The post Inequalities Question Formats on the GMAT appeared first on Veritas Prep Blog.

]]>Let’s look at three different question formats today to understand the difference between them:

- Must Be True
- Could Be True
- Complete Range

**Case 1: Must Be True**

*If |-x/3 + 1| < 2, which of the following must be true?*

* (A) x > 0*

* (B) x < 8*

* (C) x > -4*

* (D) 0 < x < 3*

* (E) None of the above*

We have two linked inequalities here. One is |-x/3 + 1| < 2 and the other is the correct answer choice. We need to think about how the two are related.

We are given that |-x/3 + 1| < 2. So we know that x satisfies this inequality. That will give us the universe which is relevant to us. x will take one of those values only. So let’s solve this inequality. (We will not focus on how to solve the inequality in this post – it has already been discussed here. We will just quickly show the steps.)

|x/3 – 1| < 2

(1/3) * |x – 3| < 2

|x – 3| < 6

The distance of x from 3 is less than 6, so -3 < x < 9. Now we know that every value that x can take will lie within this range.

The question now becomes: what must be true for each of these values of x? Let’s assess each of our answer options with this question:

(A) x > 0

Will each of the values of x be positive? No – x could be a negative number greater than -3, such as -2.

(B) x < 8

Will each of the values of x be less than 8? No – x could be a number between 8 and 9, such as 8.5

(C) x > -4

Will each of the values of x be more than -4? Yes! x will take values ranging from -3 to 9, and each of the values within that range will be greater than -4. So this must be true.

(D) 0 < x < 3

Will each of these values be between 0 and 3. No – since x can take any of the values between -3 and 9, not all of these will be just between 0 and 3.

Therefore, the answer is C (we don’t even need to evaluate answer choice E since C is true).

**Case 2: Could Be True**

*If −1 < x < 5, which is the following could be true?*

*(A) 2x > 10*

*(B) x > 17/3*

*(C) x^2 > 27*

*(D) 3x + x^2 < −2*

*(E) 2x – x^2 < 0*

Again, we have two linked inequalities, but here the relation between them will be a bit different. One of the inequalities is −1 < x < 5 and the other will be the correct answer choice.

We are given that -1 < x < 5, so x lies between -1 and 5. We need an answer choice that “could be true”. This means only some of the values between -1 and 5 should satisfy the condition set by the correct answer choice – all of the values need not satisfy. Let’s evaluate our answer options:

(A) 2x > 10

x > 5

No values between -1 and 5 will be greater than 5, so this cannot be true.

(B) x > 17/3

x > 5.67

No values between -1 and 5 will be greater than 5.67, so this cannot be true.

(C) x^2 > 27

x^2 – 27 > 0

x > 3*√(3) or x < -3*√(3)

√(3) is about 1.73 so 3*1.73 = 5.19. No value of x will be greater than 5.19. Also, -3*1.73 will be -5.19 and no value of x will be less than that. So this cannot be true.

(Details on how to solve such inequalities are discussed here.)

(D) 3x + x^2 < −2

x^2 + 3x + 2 < 0

(x + 1)(x + 2) < 0

-2 < x < -1

No values of x will lie between -2 and -1, so this also cannot be true.

(E) 2x – x^2 < 0

x * (x – 2) > 0

x > 2 or x < 0

If -1 < x < 5, then x could lie between -1 and 0 (x < 0 is possible) or between 2 and 5 (x > 2 is possible). Therefore, the correct answer is E.

**Case 3: Complete Range**

*Which of the following represents the complete range of x over which x^3 – 4x^5 < 0?*

*(A) 0 < |x| < ½*

*(B) |x| > ½*

*(C) -½ < x < 0 or ½ < x*

*(D) x < -½ or 0 < x < ½*

*(E) x < -½ or x > 0*

We have two linked inequalities, but the relation between them will be a bit different again. One of the inequalities is *x*^3 – 4*x*^5 < 0 and the other will be the correct answer choice.

We are given that *x*^3 – 4*x*^5 < 0. This inequality can be solved to:

*x*^3 ( 1 – 4*x*^2) < 0

*x*^3*(2*x* + 1)*(2*x* – 1) > 0

*x *> 1/2 or -1/2 < *x* < 0

This is our universe of the values of *x*. It is given that all values of *x* lie in this range.

Here, the question asks us the complete range of *x*. So we need to look for exactly this range. This is given in answer choice C, and therefore C is our answer.

We hope these practice problems will help you become able to distinguish between the three cases now.

*Getting ready to take the GMAT? We have **free online GMAT seminars** **running all the time. And, be sure to follow us on **Facebook**, **YouTube**, **Google+**, and **Twitter**!*

*Karishma**, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the **GMAT** for Veritas Prep and regularly participates in content development projects such as **this blog**!*

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]]>The post Investing in Success: The Best In-Person or Online GMAT Tutors Can Make a Difference appeared first on Veritas Prep Blog.

]]>**Knowledge of All Aspects of the GMAT**

The best private GMAT tutor has more than just general advice regarding the GMAT. The person has thorough knowledge of the exam and its contents. There are several parts to the GMAT, including the Verbal, Quantitative, Integrated Reasoning, and Analytical Writing sections. A qualified tutor will have plenty of tips to share that can help you to navigate all of the sections on the GMAT. Plus, an experienced tutor will be able to evaluate the results of your practice GMAT to determine where you need to focus most of your study efforts. This puts the element of efficiency into your test prep.

The GMAT instructors at Veritas Prep achieved scores on the exam that placed them in the 99th percentile, so if you work with a Veritas Prep tutor, you know you’re studying with someone who has practical experience with the exam. Our tutors are experts at describing the subtle points of the GMAT to their students.

**Access to Quality Study Resources**

If you want to thoroughly prepare for the GMAT, you must use quality study materials. At Veritas Prep, we have a GMAT curriculum that guides you through each section of the test. Your instructor will show you the types of questions on the test and reveal proven strategies you can use to answer them correctly. Of course, our curriculum teaches you the facts you need to know for the test. But just as importantly, we show you how to apply those facts to the questions on the exam. We do this in an effort to help you think like a business executive as you complete the GMAT. Private tutoring services from Veritas Prep give you the tools you need to perform your best on the exam.

**Selecting Your Method of Learning**

The best GMAT tutors can offer you several options when it comes to preparing for the exam. Perhaps you work full-time as a business professional. You want to prepare for the GMAT but don’t have the time to attend traditional courses. In that case, you should search for an online GMAT tutor. As a result, you can prep for the GMAT without disrupting your busy work schedule. At Veritas Prep, we provide you with the option of online tutoring as well as in-person classes. We recognize that flexibility is important when it comes to preparing for the GMAT, and we want you to get the instruction you need to earn a high score on this important test.

**An Encouraging Instructor**

Naturally, when you take advantage of GMAT private tutoring services, you will learn information you need to know for the test. But a tutor should also take the time to encourage you as you progress in your studies. It’s likely that you’ll face some stumbling blocks as you prepare for the different sections of the GMAT. A good instructor must be ready with encouraging words when you’re trying to master difficult skills.

Encouraging words from a tutor can give you the push you need to conquer especially puzzling questions on the test. The understanding tutors at Veritas Prep have been through preparation for the GMAT as well as the actual test, so we understand the tremendous effort it takes to master all of its sections.

If you want to partner with the best GMAT tutor as you prep for the test, we have you covered at Veritas Prep! When you sign up to study for the GMAT with Veritas Prep, you are investing in your own success. Give us a call or write us an email today to let us know when you want to start gearing up for excellence on the GMAT!

*Getting ready to take the GMAT? We have **free online GMAT seminars** **running all the time. And, be sure to follow us on **Facebook**, **YouTube**, **Google+**, and **Twitter**!*

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]]>The post 3 Things to Avoid When Crafting a Thank You Note appeared first on Veritas Prep Blog.

]]>(Before diving into what not to do, be sure to take a look at Part 1 of this lesson: *3 Ways to Write a Successful Thank You Note.)*

** Do not **copy and paste thank you emails and send them to multiple people. This should be a given, but unfortunately, I don’t think it is. When you copy and paste, the format of your email sometimes gets messed up, but you won’t realize it. Only the reader will notice, and it just looks tacky if the only thing you changed is the recipient’s name. This also goes back to authenticity – it’s hard to create an authentic email if you end up sending the same message to multiple people.

** Do not **add people on LinkedIn. This is especially true for admissions officers (and corporate recruiters once you start interviewing for internships and jobs). Admissions officers do not want to be connected to thousands of prospective students who they may or may not remember, and who may or may not end up at their school. If you have a really great conversation with an alumnus or a current student, feel free to ask them in person if it is alright to add them on LinkedIn. Chances are they will say yes, but they will appreciate the gesture before you just go home, find them on the internet, and add them into your network because you think they have something to offer you.

** Do not **freak out if they don’t respond to you. The people you are meeting are incredibly busy. Put yourself in their shoes – if you met them on the road, it is very likely that they have other events and cities that they are traveling to before going home to get back to their work and catch up on everything that happened since they left.

Next time you go to a recruiting event, keep in mind the conversations you are having and make sure to follow these tips as you write those thank you emails. Good luck in the admissions process!

*Applying to business school? Call us at 1-800-925-7737 and speak with an MBA admissions expert today, or take our free MBA Admissions Profile Evaluation for personalized advice for your unique application situation! As always, be sure to find us on Facebook, YouTube, Google+ and Twitter.*

*Colleen Hill is a Veritas Prep consultant for the Ross School of Business at the University of Michigan. You can read more articles by her here. *

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]]>The post GMAT Integrated Reasoning Practice: Sample Questions and Prep Tips appeared first on Veritas Prep Blog.

]]>**Take a Timed Practice Test**

One way you can get GMAT Integrated Reasoning practice is to take a timed practice test. When you take the entire test or a set of GMAT Integrated Reasoning practice questions, you get an idea of what to expect on test day. More importantly, your results will reveal which skills need improvement.

Timing yourself is an important factor when taking a practice test. You get just 30 minutes to complete the 12 Integrated Reasoning questions on the GMAT. Establishing a reasonable testing pace can lower your stress level and help you to finish all of the questions in the allotted time. At Veritas Prep, we have a free GMAT test that you can take advantage of for this purpose.

**Get Into the Mindset of a Business Executive**

Taking the GMAT is one of the steps necessary on your path to business school, so it makes perfect sense that the GMAT gauges your skills in business. One of the best prep tips you can follow is to complete all GMAT Integrated Reasoning sample questions with the mindset of a business executive. Think of the questions as real-life scenarios that you will encounter in your business career. Taking this approach allows you to best highlight your skills to GMAT scorers.

**Become Familiar With the Question Formats**

As you tackle a set of GMAT Integrated Reasoning sample questions, you’ll see that there are a few different question formats – Graphics Interpretation, Two-Part Analysis, Multi-Source Reasoning, and Table Analysis are the different types of questions on the GMAT.

The Graphics Interpretation questions feature a chart, graph, or diagram. For instance, you may see a question that features a bar chart that asks you to answer two questions based on the data in the chart. Other graphics you may see include scatterplots, pie charts, bubble charts, and line charts.

Two-Part Analysis problems involve a chart with three columns of data and accompanying questions. One tip to remember about these questions is that you have to answer the first question presented before you tackle the second one because the answers will work together in some way. Multi-Source Reasoning questions contain a lot of data. These questions test your ability to combine the data contained in different graphs, formulas, and diagrams to arrive at the correct answer choice. Table Analysis questions ask you to look at a table that may contain four or more columns of data. You have to examine this data closely to answer the questions.

**Practice Working With Different Types of Graphs and Diagrams**

Effective GMAT Integrated Reasoning practice involves learning the details about the different types of graphs, charts, and diagrams featured on the test. Financial magazines and newspapers are great resources for different graphics that you may see on the GMAT. Take some time to make sure you understand the purpose behind various graphs and charts so you feel at ease with them on test day.

**Work With a Capable Tutor**

When studying for the section on Integrated Reasoning, GMAT practice questions can be very useful. Another way to boost your preparation for this section is to partner with an experienced tutor. The instructors at Veritas Prep follow a thorough GMAT curriculum as they prep you for Integrated Reasoning questions as well as the other questions on the exam. We provide you with proven test-taking strategies and show you how to showcase what you know on the GMAT. With our guidance, you can move through each section of the test with confidence.

The professional tutors at Veritas Prep have the skills and knowledge to prepare you for the section on Integrated Reasoning. GMAT questions in all of the sections are easier to navigate after working through our unique GMAT curriculum. We offer both online and in-person courses, so you can choose the option that best suits your schedule. Contact our offices today and get first-rate prep for the GMAT!

*Getting ready to take the GMAT? We have **free online GMAT seminars** **running all the time. And, be sure to follow us on **Facebook**, **YouTube**, **Google+**, and **Twitter**!*

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]]>The post 3 Ways to Write a Successful Thank You Note appeared first on Veritas Prep Blog.

]]>Whenever you meet a school representative at an event – whether that be an admissions officer, alumni, or a current student – you should ** always** send them a note to say thank you. It is a good idea to get in the habit of doing this now because once you get to business school, you will also need to send thank you notes after conferences, corporate presentations, coffee chats, etc., and if you can get the hang of crafting these quickly now, it will only save you time later.

Here are a few tips to writing a successful thank you note:

** Do **write meaningful thank you notes. The people you meet are likely meeting dozens of other prospective students too, so be sincere and authentic in your communications. Don’t say thank you because you have to, but make the content of your email somewhat substantial. Make sure to ask good questions and get to know the people you’re chatting with so you can have something to write about in your follow up email.

** Do **include the details of how you met. Because they are meeting so many others, include how and where you met, and a little bit about what you talked about. You can do this by saying something along the lines of, “

** Do **ask a follow up question, but only if your conversation prompted one. If not, don’t feel compelled to ask anything. Sometimes it is best to end the email with saying you’ll be in touch, rather than ending on a question.

If you had a conversation about a certain club on campus that sounded interesting to you but you don’t remember the name, however, feel free to ask and see if you can get in touch with someone from that club. For example, a question such as, “*You mentioned the new club on campus that works on consultant teams with social enterprises. I’d love to learn more about that. Can you please remind me of the name, and possibly put me in touch with someone involved with that club?” *would be appropriate to ask in your thank you email and show that you were truly interested in the conversation you had with that person.

Follow these tips and you’ll be able to quickly write a successful thank you email that may make a big impact on the way you are viewed by a school.

Stay tuned for our next article, *3 Things to Avoid When Crafting a Thank You Note.*

*Applying to business school? Call us at 1-800-925-7737 and speak with an MBA admissions expert today, or take our free MBA Admissions Profile Evaluation for personalized advice for your unique application situation! As always, be sure to find us on Facebook, YouTube, Google+ and Twitter.*

*Colleen Hill is a Veritas Prep consultant for the Ross School of Business at the University of Michigan. You can read more articles by her here. *

The post 3 Ways to Write a Successful Thank You Note appeared first on Veritas Prep Blog.

]]>The post The Online GRE Math Study Guide: Help and Practice Tips for the GRE Math Section appeared first on Veritas Prep Blog.

]]>Check out this GRE math study guide for tips that can simplify questions in the Quantitative or math section:

**Take Practice Exams**

When it comes to GRE math practice, online exams can prove very useful to students. Taking a practice test lets a student know what types of problems to expect on the actual test, and the results of a practice test reveal what a student needs to work on. Students who have this information are better able to make efficient use of their study time. Our instructors review practice tests with students and suggest specific ways that they can improve on various skills. Our Veritas Prep instructors partner with their students to provide the best GRE math prep available!

**Plugging in the Numbers**

One of the easiest strategies that students can use when tackling the Quantitative section of the GRE is to approach a problem starting with the answer options. For instance, an algebra question may come in the form of an equation that asks a student to find the value of X. A student can plug each of the answer options into the equation in place of X. The number that completes the equation is the correct answer option. This strategy proves especially helpful when a student works a problem in the traditional way and finds that his or her answer is not one of the answer options.

**Eliminating Answer Options**

Students looking for GRE math help should endeavor to simplify each problem as much as possible. For example, after looking at a question and considering all of the multiple choice answer options, a student may notice that one or two of the answer options are obviously incorrect. The student can cross out or eliminate these answer options. This leaves the student with fewer options to consider and makes the problem more manageable. This test-taking technique can also be used on multiple choice questions in the Verbal Reasoning section of the GRE.

**Getting Into the Habit of Using Scrap Paper**

Students should get into the habit of writing out all of the steps of a math problem on a sheet of scrap paper. This is one of those GRE math tips that many students are aware of, but decide not to put into practice; however, this tip can save a student a lot of time if there is a mistake somewhere in a problem. If a student’s answer is not displayed in the list of answer options, he or she can refer to the scrap paper and review the various steps of the problem. In addition, students should use scrap paper for drawing shapes referred to in a math question. Seeing a shape can sometimes prompt a student to figure out an answer more quickly than trying to visualize the shape.

**Reviewing High School Math Problems**

For students who want more GRE math practice, online exercises for high school students are an option. Many of the geometry and algebra skills tested in the Quantitative section are skills students learned in high school.

In addition to going online to complete practice math questions, a student can look in traditional math textbooks designed for high school students. This sort of prep helps students become familiar with working the steps of an algebra equation or successfully completing a geometry problem. Our professional instructors offer guidance and encouragement to students as they work their way through practice problems. We provide students with individualized help, so they can see great improvement as test day approaches.

Finally, students interested in learning the details about our services can look at our FAQ page to find helpful answers. We offer online courses that are convenient for individuals with busy school or work schedules. Veritas Prep has the best GRE math prep courses for students who want to enjoy success on the GRE!

*Want to jump-start your GRE preparation? Register to attend one of our upcoming free online GRE Strategy Sessions or check out our variety of GRE Course and Private Tutoring options. And as always, be sure to follow us on Facebook, YouTube, Google+ and Twitter!*

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]]>The post How Many Letters of Recommendation Should You Submit with Your MBA Applications? appeared first on Veritas Prep Blog.

]]>The formal recommendation process is a bit more straightforward than the informal process, so let us start there. Letters of recommendation require you to identify recommenders whom you feel can accurately speak to your work and contributions in an organization. Their recommendations are then formally submitted through the school’s application tool, and the Admissions Committee reviews them as part of your overall application assessment.

Now here is where things get tricky – most schools strongly discourage additional recommendations. I would guess the reason is because most admissions departments are already overwhelmed with the amount of paperwork and communication they receive from applicants, and anything additional might be tough for them to maintain, track, and evaluate. Also, more practically, allowing for additional recommendations would create an uneven playing field for MBA candidates – some applicants would submit additional letters of recommendation while others would not be able to (for a variety of reasons).

Now, not all schools have this policy and some even welcome additional recommendations, so read the fine print and identify whether there is an opportunity for you to send in additional letters of recommendation or not. If this option is available to you, using your discretion will be key. This should not be seen as an opportunity to just submit more of the same types of recommendations. If you are going to submit an additional letter of recommendation, it should really be a “letter of support”.

These additional recommendations should only be submitted if they are coming from highly visible, impactful, or unique people. The best examples of this are alumni or high-profile individuals who can speak to your business potential. Alumni tend to be a group that the Admissions Committee likes to hear from – alumni letters of recommendation should generally be submitted directly by the alumnus and be short and to the point.

As for letters of recommendation from high-profile people, these are far less well-received, especially if the person doesn’t have much of a relationship with the applicant. In most cases, if the relationship was actually strong, the person probably would have already been the applicant’s main recommender.

However, if the relationship is legit and if the person has considerable sway with the university, the program, or in the general business community, this type of recommendation can be really positive. The business school admissions process is very holistic, so schools will take information like this into consideration.

Now, if you are just not a qualified applicant, even the best of recommendations will not save your candidacy. For those fringe candidates, however, a great letter of recommendation can make or break an application.

*Applying to business school? Call us at 1-800-925-7737 and speak with an MBA admissions expert today, or take our free MBA Admissions Profile Evaluation for personalized advice for your unique application situation! As always, be sure to find us on Facebook, YouTube, Google+ and Twitter.*

*Dozie A. is a Veritas Prep Head Consultant for the Kellogg School of Management at Northwestern University. His specialties include consulting, marketing, and low GPA/GMAT applicants. You can read more articles by him here.*

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]]>The post How to Study Abroad in College appeared first on Veritas Prep Blog.

]]>Consider some helpful information for students who want to know how to study abroad in college:

**Conduct a Search for Colleges That Offer Students the Chance to Study Abroad**

Fortunately, there are many opportunities for today’s college students who want to study abroad. High school seniors who are thinking about studying abroad, but are still unsure, should go ahead and apply to colleges that offer the option. That way, if they do decide to study abroad, they’re at a school that can make that happen.

Often, colleges that offer this study opportunity provide information on their website. Some schools create short videos that give students a quick look at their international programs. Student testimonials can also help prospective students decide whether to participate in the program.

Our professional consultants at Veritas Prep help students to apply to colleges that offer invaluable opportunities, including the chance to study abroad. We have inside knowledge regarding what college officials are looking for as they evaluate students’ applications, letters of recommendation, essays, and other materials.

**Tips for Deciding on a Location**

England, Ireland, Australia, China, Africa, and Italy are just a sampling of the places that college students go to study for a semester or more. With all of the possibilities, it can be difficult for a student to decide where they want to go. One tip is to think about whether they want to study in a country with English as its native language. Of course, this is a moot issue if a student is traveling to a country to learn and practice a foreign language. But if a student is not studying a foreign language, they may feel more at ease in an English-speaking country.

Living arrangements are another consideration. Some study programs require students to live with host families, while others require them to live in dormitories. Students should consider whether they would be comfortable with the specified living arrangements during their stay.

Another thing to consider is how far a student wants to travel away from home. Some students want to be able to travel home fairly quickly, while others want to go to more remote locations. Many of the answers to these questions depend on a student’s personal preferences.

**Benefits of Studying Abroad in College**

Taking courses while living in a foreign country allows students to experience different cultures. Many students sign up for college study abroad programs because they want to learn about the arts, cuisine, and customs of people living in a particular country.

Another benefit of studying abroad is the opportunity to explore various interests that may lead to a future career. For example, a student who spends a semester studying in Kenya may feel inspired by seeing the various forms of wildlife there. As a result, the student might decide to pursue a career as a wildlife conservationist. And on a practical note, one of the biggest benefits of studying abroad is earning credits that count toward graduation.

**When to Study Abroad in College**

Some students who participate in study abroad travel to a foreign country during the regular school year, while others go during the summertime. The timing depends upon the study programs offered by a college. A student has to consider their own individual situation to determine the best time to study abroad. College students who participate in these programs are often willing to forgo their summer vacation or miss school activities during a semester so they can take advantage of this once-in-a-lifetime experience.

No matter where you choose to study, our team at Veritas Prep can help you get there. We provide students with assistance throughout the process of applying to college. We also have services for students who want to prep for the SAT. Our online SAT tutors teach students using first-rate study resources and test-taking strategies. Contact our Veritas Prep offices today and let us help you achieve your goal of attending college and earning a degree.

*Do you need more help with your college applications? Visit our **College Admissions** website and fill out our FREE Profile Evaluation for personalized feedback on your unique background! *

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]]>The post Using Special Formats on GMAT Variable Problems appeared first on Veritas Prep Blog.

]]>Here are some examples:

**An even number: 2a**

Logic: It must be a multiple of 2.

**An odd number: (2a + 1) or (2a – 1)**

Logic: It will not be a multiple of 2. Instead, it will be 1 more (or we can say 1 less) than a multiple of 2.

**Two consecutive integers: 2a, (2a + 1) or (2a – 1), 2a**

Logic: One number will be even and the other will be the next odd number (or the other way around).

**Four consecutive odd numbers: (2a – 3), (2a – 1), (2a + 1), (2a + 3)**

In this case, the sum of the numbers comes out to be a clean 8a. This can be very useful in many cases.

**Five consecutive even numbers: (2a – 4), (2a – 2), 2a, (2a + 2), (2a + 4)**

In this case, the sum of the numbers comes out to be a clean 10a. This can also be very useful in many cases.

**A prime number: (6a+1) / (6a – 1)**

Every prime number greater than 3 is of the form (6a + 1) or (6a – 1). Note, however, that every number of this form is not prime.

**Three consecutive numbers:**

If we know one number is even and the other two are odd, we will have: (2a – 1), 2a, (2a + 1).

Logic: They add up to give 6a.

In a more generic case, we will have: 3a, (3a+1), (3a+2).

This gives us some important information. It tells us that one of the numbers will definitely be a multiple of 3 and the other two numbers will not be. Note that the numbers can be in a different order such as (3a + 1), (3a + 2) and (3a + 3). (3a + 3) can be written as 3b, so the three numbers will still have the same properties.

Basically, try to pick numbers in a way that will make it easy for you to manage them. Remember, three numbers do not need to be a, b and c – there could be, and in fact often are, several other hints which will give you the relations among the numbers.

Now, let’s see how picking the right format of these numbers can be helpful using a 700-level GMAT question:

*The sum of four consecutive odd numbers is equal to the sum of 3 consecutive even numbers. Given that the middle term of the even numbers is greater than 101 and lesser than 200, how many such sequences can be formed?*

*(A) 12*

*(B) 17*

*(C) 25*

*(D) 33*

*(E) 50*

Let’s have the four consecutive odd numbers be the following, where “a” is any integer: (2a – 3), (2a – 1), (2a + 1), (2a + 3)

The sum of these numbers is: (2a – 3) + (2a – 1) + (2a + 1) + (2a + 3) = 8a

Now let’s have the three consecutive even numbers be the following, where “b” is any integer: (2b – 2), 2b, (2b + 2)

The sum of these numbers is: (2b – 2) + 2b + (2b + 2) = 6b

Note here that instead of 2a, we used 2b. There is no reason that the even numbers would be right next to the odd numbers, hence we used different variables so that we don’t establish relations that don’t exist between these seven numbers.

We are given that the sum 8a is equal to the sum 6b.

8a = 6b, or a/b = 3/4, where a and b can be any integers. So “a” has to be a multiple of 3 and “b” has to be a multiple of 4.

With this in mind, possible solutions for a and b are:

a = 3, b = 4;

a = 6, b = 8;

a = 9, b = 12

etc.

We are also given that the middle term of the even numbers is greater than 101 and less than 200.

So 101 < 2b < 200, i.e. 50.5 < b < 100.

B must be an integer, hence, 51 ≤ b ≤ 99.

Also, b has to be a multiple of 4, so the values that b can take are 52, 56, 60, 64 … 96

The number of values b can take = (Last term – First term)/Common Difference + 1 = (96 – 52)/4 + 1 = 12

For each of these 12 values of b, there will be a corresponding value of a and, hence, we will get 12 such sequences. Therefore, the answer to our question is A.

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*Karishma**, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the **GMAT** for Veritas Prep and regularly participates in content development projects such as **this blog**!*

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]]>The post What’s Next After Submitting Your Business School Application? appeared first on Veritas Prep Blog.

]]>Let’s explore a few action items to tick off your to-do list post-submission:

**Finish Other Applications**

Most MBA applicants don’t apply to only one school, so don’t bask too long in your finished application – there are probably plenty more where that came from. Keep the momentum going, buckle down and get moving on the rest of your applications. Make sure you leverage what you have learned from your previously-submitted application to make each version even better than the last.

**Thank Your Recommenders**

Recommenders play a huge role in the success of your application. Make sure you acknowledge their hard work, especially if they are providing recommendations for multiple schools. Also, don’t be afraid to send your thanks after each submitted application, or take them out for lunch to show your appreciation of their contribution to your success.

**Interview Prep**

The best time to prepare for an interview is when all of the information relating your application is still relevant. Some schools can have upwards of 2-3 months in between the application deadline and when they eventually begin interviewing candidates, so try to begin your prep for a potential interview early. Business school application interviews can have a major impact on your candidacy, so getting an early start on your preparation is never a bad thing.

**Apply for Scholarships**

Business school is not cheap and with very few full scholarships available, it is important to consider all alternatives to paying for your education. External merit-based scholarships are a great way to pay for all or a portion of your MBA. Many of the deadlines for these scholarship opportunities are much earlier in the application cycle than you would expect, so don’t wait until you are admitted to figure out how you will pay for school. There is a lot of money out there, so use your post-submission time to give yourself the best chance at securing some funding.

**Relax**

Relax! Applying to business school is stressful so it is very important to find pockets of time to relax. For those who still have additional applications to churn out relaxing may be difficult, but if you have submitted all your applications, enjoy the brief break and rest up for the next phase of the process.

**free MBA Admissions Profile Evaluation** for personalized advice for your unique application situation! As always, be sure to find us on **Facebook**, **YouTube**, **Google+ **and **Twitter**.

*Dozie A. is a Veritas Prep Head Consultant for the Kellogg School of Management at Northwestern University. His specialties include consulting, marketing, and low GPA/GMAT applicants. You can read more articles by him here.*

The post What’s Next After Submitting Your Business School Application? appeared first on Veritas Prep Blog.

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