and management disciplines. Keep in mind that many business schools screen applicants based on a range of criteria, but EA scores are among the most important screening metrics used. Others include undergraduate GPA, work and other relevant experience, application essays, recommendation letters, and personal interviews.

Strong EA results are necessary, but certainly not sufficient to gain admission to the best MBA/EMBA and business-oriented grad schools programs like Masters of Finance (MFin), Masters of Accounting (MAcct), Masters of Business Administration (MBA), Juris Doctor & Masters of Business Administration (JD-MBA) and PhDs in all these disciplines. Remember,  that while the EA is important, it’s certainly not a measure of who you are as a person and is one part of a many-faceted application. 

An investment of time and resources into the right EA preparation program or plan will result in a higher score on the test, which has a direct correlation with your admissions success and will have a positive impact on your business school experience and future professional career.

EA Structure, Sections, Timing, & Scoring

The EA test consists of three sections with categorized problems aiming to assess a different skill set. Each part differs in terms of score range and the number and types of problems:

1. Integrated Reasoning (IR) 12 questions | 30 minutes | scored from 0 to 20
There are four types of questions on the Integrated Reasoning section: 

      • Multi-source reasoning
      • Graphic interpretation 
      • Two-part analysis 
      • Table analysis

2. Quantitative 14 questions | 30 minutes | scored from 0 to 20
There are two types of problems on the Quantitative section: 

      • Data sufficiency   
      • Problem solving

3. Verbal 14 questions | 30 minutes | scored from 0 to 20
There are three types of questions on the Verbal section:

      • Reading comprehension
      • Critical reasoning 
      • Sentence correction

There are several other factors worth mentioning:

  • The Executive Assessment is meant for busy professionals. Many of whom have already been working professionally for around 7 years. 
  • The total score of the EA ranges from 100 to 200 
  • Despite the official scoring guides, the maximum you can score on EA is 174 and the minimum being 126.
  • The total time to take the EA test is 90 minutes.
  • As the total time of the EA is 90 minutes, test takers are not given any breaks. 
  • All three sections are weighted equally towards your overall score. 

EA Scoring & Validity

You’ll get your unofficial score when you complete your exam. You and your designated schools will receive your official EA score within 24 hours of the exam, and it will be valid for the following five years. In order to determine what score will be good for you, you should consider both the average (mean) EA score and the range of scores of applicants admitted to your desired university.

If you find yourself lost in the translation of the EA scores into percentiles, this article explains it in a meticulous way. 

What is a Good EA Score?

What is a good Executive Assessment score, and how can I get one? We are frequently asked this question, but the answer varies depending on who we speak with. Here at Apex, we want to help our clients obtain their goal EA scores because this is where they can truly compete for top programs and be eligible for MBA and EMBA scholarships. However a “good EA score” is determined by the applicant’s MBA program’s requirements; some programs demand a score above 150, while others require a score above 155. Selecting the programs you wish to attend and examining their MBA and EMBA class profile will supply you with this knowledge and equip you with a solid foundation from which to begin your EA preparation.

In case you are wondering what a 155 EA score can do for you, here is all you need to know!

How, When, & Where Can I Take The EA Exam?

How?

We recommend registering two to three months before your desired exam date. The scheduling can be done online (applicant needs to open an account) or through a phone call (applicant needs to call the EA Customer Service in their region). For more information visit gmac.com/executive-assessment.   

Where?

You can take the EA at one of 600+ test centers worldwide or online in the comfort of your own home. You can search for a testing location near you here. The test is administered on a computer, via a platform used worldwide: Pearson VUE. The EA is available only at designated Pearson VUE test centers, thus assuring each candidate the exact same experience as all other test takers around the world.

When?

You can take the EA test almost anytime you want, depending on the availability of dates into the test center(s) you have chosen. However, there are some requirements regarding re-taking the exam. You can retake the exam as soon as you’d like, however you may only take the exam up to two times. 

EA Exam Day FAQs

Here are the top 3 questions that clients ask us about exam day information:

1. What should I do if I fall sick on the exam day?

If you do not feel well come exam day you will have to make the decision as to whether or not you can take the test and perform at your best. Most people will not be able to do this, so it will be best to cancel. If you do so on the day of the exam, you will incur a loss of your full $350 exam fee. If you cancel the exam up to 24 hours in advance you will receive only a $250 refund. However, rescheduling the exam between 24-48 hours will only incur a fee of $75 while rescheduling the appointment more than 48 hours out does not incur a fee. 

2. What can I bring with me to the test center?

You are allowed in the test center with the following:

    • EA approved identification
    • Appointment confirmation letter or email you received from Pearson VUE
    • Prescription eyeglasses
    • Light sweater or light non-outerwear jacket
    • Comfort items only if they were pre-approved as an accommodation received in advance

Any additional personal belongings that you bring with you such as your cell phone, bag, snacks, and earphones will need to be stored in one of the provided lockers. Any cell phone use throughout the test time is prohibited.
The test center will provide you with everything that you need in order to take the test including scratch paper and a pencil.

3. What can I expect at the test center?

A usual test center is typically quite small. Once you arrive you will have to provide the administrator with the relevant documents and while these are being processed you will be asked to wait in the waiting area. In this area, you can still access all your personal belongings up until you are called into the testing room.

Once in the room, you will be allocated an individual exam station where you will find a computer.

Here is the full list of the EA Exam Day FAQs

4. How Much Does The EA Test Cost?

The cost to sit the EA exam is $350. This includes sending your results to up to five schools of your choice. There are no fees for sending your scores to any additional school. 

Rescheduling & Cancellation of your EA appointment
Regular Rescheduling fees:

  • No Fee if requested more than 48 hours prior to appointment
  • $75 if requested 24 to 48 hours prior to appointment (Temporarily waived)
  • $10 to reschedule the assessment by phone 
  • Regular Cancellation fees:
  • $100 to cancel up to 24 hours before the appointment
  • $10 to cancel the assessment by phone. 

Additional Costs Worth Considering
Apart from the test fee, there are other costs that you may want to consider. GMAC advises people preparing for the exam to utilize the EA Official Guide (as do we) alongside other learning aids as additional materials. Please note that the Official Guide is a great resource for problems, but the explanations leave something to be desired, so using only the Official Guide is not recommended.

A large percentage of test takers who wish to score in the 90th percentile or higher (157+) on the EA invest in private EA preparation as a personalized means to achieving long-term career success. Our firm, Apex , specializes in offering private, customized EA preparation and admissions consulting. We focus on individual learning and a holistic coaching environment where we tackle not only the fundamentals but the underlying structure and complexity of the EA.

We do this not just to get you a good score, but to prepare you for your MBA/EMBA program and career beyond by focusing on universal critical thinking skills, cognitive heuristics, emotional and behavioral aspects of learning and high stakes performance, and other learning techniques that can be applied widely over the course of a lifetime. We take pride in exactly this personalized approach as a means for every candidate to utilize their strengths better, focus on their weaknesses, and overcome test anxiety through an exclusively designed EA curriculum.

A lot of people try to save money on the EA preparation process. When you consider that a top EMBA can lead to millions of dollars of extra earnings over the course of a lifetime, it makes sense to invest in EA preparation. Learn more about this subject with our instructors Mike and Jaymes, here: Why is Test Prep so Expensive?

EA History & Background

In March of 2016, the Executive Assessment made its debut in the standardized test world. It was a novel test designed for working professionals who wished to undertake an EMBA. The creators of the EA, the GMAC, wished to create an exam which tested the real-world skills working professionals have gained throughout their careers. 

As the EA is a newish test on the testing market, it is only accepted at a handful of schools. This list, however, is constantly expanding. Because of this, be sure to double check the official EA site to keep up-to-date on which schools accept the EA. 

Online EA Test

The Executive Assessment is available online. However, it is encouraged by the GMAC that those who feel safe to do so, take the EA at a test center.
In terms of content, the EA online has the same structure and content as the test taken at a test center.
Registering for the EA online is the same process as registering to take the exam in person. Just be sure to select the ‘online’ (at home) option when selecting your test location. 
Interested test takers are able to take the EA at any home location so long as they have the necessary technology to do so. However, test takers in Mainland China, Cuba, Iran, North Korea, Sudan, and South Sudan are not able to take the EA online.

 

That’s it! Thanks for sticking with us to the end of this EA test crash course! If you are looking for a more comprehensive version diving deeper into what the EA has in store for you, feel free to check out our website for more information

 

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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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Cylinders & Spheres In The GMAT
Posted on
19
Apr 2022

Cylinders & Spheres In The GMAT

Welcome back to our fifth and final article on GMAT circles. Last time we explored the possibilities of treating a circle’s radius as the hypotenuse of a right triangle. This time we will introduce two 3-dimensional shapes built from circles: the cylinder and the sphere.

1. Cylinder

More than likely, you already know what these things are and could describe them. But let’s try to define them in some interesting ways. A cylinder is a “tall circle” or – to use more proper geometric terminology – a circular prism. A prism is the solid shape that results when you take any polygon and “pull it” upward into something like a pillar. The polygon you started with still exists as the “top and bottom” faces of the prism, and the faces around the sides of the prism are rectangles. (Technically they can be parallelograms, which would produce a “leaning” pillar, but this won’t happen on the GMAT.)

Since a circle doesn’t have sides, a cylinder doesn’t have faces – except for the two circles on its top and bottom. In between, there is one smoothly-curving surface. If you need to find the area of this third surface, you can treat it like a rectangle. The length of this rectangle is the height of the cylinder, and the width of this rectangle is the circumference of the circle. The volume of any prism is the area of its base polygon multiplied by the prism’s height. So for a cylinder, the equation is

V = πr²h

2. Sphere

Now for spheres. We all know that a sphere is a perfectly round ball. But think about this: a sphere is like a circle “any way you slice it” – quite literally. If you have some citrus fruits in your kitchen, you can try slicing them in different places at different angles, and the faces of the two resulting pieces will always be circles. Another way to say this is that any cross section taken from a sphere will be a circle. No matter how hard you try, you will never be able to produce an elliptical orange slice. Sorry to disappoint you.

Let’s see how the GMAT employs these shapes in some official problems. Some basic cylinder problems focus on one whole cylinder. More challenging cylinder problems compare one cylinder to another or treat a cylinder as a partially-filled tank. 

3. A Data Sufficiency Problem Featuring Two Cylinders

It costs $2,250 to fill right circular cylindrical Tank R with a certain industrial chemical. If the cost to fill any tank with this chemical is directly proportional to the volume of the chemical needed to fill the tank, how much does it cost to fill right circular cylindrical Tank S with the chemical?

1. The diameter of the interior of Tanks R is twice the diameter of the interior of Tank S.
2. The interiors of Tanks R and S have the same height.

(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. 

Solution

Since the cost to fill any tank (including tanks R and S) with this chemical is directly proportional to the volume of the cylindrical tank, the only thing we care about here is the ratio of the two tanks’ volumes. Remember that for the volume of a cylinder, we need to know (or be able to derive) both the area of the circle and the height of the cylinder.

Statement 1 gives us the ratio of the tanks’ diameters: 2:1. This means that the ratio of the areas of the tanks’ bases is 4:1 (if lost here, review article 1 on area, circumference, and pi). This is great, but it is still not enough to know the overall ratio of the tanks’ volumes. Statement 1 is insufficient.

Statement 2 tells us that tanks R and S are the same height, specifying “interior” because we are filling up space with a chemical and can’t count whatever volume is taken up by the tank walls. On its own, this information is insufficient.

Combining statements 1 and 2, we have the ratio of the tanks’ diameters (2:1) and the ratio of their heights (1:1). This means that the overall ratio of the tanks’ volumes is fixed. Statements 1 and 2 together are sufficient, and the correct answer is C.

4. Partially Filled Cylinder-as-a-tank Problem

The figures show a sealed container that is a right circular cylinder filled with liquid to 12 its capacity. If the container is placed on its base, the depth of the liquid in the container is 10 centimeters and if the container is placed on its side, the depth of the liquid is 20 centimeters. How many cubic centimeters of liquid are in the container. 

(A) 4,000 π
(B) 2,000 π
(C) 1,000 π
(D) 400 π
(E) 200 π

Solution

This problem is less complex than it might first appear. It all comes together when you realize that the 20cm depth in the second orientation of the tank represents the radius of the circle!  Now you can get the area of the circle in cm² using A = r² and then multiply the result by 10 (the depth in centimeters of the liquid in the upright tank) to get the volume of the liquid in cm³. If you can mentally square 20 and then multiply by 10, you should be just seconds away from selecting correct answer choice A.

5. Final Cylinder-as-a-tank Problem

Solve carefully before reading on.

A tank is filled with gasoline to a depth of exactly 2 feet. The tank is a cylinder resting horizontally on its side, with its circular end oriented vertically. The inside of the tank is exactly 6 feet long. What is the volume of the gasoline in the tank?

1. The inside of the tank is exactly 4 feet in diameter.
2. The top surface of the gasoline forms a rectangle that has an area of 24 square feet.

(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. 

Solution

Statement 1.

Evaluating statement 1 is fairly straightforward. Combined with the information from the question stem that the depth of the gasoline in the tank is 2 feet, the additional information that the inside of the tank has a 4-foot diameter means that the tank is filled halfway with gasoline. If 4 is the diameter, then 2 is the radius, and the gas fills the tank up to its center line. This looks just like the half-filled tank in the previous problem. The question stem also gave us the length of the tank (called a length rather than a height since this tank is a cylinder “lying down”), so the cylinder’s total and fractional volumes are calculable. Statement 1 is sufficient.

Statement 2.

Statement 2 performs something like a “double flip.” We are told that the top surface of the gasoline is a 24ft² rectangle. Remembering from the question stem that the tank is 6 feet long, you may realize that 24/6 = 4 and think that this tells you the same thing as statement 1: that the tank has a 4-foot diameter. This would be a mistake. The 24ft² rectangle formed by the surface of the gasoline indeed has a length of 6 and a width of 4, but this width of 4 is not necessarily the diameter of the tank. It could just as easily happen in a larger tank that is less than half (or more than half) full. 

Does this make statement 2 insufficient? Well so far, yes. But there’s something we’ve left out that makes it sufficient after all! From the question stem, the depth of the gasoline in the tank is 2 feet. Imagine that the circular end of this tank is transparent. Looking at it this way, the top surface of the gasoline makes a horizontal chord across the circle, and this chord has a length of 4. Simultaneously, this chord is a vertical distance of 2 feet from the bottom of the circle (since the depth of the gasoline in the tank is 2 feet). The only way this can happen is if the 4-foot chord is the diameter of the circle!

Therefore the tank is still half full, and the volume of the gasoline is half of the (calculable) volume of the cylinder. Statement 2 is also sufficient, and the correct answer choice is D.

 

 

6. Sphere Problem

For the final problem in our circles series, we’ll work with spheres. Spheres are less common on the GMAT than cylinders, and you will never have to memorize any of their formulas. If you need a sphere formula for a problem, it will be supplied with the problem.

For a party, three solid cheese balls with diameters of 2 inches, 4 inches, and 6 inches, respectively, were combined to form a single cheese ball. What was the approximate diameter, in inches, of the new cheese ball? (The volume of a sphere is 433, where r is the radius.)

(A) 12
(B) 16
(C) ∛16
(D) 8
(E) 236

Solution – Long Way

This sounds like a party you don’t want to miss. I don’t know exactly how to combine three solid cheese balls into one, but I do know how to calculate the diameter.

There are two ways to solve this problem: the long way and the best way. The long way is to calculate the volumes of the three original cheese balls, sum your answers into one volume, and then solve for the radius of the combined cheese ball. First you must divide the given diameters of the original cheese balls by 2, since the volume equation uses radius instead.

V = (4π/3)r³
V = (4π/3)1³ + (4π/3)2³ + (4π/3)3³
V = (4π/3)(1³ + 2³ + 3³)
V = (4π/3)(1 + 8 + 27)
V = (4π/3)(36)
V = 48π
V = (4π/3)r³
48π = (4π/3)r³
48 = (4/3)r³
36 = r³
∛36 = r
2(∛36) = D

And the correct answer choice is E.

Solution – Short Way

That was the long way. The best way is to think logically and exploit the answer choices. Since we are effectively adding some cheese onto a ball that already has a diameter of 6 inches, the diameter of the combined cheese ball will be greater than 6 inches. This means that answer choices C and D are nonstarters. (C is somewhere between 2 and 3, and D is exactly 6.) Let’s think next about choices A and B, since they are integers and easier to evaluate than choice E.

Can the diameter of the combined cheese ball be as great as 12 (choice A) or even 16 (choice B)? No, it can’t. Picture a “cheese ball snowman” made of the three original cheese balls – a cooler idea for a party than smashing them into one ball, I argue. His height is 12 inches, but this is not the same as having a single ball with a 12-inch diameter. Three spheres whose diameters sum to 12 cannot combine their volumes to produce a single sphere with a diameter of 12. Therefore choices A and B are also out, leaving us with correct choice E. If we approximate the value of E, it is greater than 6 but less than 8, since the cube root of 36 is greater than 3 but less than 4. A combined cheese ball this size makes logical sense.

 

This concludes our fifth and final article on GMAT circles. Cheers.

 

Contributor: Elijah Mize (Apex GMAT Instructor)

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Radius as Hypotenuse
Posted on
05
Apr 2022

Radius As Hypotenuse – Problems & Solutions

Welcome back to our fourth article on GMAT circles. Last time we considered inscribed angles and learned that where there is a 90-degree inscribed angle, there is a hypotenuse that is also a diameter of the circle. This time we will explore a class of problems where the radius, rather than the diameter, pulls double duty as a hypotenuse. Let’s dive right in with the following official problem.

1. Radius as Hypotenuse  – GMAT Official Problem

Semicircular archway over a flat street problemThe figure above represents a semicircular archway over a flat street. The semicircle has a center at O and a radius of 6 feet. What is the height h, in feet, of the archway 2 feet from its center?

A. √2
B. 2
C. 3
D. 4√2
E. 6

Problem SolutionThis problem is a straightforward application of the Pythagorean theorem. Since we are told that the radius of the semicircle is 6 feet, we can draw a 6-foot radius from center O to the point where height h meets the semicircle. Voila – a right triangle.

h = √(62 – 22)
h = √(36 – 4)
h = √32

This is where you should stop and mark answer choice D since we are taking the square root of a number that is not a perfect square. When we simplify this radical, something will get left inside. Therefore answers B, C, and E are out (Answer A is out because √2 =/= √32), and the correct choice is D.

2. Radius as Hypotenuse Problem 1 

Let’s try something a little different:

In the xy-plane, point (r,s) lies on a circle with center at the origin. What is the value of + s²?

1. The circle has radius 2.
2. The point (2,-2) lies on the circle.

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. 

This is the first problem we’ve seen where a circle is placed on the xy-plane. In such problems, it is usually helpful to remember the basic circle principle that every point on the circle (meaning on its edge or perimeter) is equidistant from its center.

Solution

If you’re unfamiliar with these problems, statement 1 may trip you up. Is the radius of the circle sufficient to determine + ? Yes, it is. If you are concerned about the unknown positivity/negativity of the coordinates r and s, recall that the square of any number (except 0) is positive. This means that for any positive/negative combination of r and s, the sum + will have the same value. 

But what you really need here is to see that the expression + matches the famous + from the Pythagorean theorem, and in fact, it functions the exact same way.

Radius as Hypotenuse ProblemIn this setup, the radius is the hypotenuse of the right triangle with legs r and s. Therefore, applying the Pythagorean theorem, the value + represents the square of the radius. So if we know the value of the radius (2), we know the value r² + s², and statement 1 is sufficient.

Statement 2 offers that the point (√2, -√2) lies on the circle. This statement should be “easier” to evaluate than statement 1. Seeing the radicals in the coordinates ought to help you make the connection to the Pythagorean theorem if you didn’t already while evaluating statement 1. But using the principle that every point on a circle is equidistant from its center, we know that this given point (√2, -√2) is the same distance from the center as the point (r, s) in the question. Therefore if we sum the squares of √2 and -√2, the result (4) will also represent the value r² + s² we were asked about.

3. Problem 2

Let’s try one more:

In cross section, a tunnel that carries one lane of one-way traffic is a semicircle with radius 4.2 m. Is the tunnel large enough to accommodate the truck that is approaching the entrance to the tunnel?

1. The maximum width of the truck is 2.4 m.
2. The maximum height of the truck is 4 m.

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. 

This one is a little more complex. Sometimes on GMAT quant problems, it is helpful to ask why certain details were specified. In this case, we are told that the tunnel “carries one lane of one-way traffic.” This is important because if it were not the case, the truck would have to drive on one side or the other, and there’s no way it would be able to get through the tunnel. Since there is only one lane going through the tunnel, the truck can “center up” to give itself the best chance of fitting through.

Solution

This is one of those less-common DS problems where each statement on its own is clearly insufficient. If all we know is that the truck is 2.4m wide at its widest point (statement 1), it may still be too tall to fit through the tunnel. If all we know is that the truck is 4m tall at its tallest point, we don’t know whether the truck is narrow enough to make it through the tunnel while being this tall.

Problem 2 - Solution But if we combine statements 1 and 2, we can use the Pythagorean theorem to calculate the max distance of a point on the “centered up” truck from the point at the “center” of the semicircle.

Now here’s the key step: don’t calculate! Running the Pythagorean theorem with our values here would be a waste of time. As long as the value p [from the graphic] is less than 4.2 (the radius of the tunnel), the truck will fit. But for DS, we don’t have to know whether the truck will fit. All we have to know is whether the value p can be calculated, and in this case, it can be. Statements 1 and 2 together are sufficient, and the correct answer choice is C.

 

This concludes our fourth article on the GMAT’s treatment of circles. Next time we will look at circles in two different 3-dimensional shapes: cylinders and spheres.

 

Contributor: Elijah Mize (Apex GMAT Instructor)

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Inscribed Angles & Inscribed Polygons In The GMAT
Posted on
29
Mar 2022

Inscribed Angles & Inscribed Polygons In The GMAT

Welcome back to our third article on GMAT circles. In the second article, we explored central angles, sectors, and arcs. This time we will introduce another kind of angle: the inscribed angle.

An inscribed angle is an angle drawn by using line segments to connect one point on a circle to two other points on the same circle, as in the graphic below:

Inscribed AngleLike a central angle, an inscribed angle creates a “wedge” shape, like a triangle where one side is rounded. The rounded side is an arc of the circle. For a central angle, the measure of the angle corresponds to the measure of the associated arc in a 1:1 relationship. For an inscribed angle, the measure of the angle corresponds to the measure of the associated arc in a 1:2 relationship. A 30 degree inscribed angle creates a 60-degree arc on the other side of the circle. A 60-degree inscribed angle creates a 12- degree arc on the other side of the circle. And, importantly, a 90-degree inscribed angle creates a 180-degree arc (half a circle or a semicircle) on the other side of the circle.

1. Inscribed Angle – GMAT Official Guide Problem

GMAT problems rarely use the term “inscribed angle” or feature an inscribed angle in isolation. Usually, the inscribed angle is part of an inscribed polygon, a polygon drawn inside a circle so that its vertices are points on the circle. Take a look at this official GMAT problem:

Inscribed Angle Official GMAT ProblemIn the figure shown, the triangle is inscribed in the semicircle. If the length of line segment AB is 8 and the length of line segment BC is 6, what is the length of arc ABC?

 

 

A. 15π
B. 12π
C. 10π
D. 7π
E. 5π

The problem refers not to an angle inscribed in a circle but to a triangle inscribed in a semicircle. Still, knowing the “1:2” factor of relationship between an inscribed angle and its associated arc is the key to solving this problem. Your logic might go something like this:

  1. This is a semicircle or a 180-degree arc.
  2. The angle at point B “opens up” to the straight edge of the semicircle, which is like the diameter of a circle. Another semicircle or 180-degree arc could be drawn across from this angle so that it makes a whole circle with the existing piece.
  3. Since the measure of an inscribed angle is 1/2 the measure of the arc it “creates” on the other side of the circle, the angle at point B is a 90-degree angle, and the triangle is a right triangle. 

At this point, your attention should return to the given information about the lengths of line segments AB and BC, which we now know to be the legs of a right triangle. These legs have lengths 6 and 8, which have a 3:4 relationship. Therefore we are looking at a 3-4-5 triangle, and the length of the hypotenuse is 10.

Finally, you must recall that this hypotenuse is the diameter of the circle. Therefore the diameter of the whole circle is 10. However, marking answer choice C would be a mistake, since we were asked for the length of arc ABC, where arc ABC is a semicircle (half a circle). So your final step is to divide your diameter of 10π by 2, leading you to the correct answer choice: E.

2. Inscribed Square – GMAT Official Guide Problem

Let’s try another problem, this time with an inscribed square:

Inscribed Square GMAT Official Guide ProblemThe figure shows a drop-leaf. With all four leaves down the tabletop is a square, and with all four leaves up the tabletop is a circle. What is the radius, in meters, of the tabletop when all four leaves are up?
A. 1/2
B. 
√2/2
C. 1
D. √2
E. 2

Notice that the problem doesn’t mention “a square inscribed in a circle,” but that is nonetheless what we have here. Many GMAT quant problems create scenarios that correspond to some mathematical phenomenon without using the math language. In this case, the fact that we are dealing with a square inscribed in a circle is relatively easy to see.

As in the previous problem, we are asked for a value of the circle (this time it is the radius instead of an arc length) but given only information about the inscribed shape: a square. As in the previous problem, the key is realizing that with any 90-degree inscribed angle, the line segments forming the angle are legs of a right triangle whose hypotenuse is also a diameter of the circle.

Using the Pythagorean theorem, the hypotenuse of this triangle (or the diagonal of the inscribed square) is √2. As before, forgetting to divide this value by 2 (since we were asked for the radius, not the diameter) will lead you to an incorrect answer choice. Don’t trip at the finish line. The value you need is √2 /2, answer choice B.

Here is a related problem:

Square inscribed in a circle problemIf rectangle ABCD is inscribed in the circle above, what is the area of the circular region?

A. 36.00
B. 42.25
C. 64.00
D. 84.50
E. 169.00

Again, we are asked for a value of the circle (its total area) but given only information about the inscribed rectangle. For our purposes, this rectangle is just as good as the square in the previous problem. With the square, we only needed the length of one side, because we know that all four sides are the same length. With a rectangle, we need both the length and the width in order to calculate the diagonal – the diameter of the circle – via the Pythagorean theorem. If you know your Pythagorean triples (like 3-4-5), you may realize immediately that the diagonal of this rectangle is 13.

D = √(5² + 12²)
D = √(25 + 144)
D = √169
D = 13

Now that we have the circle’s diameter, we can solve for its area. The radius of the circle is 13/2 or 6.5, and since Area = r², the square of 13/2 or 6.5 will be the coefficient of in the correct answer choice. It would be a waste of time to fully multiply out 6.5 * 6.5. We know that it will be of form __.25, and the only answer choice that matches this is B.

3. Data Sufficiency – GMAT Official Guide Problem

Let’s transition to data sufficiency for one final problem. Using the diagonal/diameter relationship in the previous problems, it would be possible to construct a variety of DS problems. But some DS inscription problems rely on another property of inscribed polygons.

Square ABCD is inscribed in circle O. What is the area of square region ABCD?

  1. The area of circular region O is 64π.
  2. The circumference of circle O  is 16π.

Solution

To answer this problem, all you need to know is that there is only one way to inscribe a square in a circle. The vertices of the square must lie on the circle. The perimeters and areas of the square and the circle will scale together. This means that if we know any value for either shape, we can calculate every value for both of them. Therefore each statement on its own is sufficient, and the answer to this problem is D.

As long as any polygon can be established as regular (having sides of equal length and angles of equal measure), there is only one way to inscribe it in a circle. A square is a regular quadrilateral, so this works for squares every time. But this same problem could have used a regular pentagon, a regular hexagon, or any regular polygon you like, and the correct answer would still be D. The regularity of the polygon is sufficient – and necessary – for this to work. If the regularity of the polygon cannot be established, then there are an infinite number of ways to inscribe it in a circle, each with its own unique area and perimeter.

It is also possible to flip the relationship and inscribe a circle inside a polygon. A related term is circumscription. The shape on the inside is inscribed in the shape on the outside. The shape on the outside is circumscribed around the shape on the inside. GMAT problems where the circle is on the inside usually use a square, so that the diameter of the circle is equal to the length of each side of the square. Such problems tend to be of lower difficulty level.

 

This concludes our third article on the GMAT’s treatment of circles. Next time we will look at what happens when the radius – rather than the diameter – pulls double duty as the hypotenuse of a right triangle.

 

Contributor: Elijah Mize (Apex GMAT Instructor)

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Pieces of Pi: Sectors, Arcs, and Central Angles
Posted on
22
Mar 2022

Pieces of Pi: Sectors, Arcs, and Central Angles

Welcome back to our series on GMAT circles. In the first article, we introduced the properties of radius/diameter, circumference, and area, discussing the relationships between all of these. This time we will introduce something called a central angle, which creates portions of a circle’s area and circumference called sectors and arcs, respectively.

The best way to define these things is probably with a simple visual.

Pieces of Pi

A central angle is an angle created by using line segments to connect a circle’s center to two points on its edge. A sector is the part of a circle’s area bounded by this central angle, and an arc is the part of a circle’s circumference between the two points used to draw the angle. A 90-degree central angle creates both a 90-degree sector and a 90-degree arc. An important note is that the lines used to form the central angle are radii of the circle.

As a further illustration, think about a pizza (something I do regularly). The pizza is a circle, the pieces are sectors separated by central angles, the crust is the circle’s circumference, and each piece’s section of crust is an arc. From this, you can see that any central angle creates both a sector and an arc that correspond to one another. When you pull a piece from a pizza or cut out a piece from a pie, you use a central angle to create a sector with an arc on its rounded edge.

To represent these things mathematically, we consider a circle to be like a 360-degree central angle. In this setup, the fractional relationship of a central angle to 360 corresponds to two things:

  1. The fractional relationship of the resulting sector to the circle’s total area
  2. The fractional relationship of the resulting arc to the circle’s total circumference

Since 90 is ¼ of 360, the area of a 90-degree sector is ¼ of its circle’s total area, and the length of a 90-degree arc is ¼ of its circle’s circumference.

To show all of this algebraically, let’s use the variable x for the degree measure of a central angle:

x / 360 = arc length / circumference
x / 360 = sector area / circle area 

Most pizzas are divided into 8 slices. This means that each slice has a central angle of 360/8 = 45° and that each slice is ⅛ of the area of the entire pizza.

Examples:

1. What is the central angle for three slices of pizza?
The central angle formed by 3 slices of pizza is 3 * 360 / 8 = 135 degrees.

2. What’s the area of a slice if the diameter is 20cm and there are six slices?
The area of a slice of pizza is 1/6 of its pizza’s total area. So, the area of a pizza can be found by using this formula A= π*r2 = 3.14*102 = 314cm
The area of a slice of pizza is  314/ 6 = 52.33cm


Keep in mind that you may have to consider this relationship in either direction. You may be given some info about the whole circle and then tasked with concluding something about a sector or an arc. Or you may be given some info about a sector or an arc and then tasked with concluding something about the whole circle. You may even be given info about both the whole circle (its area or circumference) and a sector or arc and then tasked with calculating the central angle. Each of these represents a perspective shift, and when doing a problem form, you can rewrite the problem from each of these perspectives to make sure you can fully navigate problems of this sort.

Pieces of Pi: Official GMAT Problems

Now for some official GMAT problems. Let’s start with two straightforward sector problems, one problem solving and one data sufficiency.

Problem-Solving Problem 

The annual budget of a certain college is to be shown on a circle graph. If the size of each sector of the graph is to be proportional to the amount of the budget it represents, how many degrees of the circle should be used to represent an item that is 15 percent of the budget? 

A. 15°
B. 36°
C. 54°
D. 90°
E. 150°

From the question, we can tell that the “circle graph” mentioned here is what we usually call a “pie chart,” a handy way to show the breakdown of a whole (like a budget) into its various parts. If we want to represent 15% of the budget, we need a sector with a central angle using 15% of the (360) available degrees in the circle. 0.15 * 360 = 54, so the correct answer is C. Piece of cake. Or piece of pie.

Now for a DS pie chart problem

TOTAL EXPENSES FOR THE FIVE DIVERSIONS OF COMPANY H

DS Pie Chart ProblemThe figure represents a circle graph of Company’s H total expenses broken down by the expenses for each of its five diversions. If O is the center of the circle and if Company H’s total expenses are $5,400,000, what are the expenses for Division R? 

1. x = 94
2. The total expenses for Division S and T are twice as much as the expenses for Division R.

Once again, this pie chart (which the GMAT apparently prefers to call a “circle graph”) is being used to represent a budget breakdown. Here we are told that the value represented by the whole circle is $5,400,000. We can think of this value as the area of the circle. We are asked for the expenses for division R, or in circle terms, the area of sector R.

Statement 1: x = 94

This is the measure of the central angle bounding the sector whose area we need to know (sector R). Since we already know the area of the whole circle, the measure of this central angle is the final piece of the puzzle. (Area of sector R = 94/360 * $5,400,000) Statement 1 is sufficient.

Statement 2: The total expenses for Divisions S and T are twice as much as the expenses for Division R.

This statement relates the total of two unknown sectors to another unknown sector. Given this statement alone, we don’t know the relationship of any of these sectors to the whole circle, so we can’t solve for any of their areas. Statement 2 is insufficient.

The answer:
Statement 1 is sufficient.
Statement 2 is insufficient.
The correct answer is A.

Pieces of Pi: More Difficult Problems

Let’s ratchet up the difficulty a bit with another sector problem that involves more smoke and mirrors.

Three identical circles problem

The figure consists of three identical circles that are tangent to each other. If the area of the shaded region is 64√3 – 32*π, what’s the radius of each circle?

A. 4
B. 8
C. 16
D. 24
E. 32

(tangent means just touching and not overlapping)

The problem mentions only three circles and a shaded region, but the graphic includes something more: an equilateral triangle drawn by connecting the centers of the three circles. You can solve this problem without knowing anything about the formula for the area of an equilateral triangle (although you should know this formula).  It should occur to you that the area of the shaded region could be expressed as the area of the triangle minus the combined area of those three sectors, which matches the given expression 64√3 – 32*π. So the (irrelevant) area of the triangle is 64√3, and the area of the three sectors is 32*π. 

You might start by trying to get the area of a single sector by dividing 32*π by 3. But 32 won’t divide nicely by 3, which should signal you to try something else. If you can’t go from the combined area of the three sectors to the area of one sector, maybe you can go from the combined area of the three sectors to the area of one circle. You might use your spatial reasoning and conclude that the three sectors together look like they make up half a circle. Or you might recall that each interior angle of an equilateral triangle measures 60 degrees. Therefore each of these sectors is ⅙ (60/360) of a whole circle, and the three of them together do indeed make up half a circle (3 * ⅙ = ½).

Now, if the sectors’ combined area is 32*π, and this is half a circle, then the area of the whole circle is 2 * 32*π = 64. Having found the area of a circle, we can now solve for the radius. 

A = 64 = π*r2
64 = r2
r = 8

And the correct answer choice is B.

Arc Length Problem

Let’s try one more problem, this time focusing on arc length.

The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 4*π/3 what is the length of line segment RU?

A. 4/3
B. 8/3
C. 3
D. 4
E.  6

Points that “lie on a circle”

A note about points that “lie on a circle.” This always means that the points are on the edge or perimeter of the circle.

It may be helpful to visualize or even draw out what has been described here.

This is a good opportunity to introduce some terminology. We see that line segment RU connects two points on the circle. Such a line segment is called a chord. If the line continues on to either side of the circle so that the circle is “skewered,” the line is called a secant (the GMAT does not expect you to know this term). When a chord or secant passes through the circle’s center, it creates a diameter. A line outside a circle that just touches the circle at one point is called a tangent.

If you aren’t sure how to calculate the length of a chord like RU, start with what you know. We are given the length of arc RTU (4*π/3) and the radius of the circle. A good step is to calculate the circumference of the circle so that we can see how it relates to arc RTU. 

C = 2*π*r
C = 2*π*4
C = 8*π

The circumference is 8*π, and arc RTU is 4*π/3. 8*π/6 = 4*π/3. Therefore arc RTU represents ⅙ of the circumference of the circle, and its corresponding central angle is 60 degrees (360/6). Drawing out this information helps us to see its relevance.

The length of line segment RUThe central angle and chord RU form an equilateral triangle. Since the radius of the circle is 4, chord RU also has length 4, and the correct answer is D.

This concludes our second article on the GMAT’s treatment of circles. Next time we will look at another kind of angle inside a circle: an inscribed angle, and at the related topic of inscribed polygons.

 

Contributor: Elijah Mize (Apex GMAT Instructor)

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Top 5 EA Memorization Techniques
Posted on
17
Mar 2022

Top 5 EA Memorization Techniques

We here at Apex always tell our clients to find what works for them and stick to it. Believe it or not, there is little need to struggle when trying to memorize certain test-taking techniques. Often a simpler solution path is always readily available. Our tutors at Apex are professionals when it comes to helping EA test takers. We teach our clients tips which suit their mental and cognitive abilities. This type of teaching is called Cognitive Empathy. How it works is that we do not force clients into a ‘one-size-fits-all’ box of EA test-prep steps and solution paths. Instead, we work with and support our clients by tailoring our approach so that they have a toolkit of skills which fit their personal needs and capabilities. Here we list four EA memorization techniques which all of our clients learn.  

1. Memorize the answer layout. 

On the EA, some question types have the same responses. On the Data Sufficiency portion, for example, answers are presented in the same way. These are: 

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
  3. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
  4. EACH statement ALONE is sufficient
  5. Statements (1) and (2) TOGETHER are NOT sufficient

To make the test easier, you can memorize these statements since their order and wording stay the same. We suggest memorizing them in a more simple form. For example: 

  1. Only Statement 1 
  2. Only Statement 2
  3. Only Both Statements together
  4. Each statement alone 

This as a memorization technique will help you cut down on the time you spend on the test. You won’t need to reread the answers each time you encounter them.  

2. Practice vocabulary during the day

This may sound like a fairly simple and obvious trick but trust us. This EA memorization technique helps! The vocabulary section of the EA can be tricky especially if you find your English language skills are subpar. Often people stick to flashcards to help them memorize terms and concepts. While this tactic can be useful, we found that to really engrain the meaning of complex words it is best to use them throughout the day.

We suggest deciding on a handful of words that you consider exceptionally difficult to memorize and commit to using them throughout the day. This will help you learn to structure the word within a sentence while learning how to use the word properly. In addition to using daily vocabulary, we suggest keeping a notebook of the most difficult terms you have come across and reviewing them as your vocabulary grows! 

3. Use Acronyms and Mnemonics

Being out of school for a while means you are likely struggling with remembering math concepts and equations? The EA quantitative portion may appear overwhelming to test-takers. We understand this, which is why we teach our clients how to avoid using math on the EA altogether! But sometimes, the best solution path is the most direct and obvious one. Here are some tricks to remembering some basic math equations and formulas: 

  • Simple Interest Formula
    • Interest = principal x rate x time 
    • I = prt 
    • Remember the equation as: I am Pretty!
  • Distance Formula 
    • Distance = rate x time
    • D = rt
    • This equation can be remembered as the word: dirt 
  • Linear Equation
    • Y = mx + b 
    • B for begin / M for move 
    • To graph a line, begin at the B-value and move according to the m-value (slope) 
  • Multiplying Binomials 
    • (x – a)(x + b) 
    • Remember FOIL for the order: 
      • First
      • Outside
      • Inside
      • Last 
  • Order of Operations
    • When answering an equation which looks something like this: 7 x (4 / 6) + 2 = remember: PEMDAS or Please Excuse My Dear Aunt Sally 
    • Parentheses 
    • Exponents 
    • Multiplication
    • Division
    • Addition
    • Subtraction 

4. Applying visual meanings to things 

This trick is most useful if you plan on taking the EA online. During your studying, look at what is around you and apply meaning to objects. For example, when working on a certain type of math problem, work out the solution while staring at the radiator in your room. Then, while taking the exam (if you are taking the EA online), look at the radiator if you come in contact with a similar type of problem. This visual trick helps your brain remember since you will be correlating that which you have recently studied with the image of the radiator. If you are taking the EA onsite, consider studying while wearing the same pieces of clothes or jewelry which you will wear during your test. Perhaps play with a bracelet or watch while memorizing words, or wear a comfy sweater which you associate with certain mnemonic devices. We teach our clients this trick and it definitely helps them during the test! 

5. Apply the knowledge you are learning often

Reading things from a textbook and taking notes is one thing. But it is a completely different thing to practically apply the information you are learning. Completing one or two practice questions won’t automatically make you a whiz at that particular type of problem (even if you got the correct answer). Instead, make sure to practice in different locations and use different mediums (such as at a restaurant, while riding the train into work, or while cooking dinner). Doing this will challenge your brain to think strategically in various situations and under different circumstances. You can do this type of learning with the quantitative and qualitative portions of the exam.

Final Thoughts 

However straightforward these EA memorization techniques may seem, they nonetheless require work and dedication. As I am sure you know, hard work does pay off in the long run! The amount of work you put into your studying can dictate where you end up attending school, plus it can help with your future job search. While you are not your EA score, your test score does play a large role in your overall application to your dream school! If you are looking for extra support while preparing for the EA, we here at Apex offer bespoke one-on-one tutoring with high-achieving clients. You can schedule a complimentary, 30-minute consultation call with one of our tutors to learn more! 

 

Contributor: Dana Coggio

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Circles On The GMAT 101 Area, Pi, and Circumference
Posted on
15
Mar 2022

Circles On The GMAT 101 – Area, Circumference, and Pi

Circles on the GMAT function like any other GMAT quant topic: the list of “knowledge bits” you need is short, but the questions creatively combine and/or disguise these few “knowledge bits” to create complex problems. 

In this first article, we will discuss the most basic properties of circles and the formulas that relate to these properties. The properties in question are area, circumference, and radius/diameter.

Circle Properties: Radius & Diameter 

I treat radius (r) and diameter (D) together because they essentially express the same thing, and because the relationship between them is so simple.

Radius (r) and diameter (D) of the circle

Diameter tells you how “wide” a circle is at its widest point. If you draw a straight line all the way across a circle, hitting the center on the way, that line is a diameter, and the length of that line is the diameter of the circle. The radius of the circle is half of this line – or any straight line drawn from the center of the circle to a point on its edge.

This is the most basic property of a circle. The two next most basic properties involve bringing in a specific number, one of the most famous numbers in mathematics: pi.

Circle Properties: Pi

Pi is the name of a Greek letter that looks (in its lowercase form) like this: π.

The value represented by this character is irrational (the numbers after the decimal never stop), but for most purposes and for the GMAT, 3.14 is enough. If you happen to be working with fractions or if you prefer fractions to decimals, 22/7 is a rather precise way to express pi. Rounded to the thousandths place, pi is 3.142, and 22/7 is 3.143. That’s close enough for jazz and certainly close enough for GMAT quant.

Interestingly – and for reasons relating to math beyond what is required for the GMAT – this same value can be combined with the radius/diameter to calculate both the circumference (C)  and area (A) of the circle. Circumference is the distance around the circle (its perimeter), and area is the space inside the circle.

C = π*D     or     C = 2*π*r
A = π*r²

The two options for the circumference equation are, in fact, equivalent, since D = 2r. You may be wondering why mathematicians split the 2 and the r around the π, instead of just saying π2r. One reason is simply the conventions that have developed for algebraic notation; it “looks wrong” to have the 2 in the middle after the π. But another reason is a (non-GMAT math) connection between the circumference and area equations. Both equations have a π, an r, and a 2. In the area equation, the 2 functions as an exponent on the r. In the circumference equations, it functions as a coefficient multiplying the expression. Area is pi times the square of the radius. Circumference is pi times the radius doubled.

Examples:

1. If a radius is 3, what’s the area of the circle?

A = π*r²= π*3² ≈ 28.27433

2. If the area of a circle is 25π, what is the diameter of the circle?

A = π*
r² = 25*π÷π
r = √25 = 5

3. If a radius is 4, what’s the circumference of the circle?

C = 2*r*π
C = 2*4*π
C = 8*π = 25.13274 

Official GMAT Problem

In all likelihood, none of this looks new. But like we said at the beginning, GMAT quant can get creative with common mathematical knowledge. Take a look at this official GMAT problem, and try to answer it before reading on:

Official GMAT Circle ProblemIn the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?

A. 4
B. 3
C. 2
D. √3
E. √2

Understanding the Problem 

The only properties at play here are area and circumference, perhaps with radius/diameter as a “bridge” between the two, but the answer to the problem may not be immediately obvious. Part of this is due to a common GMAT technique – the removal of numbers to make the problem more abstract.

This problem disguises the relationship between the two circles by referring not to the area of each circle, but to the area of the shaded region. A helpful preliminary deduction is that if, as the problem says, the area of the shaded region is 3 times the area of the smaller circular region, then the area of the larger circle is 4 times the area of the smaller circle (comprising the 3 “parts” in the shaded region and the 1 “part” in the smaller circle).

So we have the factor relating the circles’ areas: 4. But we were asked about circumference, not area. How do we get from area to circumference? Well, both the area and circumference equations have the radius in them, so one option is to pick two values for area, with one being 4 times the other, solve for the radius of each circle, and then plug each of these radius values into the circumference equation.

Solving the Problem 

Let’s say the area of the larger circle is 16, and the area of the smaller circle is 4. Since π is common to all the circle equations, in this case it is irrelevant, and we should just remove it instead of keeping it as “dead weight” to move around algebraically.

Large Circle                             Small Circle
A = π*r²                                     A = π*r² 
16 = π*r²                                   4 = π*r² 
r = 4                                         r = 2

So when the areas of two circles are related by a factor of 4, their radii (plural for radius) are related by a factor of 2: that is, the square root of 4. This makes sense, since radius is a linear value and area is a square value. This is just like how when you double the length of the side of a square, you quadruple its area (since 2² = 4). When you triple the length of the side of a square, you make its area nine times what it was before (since 3² = 9). The factor of increase for area is the square of the factor of increase for the linear measure.

C = 2*π*r
C = 2*π*4
C = 2*π*2

Since we are only concerned about the factor relating the circumferences of the circles, we can ignore whatever is common to both (2*π), leaving us with 4 and 2. Since 4 is twice as much as 2, the circumference of the larger circle is twice the circumference of the smaller circle, and the correct answer choice is C.

The Final Step

That last step (and any real calculation) is avoided with two insights:

  1. There is a square relationship between area and radius. Since the area of the larger circle is 4 times that of the smaller circle, the radius of the larger circle is the square root of 4 (2) times the radius of the smaller circle.
  2. There is a linear relationship between circumference and radius. Since the radius of the larger circle is twice that of the smaller circle, the circumference of the larger circle is also twice that of the smaller circle.

When you move beyond rote memorization and understand the circle equations, these insights happen naturally and lead you to the correct answer choice quickly, with virtually no calculation.

 

This concludes the first article in our series on the GMAT’s treatment of circles. Next, we will dive into what happens when you use something called a central angle to mark off only a part of the area (a sector) and circumference (an arc) of a circle.

 

Contributor: Elijah Mize (Apex GMAT Instructor) 

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EA as a returning student
Posted on
08
Mar 2022

How To Study For The EA As A Returning Student!

Been a while since you attended university? In regular circumstances, the EA can be a daunting undertaking. But the thought of taking the EA as a returning student can be downright frightening. We here at Apex work often with clients who have spent years outside of an academic setting. Our experts have compiled tips and tricks for returning students to make sure they are on the studying path of ‘least resistance’. Take a look at our 5 suggestions to make your return to high-caliber EA studying as easy and productive as possible. 

1- Take an EA practice test

This may sound straightforward, but we cannot emphasize enough how important it is that you take a practice test before you begin studying for the EA. This test gives you a baseline understanding of where your strengths and where your weaknesses lie. Though you may use math skills on a daily basis, your quantitative knowledge – as it pertains to test-taking – are of a different ilk. By taking a practice test right out of the gate, you can be certain to accurately assess your current skills level and knowledge. From there, you can build your EA study schedule and timeline and figure out which parts of the EA deserve the majority of your dedication. 

2- Find the school and EA score that suits you

What are your goals? It may sound like a perfectly simple question, but unpacking the answer could take time. It is important that you are honest with yourself as to what your goals are and if they are achievable. Achievable being the key term. A mere desire to attend a top B-school and earn an EA score of 165+ is a difficult challenge, especially if your time out of school has been full of non-business-related opportunities. Perhaps your goal is simply to earn an EMBA, and your dream isn’t to attend Harvard or INSEAD. Decide on which schools you want to attend and the EA score needed for admission. Our advice is to find the average EA score of the most recently accepted class and aim for a score of 10+ points over the average. 

3- Get a consistent EA schedule

You are no doubt busy. Working full-time, having a family, living a 9-5 life for a decade or so can truly make you forget the rigors of school. Wanting to earn an EMBA will throw you back into the world of late-night studying and early morning cramming. The EA is your first step into that world. So be sure to create an EA schedule that works with your timeline and personal life. We have created a 3-month timeline template which you can adjust to fit your personal needs. Once you have created a schedule, be sure to Stick. To. It. This may sound like a ‘no-brainer’ but we find our clients have a difficult time with this. We get it, your personal life is always changing, but your EA journey is a short – though intense – one. If your goal is to earn an EMBA, the EA is a necessary stepping stone on that journey. 

4- Learn the EA basics

So you have taken a practice test, have decided on which school(s) you wish to attend, and come up with a consistent EA schedule which works for you. From here, you should unwrap the basics of the EA. Become comfortable with the layout of the test, and the different types of questions you will be confronted with. But the ‘basics’ go beyond a basic understanding of the test structure. You also need to get comfortable with skills you learned during high school, yes, that’s right…HIGHSCHOOL. The quantitative, qualitative, and analytical skills learned during high school play a massive role in your success on the EA. While this may sound astounding, remember how much you have grown intellectually since your time in high school. The skills you gained have just developed and grown since those years, you may just have to unlock your potential. 

5- Utilize the proper resources and Find Help! 

Not all EA prep books are made the same – nor are all EA tutors. You need to look on the market and see which books are structured best for you. With so many on the market, it might be difficult to discern which are best for you. We suggest looking for books which offer numerous solution paths to the same question. This gives you the chance to find the strategies which work for you and your skillset. Additionally, private EA tutors are ideal for students who are taking the EA as returning students. Our Apex tutors are professionals in working with our clients’ strengths and weaknesses. We also have a unique way of teaching the exam where we show our clients how to consider testing questions from a test-maker’s point of view, not a test-taker. 

If you are considering taking the EA as a returning student and are interested in getting help on the EA, we offer 30-minute complimentary consultation calls with one of our top EA scoring instructors. You can learn more about our program by visiting www.apexgmat.com

6- Be proud of yourself! 

If you have decided to return to school and earn an EMBA after years out of academics, you should be incredibly proud of yourself. Such a decision is not an easy one to make, and yet your commitment to achieving your goals is inspiring. During your EA journey, remember to stick with a structured schedule and find help if you need it. Most people don’t go down the EA journey alone, and neither should you!

 

Contributor: Dana Coggio 

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GMAT vs EA
Posted on
01
Mar 2022

GMAT vs EA – The Differences Between These Exams

GMAT vs EA: What are they?

The Executive Assessment (EA) and the GMAT are both admissions exams designed for MBA or EMBA programs. Both are accepted among most MBA programs, with the GMAT being the gold standard of MBA admissions since its release in 1953. In 2016 GMAC, the company that created the GMAT, released the EA. The EA is specifically tailored towards those applying for Executive MBA (EMBA) programs and those who have spent around a decade in the professional business world. Even though the EA is specifically tailored towards EMBA programs it is being more widely used for MBA program admissions. 

Who takes the EA?

The EA is an exam specifically tailored towards experienced professionals. The EA is shorter, with stringent math sections, and is often considered an easier test. It is meant for those who do not have the time to prepare for the standardized tests for MBA programs. In fact, the GMAC specifies that extensive preparation is not meant for the EA and that the EA is meant for those who have acquired skills and knowledge through work experience. This differs from the GMAT in which we recommend a three-month study plan.

GMAT vs EA: Test Structure 

The structure of the EA is simpler than the GMAT, with only three sections instead of four. Both tests have Quantitative, Verbal, and Integrated reasoning sections, but the GMAT has an additional section, the Analytical Writing Assessment (AWA). The EA also only has 40 questions, compared to the GMAT’s 80. But both have drastically different times with the GMAT taking 3 hours and 7 minutes and the EA taking only 90 minutes. 

All three of the EA’s sections take under fifteen minutes, with the GMAT taking over 30 minutes each on both Verbal and Quantitative sections.

Number of Questions: The EA has 40 questions: 12 Integrated Reasoning, 14 Verbal, and 14 Quantitative. On the other hand, the GMAT has 80 questions: 12 Integrated Reasoning, 36 Verbal, 31 Quantitative questions, and 1 question in the AWA section. 

Time of Each Section: The EA has 30 minutes on each section. Whereas the GMAT has 30 minutes on the Integrated Reasoning, 65 on the Verbal, and 62 on the Quantitative. It gives you 30 minutes for the AWA. 

Types of Questions: The two exams have the same types of questions for every section. 

  • IR: Graphics and Table Analysis, Two-Part Analysis, Multi-Source Reasoning
  • V: Reading Comprehension, Critical Reasoning, Sentence Correlation
  • Q: Data Sufficiency, Problem Solving
  • AWA: The GMAT’s AWA tests your argument analysis skills. 

GMAT vs EA: Scoring 

The EA and GMAT score differently. With the GMAT being a more rigorous test, the scoring ranges from 200-800 while the EA ranges from 100 to 200. In the EA you can score up to a 20 on each section, while GMAT scoring is broken down as follows:

GMAT SCORING
Quant: 0-60
Verbal: 0-60
IR: 1-8
AWA: 1-6

When it comes to the scores of the EA and GMAT remember that a good EA score is about 150 or above, while a good GMAT score is 650 or above. In the EA all the sections are weighted equally, while in the GMAT that is not the case. In the GMAT your AWA score is not weighted as heavily as your Quant or Verbal score. So when studying for both tests you must decide your study habits. In the GMAT you may focus on the Integrative Reasoning section less than the Quantitative for example. It is important to keep in mind where your strengths and weaknesses lie. 

To Review

The EA and GMAT are both exams that can help you get into an MBA or EMBA, so it can be difficult to choose between. However, the GMAC designed the two exams differently for a reason. Understanding why they did so is helpful in choosing which one you would like to take. Recognizing your strengths and weaknesses within testing and your goals within admissions can help you determine which one to take.

 

Contributor: Lukas Duncan

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