# Quarter Wit, Quarter Wisdom: When Can You Divide by a Variable?

We have often come across test takers confused about division by a variable. When is it allowed, when is it not allowed? Why is it allowed in some cases and not in others? What are the constraints we need to look out for?

For example:

Is division by x allowed here: x^2 = 10x?
Is division by x allowed here: y = 4x?
Is division by x allowed here: x^2 < 4x?

Let’s take a detailed look at all these questions today.

The basic guidelines:

1. Division by 0 is not allowed, hence you cannot divide by a variable until and unless we know that it cannot be 0.
2. In the case of an inequality, when you divide by a negative number, the sign of the inequality flips. So we cannot divide by a variable until and unless we know that it cannot be 0 AND whether it is positive or negative.

Let’s look at the three questions given above and try to solve them using these guidelines:

Is division by x allowed here: x^2 = 10x?

The first thing to find out here is whether or not x can equal 0.

Case 1: If no other information has been given, then x can be 0 and we cannot divide by it. This is how we proceed in that case:

x^2 – 10x = 0
x(x – 10) = 0
x = 0 or 10

Case 2: If the question stem tells us that x is not 0, then we can divide by x.

x^2/x = 10x/x
x = 10

Obviously, we don’t get the second solution (x = 0) in this case, as we already know that x cannot be 0. Now let’s look at the second problem:

Is division by x allowed here: y = 4x?

Again, this is an equation and we need to know whether or not x can equal 0.

Case 1: If x can be 0, you cannot divide by it. In this case, x = 0 and y = 0 is one of the infinite possible solutions.

Case 2: If the question stem states that x cannot be 0, then we can do the following:

y/x = 4

Now let’s look at the final question:

Is division by x allowed here: x^2 > -4x?

Here, we have an inequality. Before deciding whether we can divide by x or not, we need to know not only whether x can be equal to 0, but also whether x is positive or negative.

Case 1: If we know nothing about the possible values that x can take, then this is how we proceed:

x^2 + 4x > 0
x(x + 4) > 0

Now we can use the method discussed in the first problem to arrive at the range of x.

x > 0 or x < -4

Case 2: If we know that x is positive, then we can proceed like this:

x^2/x > -4x/x
x > -4

Since we are given that x is positive, we know that that x > 0 (looking at the two options above).

Case 3: If we know that x is negative, then this is how we will proceed:

x^2/x < -4x/x (we flip the sign of the inequality because we divide by x, which is negative)
x < -4

The results obtained are logical, right? When x can be anywhere on the number line, we get the range as x > 0 or x < -4.

If x has to be positive, the range is x > 0.
If x has to be negative, the range is x < -4.

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!

# GMAT Tip of the Week: Evolving Your GMAT Quant Score with Help from The Evolution Of Rap

If it’s March, it must be Hip Hop Month at the GMAT Tip of the Week space, where this year we’ve been transfixed by Vox’s video on the evolution of rhyme schemes in the rap world.

The video below (which is absolutely worth a watch during a designated study break) explores the way that rap has evolved from simple rhyme schemes (yada yada yada Bat, yada yada yada Hat, yada yada yada Rat, yada yada yada Cat…) to the more complex “wait did he just say what I thought he said?” inside-out rhyme schemes that make you rewind an Eminem or Kendrick Lamar track because your ears must be playing tricks on you.

And if you don’t have the study break time right now, we’ll summarize. While a standard rhyme might have a one-syllable rhyme at the end of each bar (do you like green eggs and HAM, yes I like them Sam I AM), rappers have continued to evolve to the point where nowadays each bar can contain multiple rhyme schemes. Consider Eminem’s “Lose Yourself”:

Snap back to reality, oh there goes gravity
Oh there goes Rabbit he choked, he’s so mad but he won’t
Give up that easy, nope, he won’t have it he knows
His whole back’s to these ropes, it don’t matter he’s dope
He knows that but he’s broke, he’s so stagnant he knows…

Where “gravity,” “Rabbit, he,” “mad but he,” “that easy,” “have it he,” “back’s to these,” “matter he’s,” “that but he’s,” and “stagnant, he” all rhyme with one another, the list of goes/goes/choked/so/won’t/knows/whole/ropes/don’t/dope… keeps that hard “O” sound rhyming consistently throughout, too. And that was 15 years ago…since them, Eminem, Kendrick, and others have continued to build elaborate rhyme schemes that reward those listeners who don’t just listen for the simple rhyme at the end of each bar, but pick up the subtle rhyme flows that sometimes don’t come back until a few lines later.

So what does this have to do with your GMAT score?

One of the most common study mistakes that test-takers make is that they study skills as individual, standalone entities, and don’t look for the subtle ways that the GMAT testmaker can layer in those sophisticated Andre-3000-style combinations. Consider an example of an important GMAT skill, the “Difference of Squares” rule that (x + y)(x – y) = x^2 – y^2. A standard (think early 1980s Sugarhill Gang or Grandmaster Flash) GMAT question might test it in a relatively “obvious” way:

What is the value of (x + y)?

(1) x^2 – y^2 = 0
(2) x does not equal y

Here if you factor Statement 1 you’ll get (x + y)(x – y) = 0, and then Statement 2 tells you that it’s not (x – y) that equals zero, so it must be x + y. This Data Sufficiency answer is C, and the test is essentially just rewarding you for knowing the Difference of Squares.

The GMAT it cares
’bout the Difference of Squares
When there’s squares and subtraction
Put this rule into action

A slightly more sophisticated question (think late 1980s/early 1990s Rob Bass or Run DMC) won’t so obviously show you the Difference of Squares. It might “hide” that behind a square that few people tend to see as a square, the number 1:

If y = 2^(16) – 1, the greatest prime factor of y is:

(A) Less than 6
(B) Between 6 and 10
(C) Between 10 and 14
(D) Between 14 and 18
(E) Greater than 18

Here, many people don’t recognize 1 as a perfect square, so they don’t see that the setup is 2^(16) – 1^(2), which can be factored as:

(2^8 + 1)(2^8 – 1)

And that 2^8 – 1 can be factored again, since 1 remains 1^2:

(2^8 + 1)(2^4 + 1)(2^4 – 1)

And that ultimately you could do it again with 2^4 – 1 if you wanted, but you should know that 2^4 is 16 so you can now get to work on smaller numbers. 2^8 is 256 and 2^4 is 16, so you have:

257 * 17 * 15

And what really happens now is that you have to factor out 257 to see if you can break it into anything smaller than 17 as a factor (since, if not, you can select “greater than 18”). Since you can’t, you know that 257 must have a prime factor greater than 18 (it turns out that it’s prime) and correctly select E.

The lesson here? This problem directly tests the Difference of Squares (you don’t want to try to calculate 2^16, then subtract 1, then try to factor out that massive number) but it does so more subtly, layering it inside the obvious “prime factor” problem like a rapper might embed a secondary rhyme scheme in the middle of each bar.

But in really hard problems, the testmaker goes full-on Greatest of All Time rapper, testing several things at the same time and rewarding only the really astute for recognizing the game being played. Consider:

The size of a television screen is given as the length of the screen’s diagonal. If the screens were flat, then the area of a square 21-inch screen would be how many square inches greater than the area of a square 19-inch screen?

(A) 2
(B) 4
(C) 16
(D) 38
(E) 40

Now here you KNOW you’re dealing with a geometry problem, and it also looks like a word problem given the television backstory. As you start calculating, you’ll know that you have to take the diagonal of each square TV and use that to determine the length of each side, using the 45-45-90 triangle ratio, where the diagonal = x√2. So the length of a side of the smaller TV is 19/√2 and the length of a side of the larger TV is 21/√2.

Then you have to calculate the area, which is the side squared, so the area of the smaller TV is (19/√2)^2 and the area of the larger TV is (21/√2)^2. This is starting to look messy (Who knows the squares for 21 and 19 offhand? And radicals in denominators never look fun…) UNTIL you realize that you have to subtract the two areas. Which means that your calculation is:

(21/√2)^2 – (19/√2)^2

This fits perfectly in the Difference of Squares formula, meaning that you can express x^2 – y^2 as (x + y)(x – y). Doing that, you have:

[(21 + 19)/√2][(21-19)/√2]

Which is really convenient because the math in the numerators is easy and leaves you with:

(40/√2) * (2/√2)

And when you multiply them, the √2 terms in the denominators square out to 2, which factors with the 2 in the numerator of the right-side fraction, and everything simplifies to 40. And then, in classic “oh this guy’s effing GOOD” hip-hop style (like in the Eminem lyric “you’re witnessing a massacre like you’re watching a church gathering take place” and you realize that he’s using “massacre” and “mass occur” – the church gathering taking place – simultaneously), you realize that you should have seen it coming all along. Because when you subtract the area of one square minus the area of another square you’re LITERALLY taking the DIFFERENCE of two SQUARES.

So what’s the point?

Too often people study for the GMAT like they’d listen to 1980s rap. They expect the Difference of Squares to pair nicely at the end of an Algebra-with-Exponents bar, and the Isosceles Right Triangle formula to pair nicely with a Triangle question. They learn skills in distinct silos, memorize their flashcards in nice, tidy sets, and then go into the test and realize that they’re up against an exam that looks a lot more like a 2017 mixtape with layers of rhyme schemes and motives.

You need to be prepared to use skills where they don’t seem to obviously belong, to jot down and rearrange your scratchwork, label your unknowns, etc., looking for how you might reposition the math you’re given to help you bring in a skill or concept that you’ve used countless times, just in totally different contexts. The GMAT testmaker has a much more sophisticated flow than the one you’re likely studying for, so pay attention to that nuance when you study and you’ll have a much better chance of keeping your score 800.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And as always, be sure to follow us on Facebook, YouTubeand Twitter!

By Brian Galvin.

# Take the 2017 MBA Applicant Survey and Win \$500!

The Association of International Graduate Admissions Consultants (AIGAC) has just launched its annual MBA applicant survey. By filling it out you’ll be entered for a chance to win \$500!

Take the survey here.

Since 2009, AIGAC has regularly conducted a large survey to study trends among business school applicants. The results are shared with AIGAC member consultants and with MBA programs to help them better anticipate the needs of those who will soon apply to business school. Over the past few years, there have even been changes made to some business schools’ applications as a result of AIGAC survey findings, including more streamlined letters of recommendation at some MBA programs!

This online survey should take just a few minutes to complete. We would love to receive as many responses as possible before the survey closes in early April – and we would like to see one of our readers win the \$500 cash prize!

More about the Association of International Graduate Admissions Consultants: AIGAC promotes high ethical standards and professional development among graduate admissions consultants, increases public understanding of graduate admissions consulting, and enhances channels of communication with complementary organizations. The annual MBA Applicant Survey is just one way in which AIGAC serves the admissions and admissions consulting communities.

Thanks in advance for your participation, and good luck with the drawing!

# The Pros and Cons of Skipping the ACT Essay-Writing Section

As you read about the different sections on the ACT, you’ll notice that the essay (or Writing section) is optional. So should you do the ACT Writing section or opt out of it?

The best way to answer this question is to check out both the pros and cons of signing up for the ACT without the essay:

### Pros of Skipping the ACT Essay

Saving Time
One of the advantages of signing up for the ACT without the essay is you can reduce the amount of time you spend preparing for the exam. Preparation for the ACT Writing section means learning the scoring rubric to find out the elements necessary to achieve a high score. Also, you must spend time practicing your essay-writing skills to ensure that you’re ready to create an impressive essay. Skipping the ACT essay means you have more study time to dedicate to the other sections on the test. Plus, taking the ACT without writing time means your total testing period is shortened by 40 minutes.

Saving Money
The official website for the ACT displays one fee for taking the test with the Writing section and another for taking the ACT without the essay, so if you decide to skip the essay, you can save a little money on your testing fees. This can be important, especially if you have a tight budget for standardized tests taken in your junior and senior year in high school.

Perhaps essay-writing is not one of your strengths – when you take the ACT without the Writing section, time can be spent studying for the other sections of the test. You can focus on the Math, Reading, Science, and English sections to achieve scores that will impress college admissions officials. However, if you want to improve your essay-writing skills, our capable instructors can help you to achieve that goal. We can teach you strategies for how to set up a logical, well-organized essay and provide you with guided practice to help make your essay the best it can be.

### Cons of Skipping the ACT Essay

Lacking a Requirement?
One of the cons of taking the ACT without the essay is that you may want to apply to colleges that list a score for the Writing section as an admissions requirement. In order to apply to those colleges, you would have to go back and take the entire test again to get an essay score. Checking to see if the ACT essay is a requirement for the colleges you plan to apply to is a wise idea. But keep in mind that you may want to add a college to your list later or even transfer to another school that requires an ACT essay score.

Skipping the Opportunity to Make an Impression
Another con of skipping the essay section on the ACT is that you’ll miss out on an opportunity to show off your writing skills. Earning a high score on the essay is sure to capture the attention of college admissions officials. If writing is one of your strengths, why not take the time to highlight that talent to colleges?

Missing Out on an Intro to College-Level Work
If you skip the ACT essay, you miss out on the chance to become familiar with college-level work. The task of writing this essay is similar to what you’ll be doing in your English classes as a college freshman. You’ll be writing a lot of papers for classes once you start working toward a degree, so why not give yourself the opportunity to dip your toe into the type of academic work you’ll be doing as a college student?

Whether you decide to take the ACT with or without the essay, we are here to help you prep for the test. You may want to start by trying a free ACT trial class taught by one of our professional, 99th percentile instructors. This will give you an idea of all that we have to offer you at Veritas Prep. Sign up for our test prep services and you have the choice of online tutoring, in-person courses, or On Demand instruction. At Veritas Prep, we make it easy for you to learn what you need to know to ace the ACT!

Still need to take the ACT? We run a free online ACT prep seminar every few weeks. And be sure to find us on Facebook, YouTube, Google+ and Twitter!

# Quarter Wit, Quarter Wisdom: When a Little Information is Enough to Solve a GMAT Problem

We have reviewed what standard deviation is in a past post. We know what data is necessary to calculate the standard deviation of a set, but in some cases, we could actually do with a lot less information than the average test-taker may think they need.

Let’s explore this idea through an example GMAT data sufficiency question:

What is the standard deviation of a set of numbers whose mean is 20?

Statement 1: The absolute value of the difference of each number in the set from the mean is equal.
Statement 2: The sum of the squares of the differences from the mean is greater than 100.

We need to determine whether the information we have been given is sufficient to get us the exact value of the standard deviation of a particular set of numbers. To find the standard deviation of a set, we need to know the deviation of each term from the mean so that we can square those deviations, sum the squares, divide them by the number of terms, and then find the square root.

Essentially, to find the standard deviation we either need to know each element of the set, or we need to know the deviation of each element from the mean (which will also give us the number of terms), or we need to know the sum of the square of deviations and the number of terms in the set.

The question stem here tells us that the mean of the set is 20. We have no other information about any of the actual elements of the set or the number of elements. With this in mind, let’s examine each of the statements:

Statement 1: The absolute value of the difference of each number in the set from the mean is equal.

With this statement, we don’t actually know what the absolute value of the difference is. We also don’t know how many elements there are. The set could be something like:

19, 21 (each term is exactly 1 away from the mean 20)
or
18, 18, 22, 22 (each term is exactly 2 away from the mean 20)
etc.

The standard deviation in each case will be different. We don’t know the elements of the set and we don’t know the number of elements in the set. Because of this, there is no way for us to know the value of the standard deviation – this statement alone is not sufficient.

Statement 2: The sum of the squares of the differences from the mean is greater than 100.

“Greater than 100” encompasses a large range of numbers – it could be any value larger than 100. Again, we cannot find the exact standard deviation of the set, so this statement is also not sufficient alone.

Using both statements together, we still do not have any idea of what the elements of the set are or what the sum of the squares of the differences from the mean is. We also still don’t know the number of elements. Hence, both statements together are not sufficient, so the answer is E.

Now, let us add just one more piece of information to the problem in this similar question:

What is the standard deviation of a set of 7 numbers whose mean is 20?

Statement 1: The absolute value of the difference of each number in the set from the mean is equal.
Statement 2: The sum of the squares of the differences from the mean is greater than 100.

What would you expect the answer to be? Still E, right? The sum of the deviations are still unknown and the exact elements of the set are still unknown – all we know is the number of elements. Actually, this information is already too much. All we need to know is that the number of elements is odd and suddenly we can find the standard deviation.

Here is why:

Statement 1 is quite tricky.

If we have an odd number of elements, in which case can the absolute values of the differences of each number in the set from the mean be equal?

Think about it – the mean of the set is 20. What could a possible set look like such that the mean is 20 and the absolute values of the differences of each number in the set from the mean are equal. Try to think of such a set with just 3 elements. Can you come up with one?

19, 19, 21? No, the mean is not 20

19, 20, 21? No, the absolute value of the difference of each number in the set from the mean is not equal. 19 is 1 away from mean but 20 is 0 away from mean.

Note that in this case, the only possible set that could fit the given criteria is one consisting of just an odd number of 20s (all elements in this set must be 20). Only then can each number be equidistant from the mean, i.e. each number would be 0 away from mean. If the numbers of the set all have equal elements, then obviously the standard deviation of the set is 0. It doesn’t matter how many elements it has; it doesn’t matter what the mean is! In this case, Statement 1 alone is sufficient so the answer would be A.

Takeaway:
If a set has an even number of distinct terms, the absolute values of the distances of each term from the mean could be equal. But if a set has an odd number of terms and the absolute values of the distances of each term from the mean are equal, all the terms in the set must be the same and will be equal to the mean.

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!

Starting college courses brings with it a collection of new challenges for every student. Students with ADD or ADHD have a unique set of challenges as they settle into life at college.

Fortunately, there are steps these students can take to achieve success and earn a degree. Learn some helpful tips for college students who deal with ADD or ADHD:

The best colleges for students with learning disabilities are the ones that provide plenty of academic support. Some students need assistance with tackling the work in all of their courses, while others need limited academic support for a learning disability. A student with ADD or ADHD must take it upon themselves to inquire about these services and use them whenever needed.

Academic support comes in many forms depending on the resources of a college. Some schools offer students one-on-one tutoring services, while others offer group tutoring sessions. Supplemental instruction is another example of support offered in colleges for students with ADHD. The tutor offering supplemental instruction reviews material taught in a class to make sure that the student has absorbed all of the important points in a lecture. Sometimes it’s simply a matter of adjusting the way course material is delivered.

Some colleges also offer courses in study skills for ADHD students. Students with learning disabilities get to practice study strategies and learn how to take notes in an effective way. The best colleges for students with learning disabilities have the tools to test students who suspect that they have ADD or ADHD. If a student does have ADD or ADHD, the college takes steps to provide the person with the academic support they need to be successful.

Record Lectures
College students with ADD or ADHD sometimes find it helpful to record lectures. This allows them to go over confusing points and review various parts of the lecture at their leisure. They don’t feel as much pressure to take constant notes because they know they can go back and revisit the material. Some colleges, for students with ADHD, automatically allow students to record lectures, while others require students to seek the permission from each instructor. It’s a good idea for students with learning disabilities to let their instructors know the situation so they can contribute to the student’s success.

Use Technological Devices to Stay on Schedule
Today, students with or without a learning disability can use the alarm on their phone to keep them on schedule. For instance, a student with ADD or ADHD may set the alarm on their phone to let them know when it’s time to walk to the library to meet for a study group. Another student may use their phone to let them know they should start off to their first class of the day.

Some students with learning disabilities keep a calendar in their phone that they can refer to at any time to find dates for exams, projects, and meetings. Students may even find it helpful to send themselves reminder texts or emails regarding quizzes or tests.

Use Non-Technological Devices to Stay on Schedule
The individuals who offer academic support at colleges for ADHD students may suggest that students use a large desk calendar to keep them on schedule. For example, a student could highlight upcoming test days for various classes or start a countdown of the days before a big project is due. A desk calendar is something that a student would look at every day. Plus, students can make notes on the calendar to remind them of their progress on various assignments.

They can also purchase a cabinet with a system of drawers so they can separate the notes and other materials for each course. Often, a simple organizational system can assist students with learning disabilities in staying on schedule with all of their coursework.

Our professional tutors at Veritas Prep instruct students who have varying levels of ability. We prep students for standardized tests including the SAT. Our online SAT tutors scored in the 99th percentile on the exam, so students benefit from working with instructors who have hands-on knowledge of the SAT. We also assist students with college admissions by helping them with college essays, filling out applications, evaluating extracurricular activities, and more! Contact Veritas Prep today and let us know how we can help.

The process of applying to business school involves several steps. Filling out an admissions application, writing an essay, and submitting GMAT or GRE scores are just a few of those steps. Another important step is the interview. An interview allows business school admissions officials to get a look at the student behind the application. It also gives a student the chance to ask the admissions officials a few questions.

At Veritas Prep, our knowledgeable consultants help students prepare their admissions application, create a convincing essay, and organize all of the documents and deadlines involved in applying to business school. We know what business schools are looking for, and we share that valuable information with our students. Consider some typical questions asked of business school applicants, and learn some other helpful tips for students getting ready for an interview:

For students who want to study business, interview questions can range from the academic to the personal. Generally, the official conducting the interview starts by asking a student why they want to attend that school. The interviewer is looking for specific answers to this question. For instance, a student may bring up certain internship opportunities available due to the school’s longtime relationship with a variety of companies. Or a student may mention the school’s average class size of just 30 students. These answers show that the candidate is familiar with what the school has to offer.

Another typical question asked in business school interviews concerns a student’s strengths and weaknesses. This question reveals the character, motivation, and work ethic of a student. The answer helps to reveal a student’s suitability for the study program. It’s a good idea for a student to mention what they are doing to improve in any weak areas.

Generally, students are asked about their career plans and how a degree from business school will help them in the pursuit of a particular profession. Students will also be asked about their academic accomplishments and their leadership skills. All of these answers and others help an interviewer to envision the candidate as a student in the business school.

How to Prep for the Interview
One of the best ways to prepare for interview questions is to review a school’s website. Most school websites include information about class size and faculty member qualifications. Also, there are statistics on the number of students who find jobs after graduation. This is an efficient way to find specific facts.

Students should practice answering potential questions with a friend or family member. The person playing the interviewer can offer helpful suggestions on how the student can improve upon certain answers. Plus, students can use this opportunity to come up with questions for the interviewer about the school and its courses. Our consultants at Veritas Prep have the skills and experience to assist students as they prep for their business school interview. Our online experts have inside knowledge about the admissions process.

What to Bring to the Interview
Most of the time, a business school has a copy of a student’s résumé at the interview, but it’s a good idea for students to bring a few extra copies of their résumé with them too, since there might be additional officials in the interview room. Students may also want to bring a copy of their GMAT or GRE test scores as well as a copy of their latest transcript. A student may not need to take any of these documents out of their folder, but it’s a good idea to have them on hand just in case.

What to Wear to the Interview
Dressing in an appropriate way plays a part in a student’s success in an interview at a school of business. Interview questions and answers are the most important elements of an interview, but a student must also make a good visual impression. It’s best for a student to wear conservative clothes and have a well-groomed appearance. A student doesn’t have to invest in designer clothes to make a positive impression on an interviewer – just look neat and professional.

Our MBA consultants at Veritas Prep guide students through the process of applying to business school. We have the resources to prepare students for the GMAT, advise them on their admissions application, and offer strategies for success in business school interviews. Call or email Veritas Prep today and let us partner with you on the path toward an advanced degree in business.

# The SAT for International Students: What You Need to Know

How do you register for the SAT? For international students, the registration process is a little different than it is for students living in the United States. But don’t worry: if you’re an international student, there is help available if you need assistance with any part of the SAT registration process.

Let’s take a look at this process step by step:

Registering for the Test
The SAT is given six times a year in countries throughout the world. While there are some requirements that are in place for all students taking the SAT, there are additional ones for international students. You can find these requirements organized by country on the College Board’s official website. Remember that international students don’t have the option of late registration. This makes it all the more important to consult the list of test registration deadlines for international students. Listed alongside the test registration deadlines are the deadlines for changes made in your registration.

What If I Need Help With Registration?
If you’d like some guidance while registering for the SAT, you can call on an SAT International Representative in your country. There is a list of official representatives who can help you on the College Board website. Remember that you must work with a representative who has been approved by the SAT program.

When you get the assistance of a representative, you’ll be registering on paper instead of online. After the registration form is complete, your representative is responsible for mailing it in by the deadline. Customer service is given in the language you speak, so if you need to register for the SAT in Spanish, for instance, you’ll speak with a representative who knows the language. Whether you need to hear details about the SAT in Spanish, Mandarin, or another language, the process of registration for the SAT is made easier with the help of a knowledgeable representative.

Testing Fees
You can find the list of testing fees connected with the SAT for international students on the College Board website. There is a special list featuring non-U.S. fees, with the countries organized by region. If you have an International Representative, they can help you understand this step in the process.

Preparation Tips for the SAT
Once you’ve registered for the SAT, it’s time to switch your focus to test preparation. The first thing to do is take a practice SAT. Your results will reveal your strongest skills as well as the skills that need a little work. can then give you strategies to boost your scores on each section of the test. We can pair you with a tutor who understands the way you learn. Plus, we’ll create a customized study plan that helps to strengthen your weakest skills, building your confidence for the test.

Our talented instructors can provide you with guidance on everything from learning SAT vocabulary to refreshing your algebra skills. When you study with Veritas Prep, you work with instructors who scored in the top one percent on the SAT. We believe that if you’re going to prepare for the SAT, it pays to have the best teachers!

More Advice for Success on the SAT
After registering for the SAT and dedicating plenty of time to preparation, make sure to take a few final precautions as your test day arrives. Be sure to start out the day with a high-protein breakfast to maintain your energy level as you tackle all of those challenging SAT questions. Be sure you have the proper identification and other paperwork you need so you can check into the testing center right away and sit for the test. Practice calming breathing techniques to relax a bit before the SAT begins. Getting in the right frame of mind is very helpful on test day.

Check out our free video tutorials to get a taste of what we have to offer students who study with us for the SAT. In addition to having a staff of experienced, professional instructors, we use proven learning materials and resources in our instructional program. This combination provides you with solid preparation for every question you encounter on the SAT. We are proud to offer in-person and online courses as well as private tutoring and On Demand instruction. You can choose the option that best fits into your schedule of activities and obligations. Contact Veritas Prep today and get ready to ace the SAT!

# Quarter Wit Quarter Wisdom: How to Read GMAT Questions Carefully

We all know that we need to be very careful while reading GMAT questions – that every word is important. Even small oversights can completely change an answer for you. This is what happens with many test takers who try to tackle this official question. Even though the question looks very simple, the way it is worded causes test-takers to often ignore one word, which changes the solution entirely. Let’s look at this question now:

Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?

(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6

Let’s consider the question stem sentence by sentence:

“Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month.”

Say Alice’s take-home pay last year was \$100 each month. She saves a fraction of this every month – let the amount saved be x.

“The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did NOT save.”

What would be “the total amount of money that she had saved at the end of the year”? Since Alice saves x every month, she would have saved 12x by the end of the year.

What would be “the amount of that portion of her monthly take-home pay that she did NOT save”? Note that this is going to be (100 – x). Many test takers end up using (100 – x)*12, however this equation is not correct. The key word here is “monthly” – we are looking for how much Alice does not save each month, not how much she does not save during the whole year.

The total amount of money that Alice saved at the end of the year is 3 times the amount of that portion of her MONTHLY take-home pay that she did not save. Now we know we are looking for:

12x = 3*(100 – x)
x = 20

“If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?”

From our equation, we have determined that Alice saved \$20 out of every \$100 she earned every month, so she saved 20/100 = 1/5 of her take-home pay.

Often, test-takers make the mistake of writing the equation as:

12x = 3*(100 – x)*12
x = 300/4

However, this will give them the fraction (300/4)/100 = 3/4, and that’s when they will wonder what went wrong.

Be extra careful when reading GMAT questions so that precious minutes are not wasted on such avoidable errors.

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!

# ACT Vocabulary Tricks and Tips

Studying vocabulary should be on your schedule of things to do as you prepare for the English and Reading sections on the ACT. Numerous lists are available online that feature words commonly seen on the test.

Fortunately, there are many simple tricks and techniques to help you learn and remember ACT vocabulary words and definitions.

Flashcards are a traditional tool for students who are learning vocabulary for the ACT. But you can make your flashcards more effective by taking them a step further. Include the word, its definition, and a personalized sentence on each flashcard. For instance, if you’re learning the word “cunning,” you may create a sentence about your little sister such as, “My sister is cunning about stealing cookies out of the cookie jar.” The word “cunning” means “crafty” or “clever.” You’re more likely to remember a word and its definition when you study it in a personalized context.

The creators of the ACT are interested in measuring your understanding of words and how they are used as opposed to just the number of words you’re able to memorize, so it’s important to thoroughly understand each word you learn.

Another successful strategy to use when learning vocabulary for the ACT is to read a wide variety of material. For instance, if you usually limit your recreational reading to fiction, try reading some biographies or articles in science or nature magazines, or choose a subject you want to learn more about, such as an animal, a country, space travel, the Industrial Revolution, or a famous individual in history. You are more likely to be an active reader when delving into a subject you’re curious about.

When you vary your reading material, you are exposing yourself to larger amounts of unfamiliar vocabulary. As you read, make a list of the words you don’t know and look up the definitions later. Try to determine the definition of a word by looking at the context in which it’s used, then check the dictionary to see if you were right.

Use New Words on a Daily Basis
As you are focusing on learning ACT vocabulary, try using some of your newly acquired words in your daily life. Saying a word aloud in the correct context is an excellent way to solidify it in your memory. You could do this in your classes at school, during club meetings, or at home with your family. In addition, try including a few of the words in papers and other assignments for your English classes. Why not score some extra points on your schoolwork as you prepare for the English and Reading sections on the ACT?

Play Word Games
Playing word games is one of the best ways to prepare for the ACT. There are many online games that ask you to match a definition with the correct word or vice-versa. Some games test your speed at unscrambling letters to make a word that pairs with a definition. Various types of word games can be played by two or more people, so you can get together to play a game with a few friends who are also preparing for the ACT. Making the learning process fun with colorful graphics, music, and exciting challenges helps you add to your growing supply of words.

Take Several Practice Tests
Another effective way to prep for the Reading and English sections on the ACT is to take practice tests. This helps you to figure out which skills you’ve mastered as well as the ones that need work. If you’re worried about these two sections on the ACT, completing practice questions can make you feel more prepared on test day.

Our instructors achieved extremely high scores on the ACT, so when you study with us, you have access to the proven tips and tricks used by our instructors to learn ACT vocabulary. But the ACT tutors at Veritas Prep are more than experts at helping you learn ACT vocabulary: we can also teach you strategies you can use on all parts of the exam. Take advantage of our free trial class to become familiar with the material on the ACT and discover what our instructors at Veritas Prep can do to help you succeed on test day.

Still need to take the ACT? We run a free online ACT prep seminar every few weeks. And be sure to find us on Facebook, YouTube, Google+ and Twitter!

# Quarter Wit, Quarter Wisdom: Solving the Fuel-Up Puzzles

We hope you are enjoying the puzzles we have been putting up in the last few weeks. Though all of them may not be directly convertible to GMAT questions, they are great mathematical brain teasers!

(Before we tackle today’s puzzle, first take a look at our posts on how to solve pouring water puzzles, weighing puzzles, and hourglass puzzles.)

Another variety of puzzle involves distributing fuel among vehicles to reach a destination. Let’s look at this type of question today:

A military car carrying an important letter must cross a desert. There is no petrol station in the desert, and the car’s fuel tank is just enough to take it halfway across. There are other cars with the same fuel capacity that can transfer their petrol to one another. There are no canisters to carry extra fuel or rope to tow the cars.

How can the letter be delivered?

Here, we are given that a single car can only reach the midpoint of the desert on its own tank of gas. Since there are no canisters, the car cannot carry extra fuel, so it will need to be fueled up by other cars traveling along with it.

Let’s fill up 4 cars and get them to start crossing the desert together. By the time they cover a quarter of the desert, half of their fuel tanks will be empty. Hence, we will have 4 cars with half tanks, and the status of their fuel tanks will be:

(0.5, 0.5, 0.5, 0.5)

If we transfer the fuel from two of the cars into two other cars, we will have:

(1, 1, 0, 0)

The two cars with fuel in their tanks will continue to cross the desert and cover another quarter of it. Now both of the cars will have half tanks again, and they will have reached the middle of the desert:

(0.5, 0.5, 0, 0)

Now one car will transfer all of its fuel to the other car, allowing that car to have one full tank:

(1, 0, 0, 0)

That car can then carry the letter through the remaining half of the desert.

For this problem, we didn’t really care about the stalled cars in the middle of the desert since we are not required to bring them back. The only important thing is to get the letter completely across the desert. Now, how do we handle a puzzle that asks us to get all of the vehicles back, too? Let’s look at an example question with those constraints:

A distant planet “X” has only one airport located at the planet’s North Pole. There are only 3 airplanes and lots of fuel at the airport. Each airplane has just enough fuel capacity to get to the South Pole (which is diametrically opposite the North Pole). The airplanes can land anywhere on the planet and transfer their fuel to one another.

The mission is for at least one airplane to fly completely around the globe and stay above the South Pole; in the end, all of the airplanes must return to the airport at the North Pole.

For this problem, we are given that a plane with a full tank of fuel can only reach the South Pole, i.e. cover half the distance it needs to travel for the mission. We need it to take a full trip around the planet – from the North Pole, to the South pole, and back again to North Pole. Obviously, we will need more than one plane to fuel the plane which will fly above the South pole.

Let’s divide the distance from pole to pole into thirds (from the North Pole to the South Pole we have three thirds, and from the South Pole to the North Pole we have another three thirds).

Step #1: 2 airplanes will fly to the first third. A third of their fuel will be used, so the status of their fuel tanks will be:

(2/3, 2/3)

One airplane will then fuel up the other plane and go back to the airport. Now the status of their tanks is:

(3/3, 1/3)

Step #2: 2 airplanes will again fly from the airport to the first third – one airplane will fuel up the other plane and go back to the airport. So the status of these two airplanes is this:

(3/3, 1/3)

Step #3: Now there are two airplanes at the first third mark with their tanks full. They will now fly to the second third point, giving us:

(2/3, 2/3)

One of the airplanes will fuel up the second one (until its tank is full) and go back to the first third, where it will meet the third airplane (which has just come back from the airport to support it with fuel) so that they both can return to the airport.

In the meantime, the airplane at the second third, with a full tank of fuel, will fly as far as it can – over the South Pole and towards the North pole, to the last third before the airport.

Step #4: One of the two airplanes from the airport can now go to the first third (on the opposite side of the North pole as before), and share its 1/3 fuel so that both airplanes safely land back at the airport.

And that is how we can have one plane travel completely around the planet and still have all airplanes arrive back safely!

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!

# Applying to Business School with a Gap in Employment on Your Resume

One of the biggest red flags Admissions Committees encounter during the business school application process is an employment gap on an applicant’s resume. This is unfortunate because for those afflicted, this is often an area that is usually out of the applicant’s control.

Most people are not looking to have an employment gap on their resume, and such periods of joblessness are usually the result of a series of unfortunate events. This problem was much bigger during the global economic crisis a few years back, but the effects of this event still remain on many resumes.

If you have a work gap on your resume, know that it is not the end of the world and that you are not alone on this front – how you mitigate this blip on your resume will be more important to MBA programs than the gap itself – however, don’t completely ignore this issue altogether. Do not treat a gap in employment as something that will not be a concern for the Admissions Committee.

At the very least, if it is a material employment gap, this issue should be addressed in the optional essay. As with most topics you discuss in your optional essay, your explanation and clarification of the employment gap should be concise and to the point. Admissions Committees are not looking for a long-winded string of excuses here – be direct, take ownership of the incident, and identify lessons you learned from it, if appropriate.

Another way to confront an employment gap is through one of the more traditional MBA application essays. If the reason behind the gap or the results of the gap have had a profound impact on your life or career (and it makes sense given the essay prompt), it may be appropriate to take a deeper dive into your situation. A full-blown response like this requires a more nuanced degree of thoughtfulness, so it will be key to do some self-reflection and really identify the underpinnings of your employment gap.

The business school interview represents another area where your employment gap can be addressed by a member of the Admissions Committee. This is probably the most direct way your employment gap will be explored. Keep your explanation simple and avoid making excuses or blaming others. A major mistake many in this position make is disparaging an old employer or an ex-boss. This may actually come across as unprofessional and it generally leaves a bad impression on the interviewer.

Do not let a past employment gap set the tone for your future success at business school. Be prepared to address your history, and take ownership of it in a way that positions yourself for success in the MBA application process.

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.

# How to Choose a College Major

Our college admissions consultants at Veritas Prep are experts at helping students navigate their way through the admissions process. We help students with everything from filling out college applications to crafting a convincing college essay. Of course, once a student is accepted into a college, they must choose a major.

We’ve found that there are many students who wonder how to choose a college major. One student may have so many interests that they don’t know where to focus their studies. Another student may not know how to translate their interest in one subject into a future career. Fortunately, there are many helpful tips for students wondering how to pick a college major.

Identify Interests
Is it a passing interest or an enduring one? Generally, most high school students can put each of their interests into one of those two categories. Some students can recognize an enduring interest right away. For instance, one student might remember being interested in science ever since the first grade – they always enjoyed collecting data, performing lab experiments, and making observations in science classes. This student knows that they’d like to translate their love of science into a career.

Alternatively, there are other students who need to examine several of their interests in order to find an enduring one. One student may love caring for animals but also relishes spending time working at an uncle’s law firm as an office assistant. This student needs to compare their level of interest in each of these activities to figure out which one appeals to them the most. Once a student pinpoints their enduring interests, it’s time to do some online research.

Research Occupations
There are many websites that provide students with examples of occupations within a particular field. The Occupational Outlook Handbook from the Bureau of Labor Statistics is one of the most valuable resources available to high school students. Also, online research makes it possible for a student to learn the details of specific occupations. Salary, opportunities for promotion, and average hours worked are all facts included in a job’s profile.

It’s a good idea for students to keep a list of pertinent questions handy so they can take a good look at the viability of a particular career. All of this research enables a student to choose a major with coursework that prepares them for a desirable occupation.

Talk to Professionals in Various Fields
Talking with a professional who works in a particular occupation can be very useful to a student who is looking for a major. For instance, the student with a passion for science may want to talk with a science teacher at a local elementary school. They can find out what the instructor likes and dislikes about the work. Plus, they can ask the teacher about daily responsibilities and how to get students interested in a lesson. The science teacher can offer a personal perspective on the occupation that can’t be found via online research.

Participate in Volunteer Work
Students wondering how to choose a college major based on an interest may want to engage in some volunteer work. For example, a student who thinks they want to major in veterinary medicine may want to ask a local vet if they can volunteer at their office. This gives the student a chance to talk with the vet and observe the daily activities of a veterinary practice. The time spent volunteering can either strengthen a student’s interest in a certain activity or persuade them to examine other interests.

Meet With a College Counselor
Meeting with a college counselor is helpful even if a student is still undecided on a major. This professional has experience with students who are wondering how to pick a college major out of all of the options available. They will be able to offer simple strategies for how to evaluate various interests. Once a student decides on a major, the counselor can direct them toward the next step of officially declaring the major and beginning on a specific path of study.

Contact Veritas Prep today and we can assist you with the college admissions process, SAT and ACT preparation, and much more. Give us the opportunity to prep you for a successful four years in college!

# Get Ahead of the GRE With Math Tutoring

The Quantitative Reasoning portion of the GRE has two sections with 20 questions in each. You are given 30 minutes to complete each of these sections. If you feel a little uncertain about this portion of the exam, getting a GRE math tutor can prove helpful in a variety of ways.

When you study with a GRE math tutor, you can start strengthening your weakest skills right away. Part of the Veritas Prep tutoring program involves evaluating your skills for every section of the GRE. If the results of your evaluation, or practice test, reveal that you need to sharpen your algebra skills, then your tutor will incorporate that into your customized study plan. Alternatively, if your results reveal that you are highly skilled in the area of geometry, then less time will be spent reviewing that particular topic. Following a specially-designed study plan allows you to get the most out of every tutoring session.

Learn Strategies to Solve Math Problems
Studying with an experienced GRE math tutor gives you the opportunity to learn solid strategies to use on the Quantitative Reasoning section. One valuable strategy is to draw illustrations for geometry problems instead of trying to mentally juggle all of the important elements of a question. Seeing an illustration can help you arrive at the correct answer more quickly.

You can use your scrap paper for writing the steps of algebra problems as well, so if you make a mistake, you can look at the steps to find the error. Another valuable strategy is to scan each math problem and eliminate answer options that are obviously wrong. Right away, this makes seemingly complicated math questions easier to handle.

Practice With an Experienced Instructor
When you work through practice geometry, data analysis, algebra, and arithmetic problems with a tutor, you’ll be getting the guidance you need to master each skill. For example, if you arrive at the incorrect answer to a practice algebra problem, your tutor can review each step with you to reveal where you went wrong. More importantly, your tutor can give you pointers that help you to avoid making the same mistake on similar math problems.

The tutors at Veritas Prep achieved high scores on the GRE, so when you study with us, you’re getting strategies straight from experts. Also, we take the time to match you with a tutor who is familiar with your learning style. This makes your tutoring sessions even more productive.

Get Support When Preparing for the Exam
You’re likely to have a lot of questions as you prep for the Quantitative Reasoning section of the GRE. In fact, questions may come up on a daily basis. Maybe you’ll think of one while you’re driving, sitting at work, or having lunch with a friend.

One option is to write down those questions and ask them during your next tutoring session. But if you’re preparing for the GRE with Veritas Prep, you could also email your questions to us. We provide our students with prompt answers so they can continue on the right track with their study efforts. Online support combined with quality instruction and study resources make our GRE tutoring services second to none.

Accountability Counts
Preparing with a math tutor can give you an extra element of accountability. You’ll spend a lot of time working with your tutor and studying independently for the Quantitative Reasoning section of the test. This makes you accountable to both your tutor and to yourself. You truly want to perform at your best on the exam so your efforts, as well as your tutor’s, pay off in the end.

When you make the decision to study with a tutor for the Quantitative Reasoning section, you’ll want to partner with the best. Our GRE study program provides you the advantages you need to achieve a high score on the test. Our experienced tutors understand what it takes to prepare for this exam and will be there to offer you encouragement at every step. We are so sure of the quality of our GRE tutoring courses that we back them up with a guarantee. We are invested in your success! Contact our offices to arrange for a knowledgeable GRE math tutor today.

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 and Private Tutoring options. And as always, be sure to follow us on Facebook, YouTube, Google+ and Twitter!

# Converting Your SAT Score to an IQ Score

When you hear the words “SAT score,” it probably brings to mind senior year, percentiles, college applications, and lots of studying. But have you ever considered SAT scores vs. IQ scores? Does your SAT score have anything to do with your IQ?

What Does the SAT Measure?
There are many helpful study tips to take advantage of when you’re preparing for the SAT. But have you ever paused to consider what the SAT actually measures? The Reading, Writing & Language, Math, and Essay sections on the SAT are designed to gauge how ready you are for college-level work.

For instance, the Reading section tests your reading comprehension skills, including your ability to recognize an author’s tone and determine the meaning of various words in context. Alternatively, the Math section tests your skills in geometry, algebra, data analysis, and more. Naturally, most college admissions officials want to select applicants who they believe will thrive in their academic endeavors, and a student’s SAT score is one factor in an admissions official’s decision.

Your intelligence quotient, or IQ, is another type of measurement. An IQ test measures things like your ability to use logic, your verbal reasoning skills, spatial awareness, and visual abilities. Basically, your IQ score shows how versatile of a thinker you are and how good you are are problem-solving. According to Mensa, the high IQ society, a “genius” IQ is generally one that’s 132 or higher. Someone with average intelligence typically has an IQ between 85 and 114.

SAT vs. IQ Scores
There is one major difference to point out when considering SAT vs. IQ scores: the SAT measures a person’s knowledge of certain subjects, while an IQ test measures a person’s general thinking abilities. You can take steps to practice for the SAT and improve your score, but you can’t study for an IQ test. Additionally, many colleges require students to submit an SAT score (or ACT score) along with their applications, but do not ask for an IQ score submission.

SAT-to-IQ Conversion
There are SAT-to-IQ conversion charts and calculators online that ask you to plug in the scores you received on the Verbal and Math sections of the SAT. Within seconds, the conversion calculator displays an IQ connected with your total SAT score.

There is usually a disclaimer attached to the results reminding you that the number you see is only an estimate of your IQ. But are these figures really accurate? It depends. Scores on some versions of the SAT have been shown to strongly correlate with IQ scores, but for more recent test-takers, that’s not necessarily the case.

Also, it’s important to consider whether your SAT scores paint an accurate picture of your abilities. Perhaps you were sick on test day and weren’t able to stay focused on the work, resulting in an inaccurate SAT score. Also, some individuals feel a lot of pressure when taking standardized tests, so their test score may not be a true reflection of their abilities. These factors and others can have a big effect on a person’s SAT scores, meaning that even if you can convert your SAT score to an IQ, the result might not be accurate.

Preparing for the SAT
If you want help studying for the SAT, we have what you need at Veritas Prep! Each of our SAT instructors scored in the top one percent themselves, so when you take our SAT prep courses, you are learning test-taking strategies from individuals who’ve conquered the exam. In addition to practical advice about the SAT, our instructors provide you with encouragement as you work your way through our study resources that address all parts of the test.

It’s important to know that your tutor is behind you 100 percent. We’ll evaluate the results of your practice SAT to find out where we can be of the most help. And we have several options to choose from when it comes to SAT prep, providing both online and in-person courses, because we know that high school students are busy people who need a study program that fits with their schedule. Private tutoring is another option if you like to learn one-on-one.

Feel free to check out our video tutorials to get some valuable SAT tips right away: These tutorials are just a preview of what we can do to boost your test performance. Email or call Veritas Prep now to start preparing for excellence on the SAT!

# How to Use a 1-Year MBA Program to Make Your Career Switch

1-year MBA programs represent a great opportunity to secure a graduate business education at an accelerated pace. This program format has long been a staple in Europe, with venerable programs like INSEAD establishing a successful track record of success in producing top flight candidates via their accelerated curriculum.

The 1-year program has taken a bit longer to gain steam in the United States, but largely pioneered by Kellogg’s 1-year program, this format has begun to pick up in popularity in the U.S. as well.

The benefits of these 1-year programs are obvious to interested students – the ability to shave a year off of one’s time away at business school is attractive to many MBA applicants. This shorter program format also typically comes with a reduced price tag and a much lower opportunity cost, allowing students to get back into the work force much faster.

Time and money aside, most applicants are primarily considering business school for career reasons. The ability to pursue desired career opportunities, which are directly provided by their business school, tends to be the leading decision driver for those interested in a 1-year program. Given the shorter timeline of a 1-year program, it has largely been seen as an ideal choice for MBA candidates seeking to remain in the same industry or with the same employer. For those seeking to make a career switch post-MBA this program may not be ideal, but it certainly presents some opportunities.

For more traditional MBA feeder industries like management consulting and investment banking – where recruiters are looking more for raw talent and intellectual horsepower than for work experience – having pre-existing industry experience is less important. The key loss here is the inability to test out an industry through internships prior to accepting a job, which many MBA candidates on the traditional 2-year track have the opportunity to do. Also, the reduced opportunities to secure a job offer, given the 1-year program’s tendency to focus only on full-time employment, puts an intense emphasis on making the most of the chances a 1-year business school student does have.

Many 1-year MBA programs do offer in-term internship opportunities that give interested students the chance to test out industries and jobs in other fields. The key for 1-year students is to really come into business school with a plan. By understanding the limitations of the 1-year program, students can better plan paths to achieve their post-MBA goals. The clearer one’s goals are prior to matriculation, the more realistic it will be to make a career switch after graduation.

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.

# Quarter Wit Quarter Wisdom: Solving the Weighing Puzzle (Part 2)

A couple of weeks back, we discussed how to handle puzzles involving a two pan balance. In those problems, we learned how to tackle problems that ask you to measure items against one another.

Today, we will look at some puzzles that require the use of a traditional weighing scale. When we put an object on this scale, it shows us the weight of the object.

This is what such a scale looks like:

Puzzles involving a weighing scale can be quite tricky! Let’s take a look at a couple of examples:

You have 10 bags with 1000 coins in each. In one of the bags, all of the coins are forgeries. A true coin weighs 1 gram; each counterfeit coin weighs 1.1 grams.

If you have an accurate weighing scale, which you can use only once, how can you identify the bag with the forgeries?

We are allowed only a single weighing, so we cannot weigh all 10 bags on the scale individually to measure which one has counterfeit coins. We need to find the bag in only one weighing, so we need to somehow make the coins in the bags distinctive.

How do we do that? We can take out one coin from the first bag, two coins from the second bag, three coins from the third bag and so on. Finally, we will have 1 + 2 + 3 + … + 10 = 10*11/2 = 55 coins.

Let’s weigh these 55 coins now.

If all coins were true, the total weight would have been 55 grams. But since some coins are counterfeit, the total weight will be more. Say, the total weight comes out to be 55.2 grams. What can we deduce from this? We can deduce that there must be two counterfeit coins (because each counterfeit coin weighs 0.1 gram extra). So the second bag must be the bag of counterfeit coins.

Let’s try one more:

A genuine gummy bear has a mass of 10 grams, while an imitation gummy bear has a mass of 9 grams. You have 7 cartons of gummy bears, 4 of which contain real gummy bears while the others contain imitation bears.

Using a scale only once and the minimum number of gummy bears, how can you determine which cartons contain real gummy bears?

Now this has become a little complicated! There are three bags with imitation gummy bears. Taking a cue from the previous question, we know that we should take out a fixed number of gummy bears from each bag, but now we have to ensure that the sum of any three numbers is unique. Also, we have to keep in mind that we need to use the minimum number of gummy bears.

So from the first bag, take out no gummy bears.

From the second bag, take out 1 gummy bear.

From the third bag, take out 2 gummy bears (if we take out 1 gummy bear, the sum will be the same in case the second bag has imitation gummy bears or in case third bag has imitation gummy bears.

From the fourth bag, take out 4 gummy bears. We will not take out 3 because otherwise 0 + 3 and 1 + 2 will give us the same sum. So we won’t know whether the first and fourth bags have imitation gummy bears or whether second and third bags have imitation gummy bears.

From the fifth bag, take out 7 gummy bears. We have obtained this number by adding the highest triplet: 1 + 2 + 4 = 7. Note that anything less than 7 will give us a sum that can be made in multiple ways, such as:

0 + 1 + 6 = 7 and 1 + 2 + 4 = 7
or
0 + 1 + 5 = 6 and 0 + 2 + 4 = 6

But we need the sum to be obtainable in only one way so that we can find out which three bags contain the imitation gummy bears.

At this point, we have taken out 0, 1, 2, 4, and 7 gummy bears.

From the sixth bag, take out 13 gummy bears. We have obtained this number by adding the highest triplet: 2 + 4 + 7 = 13. Note that anything less than 13 will, again, give us a sum that can be made in multiple ways, such as:

12 + 1 + 0 = 13 and 2 + 4 + 7 = 13
or
0 + 1 + 9 = 10 and 1 + 2 + 7 = 10
…etc.

Note that this way, we are also ensuring that we measure only the minimum number of gummy bears, which is what the question asks us to do.

From the seventh bag, take out 24 gummy bears. We have obtained this number by adding the highest triplet again: 4 + 7 + 13 = 24. Again, anything less than 24 will give us a sum that can be made in multiple ways, such as:

0 + 1 + 15 = 16 and 1 + 2 + 13 = 16
or
0 + 1 + 19 = 20 and 0 + 7 + 13 = 20
or
0 + 1 + 23 = 24 and 4 + 7 + 13 = 24
…etc.

Thus, this is the way we will pick the gummy bears from the 7 bags: 0, 1, 2, 4, 7, 13, 24.

In all, 51 gummy bears will be weighed. Their total weight should be 510 grams (51*10 = 510) but because three bags have imitation gummy bears, the weight obtained will be less.

Say the weight is less by 8 grams. This means that the first bag (which we pulled 0 gummy bears from), the second bag (which we pulled 1 gummy bear from) and the fifth bag (which we pulled 7 gummy bears from) contain the imitation gummy bears. This is because 0 + 1 + 7 = 8 – note that we will not be able to make 8 with any other combination.

We hope this tricky little problem got you thinking. Work those grey cells and the GMAT will not seem hard at all!

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!

# GMAT Tip of the Week: Keep Your GMAT Score Safe from the Bowling Green Massacre

The hashtag of the day is #bowlinggreenmassacre, inspired by an event that never happened. Whether intentionally or accidentally (we’ll let you and your news agency of choice decide which), White House staffer Kellyanne Conway referenced the “event” in an interview, inspiring an array of memes and references along the way.

Whatever Ms. Conway’s intentions (or lack thereof; again we’ll let you decide) with the quote, she is certainly guilty of inadvertently doing one thing: she didn’t likely intend to help you avoid a disaster on the GMAT, but if you’re paying attention she did.

Your GMAT test day does not have to be a Bowling Green Massacre!

Here’s the thing about the Bowling Green Massacre: it never happened. But by now, it’s lodged deeply enough in the psyche of millions of Americans that, to them, it did. And the same thing happens to GMAT test-takers all the time. They think they’ve seen something on the test that isn’t there, and then they act on something that never happened in the first place. And then, sadly, their GMAT hopes and dreams suffer the same fate as those poor souls at Bowling Green (#thoughtsandprayers).

Here’s how it works:

The Quant Section’s Bowling Green Massacre
On the Quant section, particularly with Data Sufficiency, your mind will quickly leap to conclusions or jump to use a rule that seems relevant. Consider the example:

What is the perimeter of isosceles triangle LMN?

(1) Side LM = 4
(2) Side LN = 4√2

A. Statement (1) ALONE is sufficient, but statement (2) alone is insufficient
B. Statement (2) ALONE is sufficient, but statement (1) alone is insufficient
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

When people see that square root of 2, their minds quickly drift back to all those flash cards they studied – flash cards that include the side ratio for an isosceles right triangle: x, x, x√2. And so they then leap to use that rule, inferring that if one side is 4 and the other is 4√2, the other side must also be 4 to fit the ratio and they can then calculate the perimeter. With both statements together, they figure, they can derive that perimeter and select choice C.

But think about where that side ratio comes from: an isosceles right triangle. You’re told in the given information that this triangle is, indeed, isosceles. But you’re never told that it’s a right triangle. Much like the Bowling Green Massacre, “right” never happened. But the mere suggestion of it – the appearance of the √2 term that is directly associated with an isosceles, right triangle – baits approximately half of all test-takers to choose C here instead of the correct E (explanation: “isosceles” means only that two sides match, so the third side could be either 4, matching side LM, or 4√2, matching side LN).

Your mind does this to you often on Data Sufficiency problems: you’ll limit the realm of possible numbers to integers, when that wasn’t defined, or to positive numbers, when that wasn’t defined either. You’ll see symptoms of a rule or concept (like √2 leads to the isosceles right triangle side ratio) and assume that the entire rule is in play. The GMAT preys on your mind’s propensity for creating its own story when in reality, only part of that story really exists.

The Verbal Section’s Bowling Green Massacre
This same phenomenon appears on the Verbal section, too – most notably in Critical Reasoning. Much like what many allege that Kellyanne Conway did, your mind wants to ascribe particular significance to events or declarations, and it will often exaggerate on you. Consider the example:

About two million years ago, lava dammed up a river in western Asia and caused a small lake to form. The lake existed for about half a million years. Bones of an early human ancestor were recently found in the ancient lake-bottom sediments that lie on top of the layer of lava. Therefore, ancestors of modern humans lived in Western Asia between two million and one-and-a-half million years ago.

Which one of the following is an assumption required by the argument?

A. There were not other lakes in the immediate area before the lava dammed up the river.
B. The lake contained fish that the human ancestors could have used for food.
C. The lava that lay under the lake-bottom sediments did not contain any human fossil remains.
D. The lake was deep enough that a person could drown in it.
E. The bones were already in the sediments by the time the lake disappeared.

The key to most Critical Reasoning problems is finding the conclusion and knowing EXACTLY what the conclusion says – nothing more and nothing less. Here the conclusion is the last sentence, that “ancestors of modern humans lived” in this region at this time. When people answer this problem incorrectly, however, it’s almost always for the same reason. They read the conclusion as “the FIRST/EARLIEST ancestors of modern humans lived…” And in doing so, they choose choice C, which protects against humans having come before the ones related to the bones we have.

“First/earliest” is a classic Bowling Green Massacre – it’s a much more noteworthy event (“scientists have discovered human ancestors” is pretty tame, but “scientists have discovered the FIRST human ancestors” is a big deal) that your brain wants to see. But it’s not actually there! It’s just that, in day to day life, you’d rarely ever read about a run-of-the-mill archaeological discovery; it would only pop up in your social media stream if it were particularly noteworthy, so your mind may very well assume that that notoriety is present even when it’s not.

In order to succeed on the GMAT, you need to become aware of those leaps that your mind likes to take. We’re all susceptible to:

• Assuming that variables represent integers, and that they represent positive numbers
• Seeing the symptoms of a rule and then jumping to apply it
• Applying our own extra superlatives or limits to conclusions

So when you make these mistakes, commit them to memory – they’re not one-off, silly mistakes. Our minds are vulnerable to Bowling Green Massacres, so on test day #staywoke so that your score isn’t among those that are, sadly, massacred.

By Brian Galvin.

# ACT English Tips to Improve Your Score

In the English section on the ACT, you have 45 minutes to finish all 75 multiple-choice questions. This section tests your grammar and punctuation skills. Also, you have the opportunity to showcase your skills when it comes to understanding sentence structure.

There’s also a Reading section that evaluates your comprehension skills with 40 multiple-choice questions in 35 minutes. But with a little preparation and some useful strategies, you can improve your score on both the ACT English and Reading sections.

Most students understand the importance of reading all of the passages included on the ACT Reading test, as this section includes questions designed to measure how well you can understand and interpret the text. But it’s just as important to fully read the passages on the English section of the test.

The English section is made up of five passages containing underlined phrases. You’re given several alternative options for each underlined phrase. Your job is to choose the one that’s a better fit for the sentence. You also have a “no change” option if you think the sentence is correct as it is.

One of the most valuable ACT English tips to keep in mind is to read the entire passage instead of just the underlined phrase. Other sentences in the passage can give you clues about the correct answer. The ACT instructors at Veritas Prep can help you boost your score on the English section by guiding you through practice English questions. We’ll provide you with strategies on how to evaluate the options to arrive at the correct answer. Each of our instructors scored in the top one percent of ACT test-takers, so when you study for the ACT with Veritas Prep, you’re working with someone who has mastered the material!

Be on the Lookout for Parallel Structure
Looking for parallel structure in the sentences of each passage can help you to find the correct alternative to an underlined phrase. If an underlined phrase isn’t parallel with the rest of the sentence, then it needs to be replaced with one of the answer options.

An example sentence might be, “Philip enjoys reading, horseback riding, and to swim.” This sentence is not parallel because it contains mixed verb forms. The correct version of this sentence is, “Philip enjoys reading, horseback riding, and swimming.” Philip’s third hobby, “swimming,” should have the same verb form as his first two hobbies. Reading articles in science magazines, online newspapers, and other publications can help you become familiar with parallel structure. The more reading you do, the easier it will be to recognize a passage with sentences that are not parallel in form.

Look for Subject and Verb Agreement
One of simplest tips to remember when completing the ACT English section is to look for agreement between the subject and the verb of a sentence. If the subject of a sentence is singular, then its verb should also be singular. The same goes for plural subjects and plural verbs.

Consider All of the Answer Options
This is a necessary addition to any list of ACT English tips. Understandably, many students are anxious or nervous on test day. Most want to jump right in and get started on the questions. Because of this nervousness, a student may skim passages, glance at the answer options, and choose one that looks like the obvious answer. This is a trap you want to avoid. Take the time to look at all of the answer choices before selecting one. The most obvious answer is not always the right one.

Read the Corrected Sentences to Yourself
Once you choose an alternative option for an underlined phrase, it’s a smart idea to insert it into the sentence and quietly read it to yourself. This can help you to determine whether the changed sentence flows or sounds clunky. If the sentence doesn’t sound right in your mind, it is worth your time to go back and reconsider the option you selected.

At Veritas Prep, we offer a free online ACT prep seminar that gives you the chance to see what our study program is all about. We give you the guidance you need for tackling the ACT Reading and English sections as well as the rest of the exam. Students who work with us prep for the test using the most effective study materials and resources. Our professional instructors are not only experts on the ACT, but they recognize the value of providing lots of encouragement to their students. And you have the option of either taking an online class or participating in one of our in-person courses. Either way, we’ll give you the preparation you need to excel on the ACT!

Still need to take the ACT? We run a free online ACT prep seminar every few weeks. And be sure to find us on Facebook, YouTube, Google+ and Twitter!

# Quarter Wit, Quarter Wisdom: Solving the Hourglass Puzzle

Let’s continue our puzzles discussion today with another puzzle type – time measurement using an hourglass. (Before you continue reading this article, check out our posts on how to solve pouring water puzzles and weighing and balancing puzzles)

First, understand what an hourglass is – it is a mechanical device used to measure the passage of time. It is comprised of two glass bulbs connected vertically by a narrow neck that allows a regulated trickle of sand from the upper bulb to fall into the lower one. The sand also takes a fixed amount of time to fall from the upper bulb to the lower bulb. Hourglasses may be reused indefinitely by inverting the bulbs once the upper bulb is empty.

This is what they look like:

Say a 10-minute hourglass will let us measure time in intervals of 10 minutes. This means all of the sand will flow from the upper bulb to the lower bulb in exactly 10 minutes. We can then flip the hourglass over – now sand will start flowing again for the next 10 minutes, and so on. We cannot measure, say, 12 minutes using just a 10-minute hourglass, but we can measure more time intervals when we have two hourglasses of different times. Let’s look at this practice problem to see how this can be done:

A teacher of mathematics used an unconventional method to measure a 15-minute time limit for a test. He used a 7-minute and an 11-minute hourglass. During the whole time, he turned the hourglasses only 3 times (turning both hourglasses at once counts as one flip). Explain how the teacher measured out 15 minutes.

Here, we have a 7-minute hourglass and an 11-minute hourglass. This means we can measure time in intervals of 7 minutes as well as in intervals of 11 minutes. But consider this: if both hourglasses start together, at the end of 7 minutes, we will have 4 minutes of sand leftover in the top bulb of the 11-minute hourglass. So we can also measure out 4 minutes of time.

Furthermore, if we flip the 7-minute hourglass over at this time and let it flow for that 4 minutes (until the sand runs out of the top bulb of the 11-minute hourglass), we will have 3 minutes’ worth of sand leftover in the 7-minute hourglass. Hence, we can measure a 3 minute time interval, too, and so on…

Now, let’s see how we can measure out 15 minutes of time using our 7-minute and 11-minute hourglasses.

First, start both hourglasses at the same time. After the top bulb of the 7-minute hourglass is empty, flip it over again. At this time, we have 4 minutes’ worth of sand still in the top bulb of the 11-minute hourglass. When the top bulb of the 11-minute hourglass is empty, the bottom bulb of 7-minute hourglass will have 4 minutes’ worth of sand in it. At this point, 11 minutes have passed

Now simply flip the 7-minute hourglass over again and wait until the sand runs to the bottom bulb, which will be in 4 minutes.

This is how we measure out 11 + 4 = 15 minutes of time using a 7-minute hourglass and an 11-minute hourglass.

Let’s look at another problem:

Having two hourglasses, a 7-minute one and a 4-minute one, how can you correctly time out 9 minutes?

Now we need to measure out 9 minutes using a 7-minute hourglass and a 4-minute hourglass. Like we did for the last problem, begin by starting both hourglasses at the same time. After 4 minutes pass, all of the sand in the 4-minute hourglass will be in the lower bulb. Now flip this 4-minute hourglass back over again. In the 7-minute hourglass, there will be 3 minutes’ worth of sand still in the upper bulb.

After 3 minutes, all of the sand from the 7-minute hourglass will be in the lower bulb and 1 minute’s worth of sand will be in the upper bulb of the 4-minute hourglass.

This is when we will start our 9-minute interval.

The 1 minute’s worth of sand will flow to the bottom bulb of the 4-minute hourglass. Then we just need to flip the 4-minute hourglass over and let all of the sand flow out (which will take 4 minutes), and then flip the hourglass over to let all of the sand flow out again (which will take another 4 minutes).

In all, we have measured out a 1 + 4 + 4 = 9-minute interval, which is what the problem has asked us to find.

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!

# How the SAT Works: Format Breakdown and Function

If you’re a junior or senior in high school, you’re probably planning to take the SAT. You know that the SAT is a standardized test taken by students across the country, and you know that college officials look at SAT scores when evaluating student applications. But have you ever taken a really close look at the parts of this well-known exam? Learning what’s on the new SAT and how the SAT works is an important first step in preparing for the test.

What Is the Purpose of the SAT?
The questions on the SAT are meant to reveal what you learned in your high school classes, so you should find that you’re already familiar with the types of material on this exam. In addition, the test is a way to evaluate whether you’ll be successful in your college courses. Of course, a high SAT score isn’t a guarantee of success in college, but the test serves as a way to measure your academic abilities.

The SAT Format
Reading, Writing & Language, and Math are the three tests that make up the SAT. There is also an optional Essay section. You have 65 minutes to complete the Reading section and 35 minutes to complete the Writing & Language section. In addition, you receive 80 minutes to complete the Math questions. As for the essay, you are given 50 minutes to write it.

The Reading and Writing & Language tests are multiple-choice. The Math test has multiple-choice questions as well as grid-in questions. Grid-in questions require you to figure out the answer to a math problem instead of selecting an answer option. The entire SAT takes about three hours and 50 minutes to finish. The total test time varies depending on the amount of breaks you’re given during the exam. You’re able to take the SAT either on paper or digitally.

Taking a closer look at an SAT breakdown detailing the types of questions in each section can help you perform well on the test. The Reading section includes vocabulary in context, detail, function, inference, analogy, author technique, and main idea questions. After reading each passage, your job is to answer several multiple-choice questions about what you have read. This section has a total of 52 questions.

The Math Section
The SAT format for the Math section starts students off with relatively easy problems and gradually increases in difficulty. Geometry, trigonometry, algebra, and data analysis are all topics covered by questions in the Math section. You can use a calculator on some portions of the Math section but not others. There are 58 questions on the Math test.

The Writing & Language Section
There’s a Writing & Language section on the new SAT, as well. You’ll find several shorter reading passages here that are accompanied by questions. For each question, choose the answer option that corrects a grammar, punctuation, or structure error within the passage. Some questions include a “no change” option, which you should select if there is no error present. There are 44 questions in this section.

The Essay
The SAT essay gauges your ability to analyze the author’s argument, using evidence to support your points. You’re not called upon to agree or disagree with what the author is trying to convey. You have 50 minutes to write the essay. Though this is an optional part of the test, it’s a chance to highlight your ability to write an organized, thoughtful essay. Additionally, many colleges require their applicants to write this essay, so you will want to check with the schools you are interested in applying to.

Preparing for the Test
Now that you know the SAT breakdown and how the SAT works, you must make sure you’re prepared to dive in on test day. The tutoring program at Veritas Prep can provide you with simple strategies that help you navigate all sections of the exam. Each of our instructors has already proven their mastery of the test by earning a score in the 99th percentile on the SAT, so when you work with a Veritas Prep tutor, you’re studying with the best! We’ll have you take a practice SAT and look at your results to see where you can improve.

To make your tutoring sessions as effective as possible, we’ll match you with an instructor who is familiar with your learning style. Our online and in-person courses are designed to give you the resources you need to highlight your skills on the SAT. Call or email Veritas Prep today to learn more!

A deferral is when an applicant is admitted to an MBA program they plan to attend but they desire to delay their matriculation to a later date due to some sort of extenuating circumstance. (This is different than the official deferred enrollment programs that are offered at some schools, such as the HBS 2+2 Program, which you can read about here.)

A big part of applying to business school is affirming why right now is the ideal time for you to pursue your MBA, so when a candidate asks for a deferral, it kind of flies in the face of that statement. As such, deferrals are often difficult to secure at most top MBA programs.

Generally, when deferrals are secured at top schools, it is due to personal illnesses, deaths or illnesses in the family, or military deployment – essentially, extreme circumstances that are outside of the control of the admit. Financial or work related deferrals are more commonly requested, but they are also less commonly approved. If you feel that you really need a deferral for one of these reasons by all means request one, just know the odds of the deferral being granted will not be in your favor.

If you are going to make the request to have your business school admission deferred, see if you can have a conversation about your situation with the Admissions Committee in-person, or at least on the phone, rather than over email. This will add a personal element to your request and increase the chance that the Admissions Committee will make their decision in your favor.

It also helps if you can position the reason for your deferral as a once in a life time opportunity while reaffirming your commitment to pursuing an MBA at that particular school the following year, and reminding the Admissions Committee of how you will be able to offer more to the student community upon your eventual matriculation. Remember this is a difficult decision for the Admissions Committee as well. If the school admitted you, then they are invested in you becoming a part of their community, so engaging in discussions around a deferral is equally challenging for the Admissions Committee.

Make sure to follow up your conversation with the Admissions Committee via email, and include a special thank you for their consideration as well as a reminder of the above notes, as this request is ultimately outside of the typical application process. The best thing you can do when engaging in the process of requesting an MBA deferral is to be humble. Remember, you are making a BIG request that the school does not need to grant you. Being humble and appreciative of the consideration you are receiving can only help your chances.

It is important to enter this process understanding the limited odds you have to actually secure a deferral, so follow the tips above to increase your chances, and make sure you are properly evaluating whether the alternative to matriculating in the year you applied is worth the overall hassle.

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.

# Tips on How to Start College on the Right Foot

Excitement, nervousness, and curiosity are just three of the emotions felt by a college freshman in late summer. Most students who are preparing to start college want to do everything they can to set a positive tone for the school year. Fortunately, there are several steps that students can take to accomplish this goal. Take a look at some practical tips for how to start college on the right foot:

Walk the Campus
It’s important for new students to arrive early to each class on the first day. This gives them the opportunity to choose a seat and relax a little bit before class begins. So a few days before school starts, it’s a good idea for students to get a campus map and walk to the buildings where their classes will be held. It may also be helpful to make notes on the map regarding the route. Knowing exactly where to go can reduce a student’s stress level on the first day of class.

Create a Study Schedule
Creating a study schedule is one of the most effective tips for starting college on a positive note. Once a student receives their course schedule, it’s time to create a study plan. Ideally, a student should dedicate the same amount of study time to every course. But once school starts, students may have to adjust their study schedule to focus more time on challenging courses.

It’s important for students to make efficient use of the free time they have during weekdays. For instance, say a student has just two classes on Monday and Wednesday that both take place in the morning. This gives them the opportunity to schedule study time on Monday and Wednesday afternoons. Not surprisingly, a student’s study schedule may experience frequent adjustments throughout the semester.

Record Important Dates
Lots of students who are starting college have a full schedule of courses, sports activities, club meetings, and social events. As a result, they can sometimes lose track of important dates related to various assignments, tests, etc.

One of the most helpful tips for starting college on a good note is to compile all critical dates in one place. Students can use their smartphone, a wall calendar, or even a desk calendar to help them in this process. After getting a syllabus from each professor on the first day of class, students can transfer the important due dates onto their virtual or paper calendar. With a quick check of the calendar, students can see quiz and test dates as well as due dates for papers. Those who get organized at the beginning of the school year are setting themselves up for academic success!

Get to Know Professors
Students wondering how to start college on the right foot can make a point of introducing themselves to their professors. Whether a class is held in an auditorium with 100-plus students or takes place in a small classroom with 12 individuals, it’s a good idea for students to get to know their professors. A student may go up to their professor after the first class, give their name, and ask a question about a chapter in the textbook. As a result, the professor knows who the student is and will likely recognize them again if they want to discuss a quiz grade or ask for clarification on an assignment.

Professors appreciate students who are diligent about their work and ask questions that can help them get more out of the course material. Students who start college with enthusiasm are putting themselves in the right state of mind.

Our staff at Veritas Prep understands the importance of starting college on the right foot. We prep high school students for college by teaching them effective strategies they can apply on any section of the SAT or ACT. We also review practice tests with them to pinpoint skills that need improvement. This enables them to submit their , which can expand their options when it comes time to apply to college.

Our admissions consultants have firsthand experience with what college officials across the country are looking for when they evaluate student applications. We use our expert resources to help students as they prepare to send applications to the top colleges in the United States. We are proud to offer students knowledgeable online instruction, expert guidance, and much more as they pursue their goal of higher education.

# Quarter Wit, Quarter Wisdom: Solving the Weighing and Balancing Puzzle

Let’s continue the discussion on puzzles that we began last week. Today we look at another kind of puzzle – weighing multiple objects using a two-pan balance while we are given a limited number of times to weight the objects against each other.

First of all, do we understand what a two-pan balance looks like?

Here is a picture.

As you can see, it has two pans that will be even if the weights in them are equal. If one pan has heavier objects in it, that pan will go down due to the weight. With this in mind, let’s try our first puzzle:

One of twelve coins is a bit lighter than the other 11 (which have the same weight). How would you identify this lighter coin if you could use a two-pan balance scale only 3 times? (You can only balance one set of coins against another, i.e. you have no weight measurements.)

There are various ways in which we can solve this.

We are given 12 coins, all of same weight, except one which is a bit lighter.

Let’s split the coins into two groups of 6 coins each and put them in the two pans. Since there is one lighter coin, one pan will be lighter than the other and will rise higher. So now we know that one of these 6 coins is the lighter coin.

Now split these 6 coins into another two groups of 3 coins each. Again, one pan will rise higher since it will have the lighter coin on it. Now we know that one of these three coins is the lighter coin.

Now what do we do? We have 3 coins and we cannot split them equally. What we can do is put one coin in each pan. What happens if the pans are not balanced? Then we know the pan that rises higher has the lighter coin on it (and thus, we have identified our coin). But what if both pans are balanced? The catch is that then the leftover coin is the lighter one! In any case, we would be able to identify the lighter coin using this strategy.

We hope you understand the logic here. Now let’s try another puzzle:

One of 9 coins is a bit lighter than the other 8. How would you identify this lighter coin if you could use a two-pan balance scale only 2 times?

Now we can use the balance only twice, and we are given an odd number of coins so we cannot split them evenly. Recall what we did in the first puzzle when we had an odd number of coins – we put one coin aside. What should we do here? Can we try putting 1 coin aside and splitting the rest of the 8 coins into two groups of 4 each? We can but once we have a set of 4 coins that contain the lighter coin, we will still need 2 more weighings to isolate the light coin, and we only have a total of 2 weighings to use.

Instead, we should split the 9 coins into 3 groups of 3 coins each. If we put one group aside and put the other two groups into the two pans of the scale, we will be able to identify the group which has the lighter coin. If one pan rises up, then that pan is holding the lighter coin; if the pans weight the same, then the group put aside has the lighter coin in it.

Now the question circles back to the strategy we used in the first puzzle. We have 3 coins, out of which one is lighter than the others, and we have only one chance left to weigh the coins. Just like in the first puzzle, we can put one coin aside and weigh the other two against each other – if one pan rises, it is holding the lighter coin, otherwise the coin put aside is the lighter coin! Thus, we were able to identify the lighter coin in just two weighings. Can you use the same method to answer the first puzzle now?

We will leave you with a final puzzle:

On a Christmas tree there were two blue, two red, and two white balls. All seemed the same, however in each color pair, one ball was heavier. All three lighter balls weighed the same, just like all three heavier balls weighed the same. Using a 2-pan balance scale only twice, identify the lighter balls.

Can you solve this problem using the strategies above? Let us know in the comments!

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!

# How to Start Studying for the GRE

Most students who intend to go to graduate school understand that taking the Graduate Record Examination (GRE) is an important step in the process. But, many of them wonder how to start studying for the GRE. At Veritas Prep, we offer online courses that help students prepare for this critical exam. Here are some valuable tips for students as they begin the process of studying for the GRE.

Complete a Practice Exam
Students who are wondering how to start studying for the GRE can take a step in the right direction by completing a practice test. Doing this allows them to see the type of material that’s on GRE. For example, they can get a sneak preview of the types of geometry and algebra questions on the Quantitative section of the exam. Also, students have their reading comprehension and vocabulary skills tested in the Verbal Reasoning section.

The Analytical Writing section requires students to write two essays. One of them is an issue piece while the other is an argument essay. After finishing a practice GRE, students can look at the results of the test to gain insight on what skills they need to improve.

Identify Weaknesses and Strengths on the GRE
Students working with one of our Veritas Prep instructors have the advantage of reviewing the results of their practice test with an expert. A student who needs to brush up on his geometry skills can learn lots of practical tips from his instructor to make geometry questions more manageable. Alternatively, a student who needs help in the area of reading comprehension can garner strategies from her instructor that serve to simplify lengthy written passages. Practice test results are invaluable for a student who wants to make the most efficient use of his or her study time. Practice test results also reveal a student’s strengths. Understandably, this portion of the test results can give some students a much needed confidence boost!

Implement Test-Taking Strategies
Taking more than one practice test is valuable for students who sign up for the GRE. Studying tips and strategies learned at Veritas Prep can be put into practice. One test-taking strategy involves eliminating answer options. Since many of the questions on the GRE are in multiple choice form, this strategy can prove very useful on test day.

For example, there are several questions in the Verbal Reasoning section that ask students to identify the pair of words that would make the most sense if plugged into a particular sentence. A student starts by reading the sentence and then looks at all of the answer options. In many cases, a student will see a pair of words that have nothing to do with the subject matter in the sentence – this answer option can be eliminated right away. Eliminating options helps students to focus their concentration on the most valid choices.

Enhance Study Time Using Various Resources
When studying for the GRE, students can use aids to help them strengthen various skills. For instance, it’s a good idea for students to make flashcards to learn vocabulary words found in the Verbal Reasoning section of the test. A student must find lists of vocabulary words that are likely to be on the GRE. Next, he or she creates a flashcard for each unfamiliar word and its definition. Students who quiz themselves every day with five or ten flashcards are able to absorb a reasonable number of new words each week.

Newspapers and magazines are other study aids that help students to prep for the GRE. Students who get into the habit of reading newspaper and magazine articles are likely to encounter some of the vocabulary words they are learning for the GRE. Seeing these words in context is tremendously helpful to a student who is trying to remember them for the test. Geometry and algebra textbooks are other examples of useful study aids. Students can complete various exercises in the textbook to sharpen their skills in these areas.

Finally, our instructors can be invaluable to students preparing for the GRE. Studying tips, strategies, and encouragement are just three of the things that we offer to our students at Veritas Prep. We are happy to answer questions about our services and encourage students to contact our team with inquiries about our online GRE prep classes. Students who sign up with Veritas Prep are giving themselves an advantage 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!

# Learn from the First Moon Landing: Avoid Using Technical Details in Your MBA Essays

The new movie, Hidden Figures, rightly shines light on the roles played by the mathematicians who helped the United States catch up to Russia in the Space Race and eventually land on the moon in 1969. This accomplishment was politically significant at that time as it was a show of technological prowess between the bitter Cold War rivals.

“One small step for man, one giant leap for mankind.”

Most of us are familiar with this quote and can still hear the words clearly in our heads. We can also vividly recall astronaut Neil Armstrong taking his first steps on the moon and planting an American flag.

These iconic words and images are what the general public recalls of this event, and what inspires young kids growing up today to dream of becoming astronauts or scientists. The breakthrough mathematical, technological, and research milestones that were necessary to reach this point, however, are only recalled by a limited audience (even though they created the foundation for this defining moment).

Just like the mathematical accomplishments highlighted in Hidden Figures were long forgotten by society, technical details that you mention in your business school essays may be hard for the Admissions Committee of your dream school to grasp. Let’s examine two key ways you can avoid this problem:

Create interest with highlights that appeal to the senses.
Applicants from technical fields are often so immersed in their specializations that industry jargon litter their essays; they forget to write these terms with context that non-industry readers will be able to appreciate.

One way to avoid this issue is to quantify this technical language in terms of monetary equivalents (e.g. dollar amounts), percentages or ranks to show scale of responsibilities and accomplishments. However, making the leap towards using imagery in your writing that complements these achievements will make your essays even more powerful. Always use the opportunity your MBA essays give you to show how your work has impacted other people. For instance, you can share how your accomplishments in the workplace have helped people learn new skills, save time, or be safer, rather than simply listing your technical day to day activities.

No matter what blockbuster movie you see – whether it’s about an inter-galaxy war or an animated underwater adventure – interpersonal relationships always drive the story. Even historical accounts of world events or biographies take cinematic license to play up personal aspects of the protagonists’ life stories. Thus, when you write your essays, be aware that mentioning relationships is one way to make your stories come to life.

Readers are interested in humans, so detailing relationships you have made while in the workplace will help your profile become more relatable and display empathy towards others. This can be done by describing the way you have handled challenges on projects or how you have collaborated with others towards shared accomplishments — these stories should not be ignored. Rather than utilizing all the essay space you are given for the financial details of the deal you executed or the legal intricacies of the contract you negotiated, make sure you share how you grew from these experiences. You could also include the lessons learned and how these experiences have helped you become a better leader, or simply a better person.

Follow these tips and your MBA application essay will become a more compelling and relatable piece to read.

Written by Edison Cu, a Veritas Prep Head Consultant for INSEAD. You can read more articles by him here

# Can I Apply to College as a High School Junior?

The traditional path to college involves four years of high school. Most people picture college-bound high school Seniors going to prom, attending parties, and spending a lot of time with their friends. But what about high school students who have different plans for themselves?

Some ambitious students might ask, “Can you apply to college as a Junior in high school?” The answer is yes. You can apply to college during Junior year. Discover some important details for students who want to forgo their Senior year in high school and move straight on to college:

What to Do Before Applying to College as a Junior in High School
Whether a student is a Senior or a Junior, they must fulfill the same requirements when submitting applications to colleges. Juniors in high school have to pay special attention to the various deadlines of the colleges they are applying to. This means they have to make a detailed timeline that allows them to take the SAT or ACT in plenty of time to submit their scores by the required deadline.

In addition, the student must submit an application, official transcripts, an application essay, letters of recommendation, as well as any other materials required by college admissions officials by the advertised deadline. It’s a good idea for high school Juniors to look at the specific application materials required by the colleges they are applying to. Generally, students can find a list of required materials on a college’s website. Having this information helps a Junior to create a reliable timeline of things to do.

Who to Talk to Before Applying to College as a Junior in High School
Juniors in high school who are applying to college may feel overwhelmed by all they have to do in order to achieve their goal of getting into school early. One tip is to enlist the help of a high school counselor. This professional can handle the logistics involved with helping a Junior apply to college.

In addition, our online college admissions consultants at Veritas Prep have the know-how and resources to assist ambitious high school Juniors who want to start their college career early. Our consultants have worked in the admissions offices of the country’s top colleges, so they know the ins and outs of the admissions process. Students who sign up with Veritas Prep benefit from the experience of our consultants.

The Advantages of Applying to College as a Junior
One of the main advantages of applying to college as a Junior in high school is that students can begin delving into the subjects they are most interested in. For instance, a Junior who is anxious to start on the path toward becoming a physician doesn’t need to delay those plans for an additional year – they can simply skip Senior year in high school and start on that path. Another advantage is that the person will likely graduate from college sooner than expected. This gives the individual more time to spend on their chosen vocation. Most Juniors who apply to college are anxious to get started on their future plans.

The Drawbacks of Applying to College as a Junior
A drawback of applying to college as a Junior in high school is that a student doesn’t have an opportunity to include more accomplishments in their college applications. Alternatively, a Senior in high school has the chance to improve their final grade point average, take extra courses, and participate in more extracurricular activities. In addition, a Senior in high school can learn new strategies from Veritas Prep and retake the SAT or ACT to earn a higher score, whereas a Junior is on a tight schedule to prep for these exams. They must prepare by taking practice tests and then register to take the actual test. The student’s SAT or ACT scores must be submitted to colleges without delay.

So can you apply to college as a Junior in high school? Yes, you can, and our capable staff at Veritas Prep stands ready to assist you in accomplishing that goal! From to college admissions consulting, we are ready to be of help. Contact our team today to learn more about our services designed to assist ambitious students like you!

# Quarter Wit, Quarter Wisdom: Solving the Pouring Water Puzzle

Some time back, we came across a GMAT Data Sufficiency word problem question based on the “pouring water puzzle”. That made us think that it is probably a good idea to be comfortable with the various standard puzzle types. From this week on, we will look at some fundamental puzzles to acquaint ourselves with these mind benders in case we encounter them on test day.

Today, we will look at the popular “pouring water puzzle”. You may remember a similar puzzle from the movie Die Hard with a Vengeance, where Bruce Willis and Samuel L. Jackson had to diffuse a bomb by placing a 4 gallon jug of water on a set of scales.

Here is the puzzle:

You have a 3- and a 5-liter water container – each container has no markings except for that which gives us its total volume. We also have a running tap. We must use the containers and the tap in such a way that we measure out exactly 4 liters of water. How can this be done?

Don’t worry that this question is not written in a traditional GMAT format! We need to worry only about the logic behind the puzzle – we can then answer any question about it that is given in any GMAT format.

Let’s break down what we are given. We have only two containers – one of 3-liter and the other of 5-liter capacity. The containers have absolutely no markings on them other than those which give us the total volumes, i.e. the markings for 3 liters and 5 liters respectively. There is no other container. We also have a tap/faucet of running water, so basically, we have an unlimited supply of water. Environmentalists may not like my saying this, but this fact means we can throw out water when we need to and just refill again.

STEP 1: Let’s fill up the 5-liter container with water from the tap. Now we are at (5, 0), with 5 being the liters of water in the 5-liter container, and 0 being the liters of water in the 3-liter container.

STEP 2: Now, there is nothing we can do with this water except transfer it to the 3-liter container (there is no other container and throwing out the water will bring us back to where we started). After we fill up the 3-liter container, we are left with 2 liters of water in the 5-liter container. This brings us to (2, 3).

STEP 3: We gain nothing from transferring the 3 liters of water back to 5-liter container, so let’s throw out the 3 liters that are in the 3-liter container. Because we just threw out the water from the 3-liter container, we will gain nothing by simply refilling it with 3 liters of water again. So now we are at (2, 0).

STEP 4: The next logical step is to transfer the 2 liters of water we have from the 5-liter container to the 3-liter container. This means the 3-liter container has space for 1 liter more until it reaches its maximum volume mark. This brings us to (0, 2).

STEP 5: Now fill up the 5-liter container with water from the tap and transfer 1 liter to the 3-liter container (which previously had 2 liters of water in it). This means we are left with 4 liters of water in the 5-liter container. Now we are at (4, 3).

This is how we are able to separate out exactly 4 liters of water without having any markings on the two containers. We hope you understand the logic behind solving this puzzle. Let’s take a look at another question to help us practice:

We are given three bowls of 7-, 4- and 3-liter capacity. Only the 7-liter bowl is full of water. Pouring the water the fewest number of times, separate out the 7 liters into 2, 2, and 3 liters (in the three bowls).

This question is a little different in that we are not given an unlimited supply of water. We have only 7 liters of water and we need to split it into 2, 2 and 3 liters. This means we can neither throw away any water, nor can we add any water. We just need to work with what we have.

We start off with (7, 0, 0) – with 7 being the liters of water in the 7-liter bowl, the first 0 being the liters of water in the 4-liter bowl, and the second 0 being the liters of water in the 3-liter bowl – and we need to go to (2, 2, 3). Let’s break this down:

STEP 1: The first step would obviously be to pour water from the 7-liter bowl into the 4-liter bowl. Now you will have 3 liters of water left in the 7-liter bowl. We are now at (3, 4, 0).

STEP 2: From the 4-liter bowl, we can now pour water into the 3-liter bowl. Now we have 1 liter in the 4-liter bowl, bringing us to (3, 1, 3).

STEP 3: Empty out the 3-liter bowl, which is full, into the 7-liter bowl for a total of 6 liters – no other transfer makes sense [if we transfer 1 liter of water to the 7-liter bowl, we will be back at the (4, 0, 3) split, which gives us nothing new]. This brings us to (6, 1, 0).

STEP 4: Shift the 1 liter of water from the 4-liter bowl to the 3-liter bowl. We are now at (6, 0, 1).

STEP 5: From the 7-liter bowl, we can now shift 4 liters of water into the 4-liter bowl. This leaves us with with 2 liters of water in the 7-liter bowl. Again, no other transfer makes sense – pouring 1 liter of water into some other bowl takes us back to a previous step. This gives us (2, 4, 1).

STEP 6: Finally, pour water from the 4-liter bowl into the 3-liter bowl to fill it up. 2 liters will be shifted, bringing us to (2, 2, 3). This is what we wanted.

We took a total of 6 steps to solve this problem. At each step, the point is to look for what helps us advance forward. If our next step takes us back to a place at which we have already been, then we shouldn’t take it.

Keeping these tips in mind, we should be able to solve most of these pouring water puzzles in the future!

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!

# 4 Predictions for Test Prep and Admissions in 2017

There goes another year. Seemingly no sooner than it started, 2016 has packed up and stormed off, leaving many dizzy in its wake. Now that 2017 is underway, it’s time to dust off the old Veritas Prep crystal ball and see what may be in store for 2017 in the worlds of test preparation and admissions. Odds are that we won’t be right on all of these — and we may even manage to get all four wrong — but let’s dig in and predict a few things that we expect to see in 2017:

One-year MBA programs will reach a tipping point in the United States.
For decades, one-year programs have been more popular in Europe than in the United States, although some prominent American programs, such as Kellogg, have moved to expand their one-year programs in recent years. With more and more articles appearing in the media about students and their families questioning the costs of higher education, accelerated programs will keep looking more and more appealing to applicants who don’t want to spend six figures on an MBA. The globalization of management graduate education will continue, and more American business schools will start to embrace what’s traditionally been a more Euro-flavored program type.

Video prompts will become much more common in business school applications.
Yes, we predicted this last year, and it didn’t quite come to fruition. But, schools are becoming more and more comfortable with video as a medium for learning about applicants, and — probably more importantly — applicants themselves mostly seem to be comfortable with video. In AIGAC’s 2016 MBA Applicant Survey, only 16% of applicants surveyed said that video responses were the most challenging part of the application. That’s far smaller than the percentage of applicants who said that standardized tests (61%) and written essays (46%) were the most challenging! Rotman, Yale, Kellogg, and McCombs have helped blaze a video trail that we expect others will soon follow.

An Asia-scale cheating scandal will hit the SAT or ACT in the United States.
News articles about standardized test cheating scandals like this one and this one seem to come out nearly every month. Much of the blame lies with the pressure that students — and especially their families — put on themselves to do well on these exams.

It’s also greed. For every student that will do anything to do well on an exam, there’s a person or company who’s happy to take their money and do whatever it takes to give that student a leg up. Sometimes that means legally and ethically training that student to perform to the best of their ability, but many other times it means falsifying documents or providing students with live test questions for large sums of money. This kind of greed exists everywhere in the world, and it’s only a matter of time until a similar large-scale scandal happens in the U.S.

Community colleges will gain a lot more recognition.
Did you know that more than half of students who enroll in college first do so at a community college? Most Americans don’t know that, even though community colleges have been the engine that educates millions of Americans each year. We’ll see the federal government putting more emphasis on jobs and job training in the coming year, and community colleges are perfectly positioned to serve that role. While it remains to be seen whether community colleges get all of the funding they need to keep serving their mission, we expect that, at a minimum, they’ll start to get more recognition for the job they do to train and retrain America’s workforce.

Happy New Year, everyone. We can’t wait to check back in 2018 and see how this year turned out!

By Scott Shrum

# How Late is Too Late? Late College Applications and Admission

Most high school seniors who want to apply to college start the process around September or October. If they want their application considered for early decision, they start the process even sooner.

The deadline for regular-decision college applications usually falls from January to mid-February. But what if a student misses the regular-decision deadline? Take a look at some considerations for students who want to submit a late college application as well as a few common reasons behind this decision:

Reasons Why Students Are Late in Submitting College Applications
Some high school students choose to direct all of their efforts toward improving their performance in second-semester courses. They want to present an impressive academic record to college officials. This sometimes causes them to miss regular application deadlines to colleges. As a result, they must submit a late college application to several schools.

Another reason why some students find themselves looking for colleges with late deadlines is because they were thinking about taking a gap year. Unfortunately, by the time they made the decision to start college, the regular application deadline had passed. Other students submit late applications to colleges because they focus all of their attention on gaining admission into one particular school. If they don’t get into that school, they must start applying late to other colleges.

Regardless of a student’s reasons, there are still options for those who miss the regular-decision deadline. At Veritas Prep, our online college admissions consultants are experts at guiding students through the process of applying to colleges. We provide them with transcript evaluations, tips on letters of recommendation, suggestions regarding extracurricular activities, and much more!

Submitting Applications to Colleges with Late Deadlines
One of the first things a student in this situation must do is find colleges that accept late applications. Fortunately, there are many late-admission colleges for students to choose from. Individuals who are submitting a late college application have to meet all of the same requirements as students who apply during the regular or early application periods. Students who need help with tuition costs must take note of the deadlines related to financial aid packages. In addition, students who are looking at late college application deadlines should inquire about the available student housing. Sometimes, all of the housing is taken by the time a student’s late application is accepted.

Some students have the impression that rolling admissions and late admissions are the same thing. This is not true. A college that participates in rolling admissions doesn’t have a concrete deadline for applications. They are accepted until every space in the freshman class is filled. Alternatively, late-admission colleges have a concrete deadline for students who apply after the regular-decision deadline has passed. A student who applies via rolling admissions is taking the risk that there will still be available spaces whenever their application arrives at the school.

How to Make a Late Application Stand Out to College Officials
An impressive admissions essay can help a student’s late application stand out from the crowd. At Veritas Prep, our professional consultants assist students with the prep work necessary to create an essay that is sure to be memorable to college officials. We give students writing strategies they can practice to make their essay all the more convincing.

Our consultants worked in the admissions offices of top colleges across the country. As a result, they know what college officials are looking for when reading a student’s essay. A student who participated in some special extracurricular activities during their second semester in high school can highlight those on a late application. A student who dedicates their time and energy to a few extracurricular activities is sure to be a standout in a crowd of late applicants.

Our staff at Veritas Prep has the experience and know-how to help students whether they are looking at late college application deadlines or regular-decision admissions. Students may want to try our College Chanculator to get an idea of their chances of getting into a specific college or university based on their qualifications. We have a variety of resources designed to make the college application process easier for students. Contact Veritas Prep and get started on the path to college today!

# 4 Things to NOT Do When Waiting On an MBA Admissions Decision

One of the most nerve-racking times for MBA applicants is not before they submit their applications, but rather, is while they are waiting to hear back from their dream schools after they have sent in their application components.

In fact, I firmly believe that more strange activity and anxiety manifests during the two months applicants spend waiting on their admissions decisions than during any other time of MBA application process. With this in mind, it is important to maintain your composure AND your sanity when handling your post-submission moves.

Let’s explore a few things to avoid while you are waiting to receive your MBA admissions decision:

Online message boards and forums are often a good source of information from other like-minded individuals experiencing similar situations to yours during the application process. On the negative side, however, message boards can also encourage and exacerbate a fair amount of anxiety when it comes to waiting for your official admissions decision. Sometimes message boards become bastions for fear mongering and misinformation, and when coupled with the stress of the application process, this can manifest into some really irrational thoughts and behavior. I highly recommend avoiding these boards if possible while you are waiting on an admissions decision, especially around decision days when programs release their application decisions.

2) Unnecessarily Contact the Program:
MBA admissions committees evaluate all touchpoints they have with a candidate. So just because your application has been submitted does not mean the non-application evaluation period is over. Avoid the temptation to call into the admissions offices of the business schools you have applied to asking questions about decision timelines or other publicly-available information.

Keep in mind, MBA admissions officers receive tons of outreach from candidates all over the world, so although you think your question is unique and necessary, more than likely it is not. Use your discretion here when deciding whether to reach out or send additional information to schools, but keep in mind that a major part of being a good business person is judgment – make sure you use good judgement in deciding whether or not that outreach is truly necessary .

3) Slack Off at Work:
For many business school applicants, it is easy to slack off on day-to-day work activities during MBA application season and divert all of one’s energy to crafting the perfect application, but anything can happen once an MBA application is submitted. Once you send your application to your schools of choice, it is a great time to double down on tasks in the office. Also, if you are not admitted to your school of choice, you may need to stay at your company longer than expected, in which case, you will want to continue to position yourself for success in your current role (especially if you plan to reapply to business school in future application cycles).

4) Get Into Trouble:
This probably goes without saying, but keep yourself out of trouble while you are waiting for you MBA admissions decision to arrive. Post-application-submission is not the time to completely let loose. Keep your social media account clear (and private) and avoid any other problematic activity – it would be a shame to lose an admission to your dream school based on poor post-submission behavior.

Remember, maintain your composure and positive behavior during that dreaded post-submission waiting period to avoid compromising a potential admission.

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 New SAT vs. the ACT: A Simple Test Comparison

“Are ‘SAT’ and ‘ACT’ the same thing?” If you’ve been thinking about this question, you’re not alone. Many high school students are curious about the similarities between these two tests and how different they really are.

A quick SAT-to-ACT comparison can help you to decide whether to take the new SAT, the ACT, or both.

Scoring
The scoring scales for the ACT versus new SAT are very different. The highest score you can earn on the ACT is a 36. There are four sections on the ACT, and you receive a raw score for each section, which is changed into a scaled score ranging from one to 36. Your final score is the average of your four scaled scores. On the other hand, the highest score you can achieve on the new SAT is 1600. You receive a subscore for each section of the new SAT, and your final score is the sum of your subscores.

Math Questions
When making an SAT-to-ACT comparison, you’ll find that both tests include questions on advanced math concepts such as geometry and trigonometry as well as algebra. Of course, knowledge of arithmetic is necessary on both tests. One difference between the two Math sections is that you’re given 60 minutes to complete 60 questions on the ACT and 80 minutes to complete 58 questions on the new SAT. You’re also allowed to use a calculator throughout the Math section on the ACT, but your calculator use is limited on the new SAT.

Science Questions
One major difference in the new SAT versus ACT test is that there’s no specific Science section on the new SAT. However, some of the skills you use in science class are tested in other sections on the new SAT. For instance, in the Math section you’re often asked to analyze the information given on a chart or graph, and the Reading section contains passages that cover science-related topics. The ACT does have a section of Science questions – earth science, chemistry, and biology are among the sciences found on the ACT. You must answer a total of 40 questions in 35 minutes in the Science section of the ACT.

When making an SAT-vs.-ACT comparison, you’ll see that the Reading sections on both tests share a lot of similarities. The Reading sections on both exams feature several passages accompanied by questions. The SAT has five passages, while the ACT has four. In addition, the two tests share many of the same question types. For instance, they both have main idea, detail, vocabulary-in-context, and inference questions. In addition to those, the new SAT has data reasoning, technique, and evidence support questions. You’re given 35 minutes to finish 40 questions on the ACT and 65 minutes to finish 52 questions on the new SAT Reading section.

Writing and English Tests
There is a Writing & Language section on the new SAT that requires you to improve on phrases found within the given passages. There may be grammar or punctuation errors in the passage or problems with sentence structure. You’ll read the passage and select the better options for the underlined phrases.

The ACT has an English section with passages that also contain underlined phrases. Your task is to find a better alternative to the phrase or, in some cases, select the “no change” option. Once again, there may be grammar errors or problems with punctuation, sentence structure, or organization. You are given 45 minutes to finish 75 questions in the English section on the ACT and 35 minutes to complete 44 Writing & Language questions on the new SAT.

The Essay
When it comes to the essay on the ACT vs. new SAT, both tests make this section optional. For the new SAT Essay section, you’re required to analyze an argument and offer evidence as to why the author’s argument is valid or invalid. Alternatively, the ACT Essay section presents you with three different perspectives on a particular issue, and your job is to evaluate each of them. On both essays, your score depends on your ability to organize your thoughts, present evidence, and convey your ideas in a clear way.

Are “SAT” and “ACT” the same? In some ways, the answer is “yes,” but in many others, the answer is “no.” Regardless of which test you take, our professional instructors can help you practice for it. Look at our video tutorials and sign up for our in-person or online test prep courses today!

Want to learn more about how the SAT and ACT differ? Attend one of our upcoming free live online SAT vs. ACT workshops to determine which exam is right for you. And be sure to find us on Facebook, YouTube, Google+ and Twitter!

# How to Answer GMAT Questions That are About an Unfamiliar Topic

Usually, GMAT questions that are based on your field of work or interests are simple to comprehend and relatively easy to answer correctly. But what happens when, say, an engineer gets a question based on psychiatry? Is he or she bound to fail? No.

Remember that the GMAT offers a level playing field for test takers from different backgrounds – it doesn’t matter whether your major was literature or physics. If you feel lost on a question about renaissance painters, remember that the guy next to you is lost on the problem involving planetary systems.

So how can you successfully handle GMAT questions on any topic? By sticking to the basics. The logic and reasoning required to answer these questions will stay the same no matter which field the information in the question stem comes from.

To give an example of this, let’s today take a look at a GMAT question involving psychoanalysis:

Studies in restaurants show that the tips left by customers who pay their bill in cash tend to be larger when the bill is presented on a tray that bears a credit-card logo. Consumer psychologists hypothesize that simply seeing a credit-card logo makes many credit-card holders willing to spend more because it reminds them that their spending power exceeds the cash they have immediately available.

Which of the following, if true, most strongly supports the psychologists’ interpretation of the studies?

(A) The effect noted in the studies is not limited to patrons who have credit cards.
(B) Patrons who are under financial pressure from their credit-card obligations tend to tip less when presented with a restaurant bill on a tray with credit-card logo than when the tray has no logo.
(C) In virtually all of the cases in the studies, the patrons who paid bills in cash did not possess credit cards.
(D) In general, restaurant patrons who pay their bills in cash leave larger tips than do those who pay by credit card.
(E) The percentage of restaurant bills paid with given brand of credit card increases when that credit card’s logo is displayed on the tray with which the bill is prepared.

Let’s break down the argument:

Argument: Studies show that cash tips left by customers are larger when the bill is presented on a tray that bears a credit-card logo.

Why would that be? Why would there be a difference in customer behavior when the tray has no logo from when the tray has a credit card logo? Psychologists’ hypothesize that seeing a credit-card logo reminds people of the spending power given by the credit card they carry (and that their spending power exceeds the actual cash they have right now).

The question asks us to support the psychologists’ interpretation. And what is the psychologists’ interpretation of the studies? It is that seeing a logo reminds people of their own credit card status. Say we change the argument a little by adding a line:

Argument: Studies show that cash tips left by customers are larger when the bill is presented on a tray that bears a credit-card logo. Patrons under financial pressure from credit-card obligations tend to tip less when presented with a restaurant bill on a tray with credit-card logo than when the tray has no logo.

Now, does the psychologists’ interpretation make even more sense? The psychologists’ interpretation is only that “seeing a logo reminds people of their own credit card status.” The fact “that their spending power exceeds the cash they have right now” explains the higher tips. If we are given that some customers tip more upon seeing that card logo and some tip less upon seeing it, it makes sense, right? Different people have different credit card obligation status, hence, people are reminded of their own card obligation status and they tip accordingly.

Answer choice B increases the probability that the psychologists’ interpretation is true because it tells you that in the cases of very high credit card obligations, customers tip less. This is what you would expect if the psychologists’ interpretation were correct.

In simpler terms, the logic here is similar to the following situation:

A: After 12 hours of night time sleep, I can’t study.
B: Yeah, because your sleep pattern is linked to your level of concentration. After a long sleep, your mind is still muddled and lazy so you can’t study.
A: After only 4 hrs of night time sleep, I can’t study either.

Does B’s theory make sense? Sure! B’s theory is that “sleep pattern is linked to level of concentration.” If A sleeps too much, her concentration is affected. If she sleeps too little, again her concentration is affected. So B’s theory certainly makes more sense.

(E) The percentage of restaurant bills paid with given brand of credit card increases when that credit card’s logo is displayed on the tray with which the bill is prepared.

This option supports the hypothesis that credit card logos remind people of their own card – not of their card obligations. The psychologists’ interpretation talks about the logo reminding people of their card status (high spending power or high obligations). Hence, this option is not correct.

Now let’s examine the rest of the answer choices to see why they are also incorrect:

(A) The effect noted in the studies is not limited to patrons who have credit cards.

This argument is focused only on credit cards, not on credit cards and their logos, so this is irrelevant.

(C) In virtually all of the cases in the studies, the patrons who paid bills in cash did not possess credit cards.

This option questions the validity of the psychologists’ interpretation. Hence, this is also not correct.

(D) In general, restaurant patrons who pay their bills in cash leave larger tips than do those who pay by credit card.

This argument deals with people who have credit cards but are tipping by cash, hence this is also irrelevant.

We hope you see that if you approach GMAT questions logically and stick to the basics, it is not hard to interpret and solve them, even if they include information from an unfamiliar field.

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!

# Sample GRE Questions

Students planning to take the Graduate Record Examination (GRE) need to make sure they are ready when test day arrives. At Veritas Prep, we know that practice exams are valuable resources for students. Completing a set of GRE example questions serves many purposes. For one, answering GRE prep questions allows a student to see the topics that will appear on the GRE – test sample questions serve as a preview of the exam.

Today, students have the convenience of finding GRE practice questions online. Take a look at some examples:

The Verbal Reasoning Section
These GRE practice test questions include reading comprehension, sentence equivalence, and text completion question types. The reading comprehension portion of the test includes several written passages. Students answer various questions based on the information in a passage by choosing from a set of multiple choice answer options. After reading a lengthy passage, students may be asked about the theme of a passage or the intent of its author. Or, they may be asked about the implied meaning of a passage or the reasons behind a statement.

Alternatively, the sentence equivalence portion of the test asks students to choose two words that would correctly complete each sentence. For example:

Example 1: The artist known for her picturesque landscapes once commented that she ____ nature.
A) idolizes
B) abhors
C) reveres
D) despises
E) detests
F) scorns

Example 2: A student who tries to cram for a biology final exam in one night will become _____ because it’s impossible to learn an entire course in so little time.
A) exacerbated
B) inspired
C) exasperated
D) lethargic
E) complaisant
F) dispassionate

The text completion questions feature a passage consisting of four or five sentences. There may be one or several blank spaces in the passage. Students have a choice of three or more options for each blank. If a student is not sure about the definition of a word, sometimes looking at a word’s prefix can offer clues. Our professional instructors provide tips to students who need help on this or any other section of the GRE.

Example: The horse and rider emerged from the woods and cantered up a hillside ______ by the moon. The horse made a sharp turn sending the rider tumbling to the ground. The rider slowly stood up, cursing under his breath. He was ______ at his lack of talent as an equestrian.
A) ill-lighted:abhorred
B) illuminated:vexed
C) darkened:appalled
D) enlightened:humiliated
E) obscured:angered

Looking for GRE practice questions online can be helpful when reviewing for the analogy section. In this section, students choose the pair of words that is most similar to the pair of words in the example. One of the strategies we teach our students is to determine the relationship between the words in the example to arrive at the correct answer option. For instance:

Example: ASSAUGE : SORROW
A) counsel : exacerbate
B) withhold : appreciation
C) companionship : loneliness
D) endear : criticize
E) console : aggravate

The Quantitative Section
There are a variety of math questions in this section of the GRE. Practice test questions may challenge a student’s algebra, geometry, arithmetic, or data analysis skills.

Example 1: Which of these numbers is the average of the first ten even numbers?
A) 9
B) 13
C) 11
D) 16
E) 15
2+4+6+8+10+12+14+16+18+20=110/10

Example 2: (12/3) x (8/4) =
A) 18
B) 10
C) 8
D) 12
E) 14

Example 3: If 8t + 5t +2t + 4t=114, then 5t + 3=
A) 20
B) 33
C) 25
D) 32
E) 40

The Analytical Writing Section
This section requires students to write both an issue and an argument essay. Students receive a prompt for both essays. A sample prompt for the issue essay may ask students whether they agree or disagree with the idea of paying high school students for perfect attendance. Alternatively, a sample prompt for the argument essay may center on the argument of legalizing medical marijuana. Regardless of what side a student takes, he or she should create a well-organized essay and a convincing argument.

We are experts at helping students prepare for the GRE. Test sample questions are easier to manage when students partner with one of our online instructors. Email or call us to find out more about our prep classes for the GRE. Our helpful team at Veritas Prep gives students the tools to succeed 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!

# GMAT Tip of the Week: Taking the Least Amount of Time to Solve “At Least” Probability Problems

In its efforts to keep everyone from getting perfect 800s, the GMAT has two powerful tools to stop you from perfection. For one, it can bait you into wrong answers (with challenging content, tempting trap answers, or a combination thereof). And secondly, it can waste your time, making it look like you need to do a lot of work when there’s a much simpler way.

Fortunately, and contrary to popular belief, the GMAT isn’t “pure evil.” Wherever it provides opportunities for less-savvy examinees to waste their time, it also provides a shortcut for those who have put in the study time to learn it or who have the patience to look for the elevator, so to speak, before slogging up the stairs. And one classic example of that comes with the “at least one” type of probability question.

To illustrate, let’s consider an example:

In a bowl of marbles, 8 are yellow, 6 are blue, and 4 are black. If Michelle picks 2 marbles out of the bowl at random and at the same time, what is the probability that at least one of the marbles will be yellow?

(A) 5/17
(B) 12/17
(C) 25/81
(D) 56/81
(E) 4/9

Here, you can first streamline the process along the lines of one of those “There are two types of people in the world: those who _______ and those who don’t _______” memes. Your goal is to determine whether you get a yellow marble, so you don’t care as much about “blue” and “black”…those can be grouped into “not yellow,” thereby giving you only two groups: 8 yellow marbles and 10 not-yellow marbles. Fewer groups means less ugly math!

But even so, trying to calculate the probability of every sequence that gives you one or two yellow marbles is labor intensive. You could accomplish that “not yellow” goal several ways:

First marble: Yellow; Second: Not Yellow
First: Not Yellow; Second: Yellow
First: Yellow; Second: Yellow

That’s three different math problems each involving fractions and requiring attention to detail. There ought to be an easier way…and there is. When a probability problem asks you for the probability of “at least one,” consider the only situation in which you WOULDN’T get at least one: if you got none. That’s a single calculation, and helpful because if the probability of drawing two marbles is 100% (that’s what the problem says you’re doing), then 100% minus the probability of the unfavorable outcome (no yellow) has to equal the probability of the favorable outcome. So if you determine “the probability of no yellow” and subtract from 1, you’re finished. That means that your problem should actually look like:

PROBABILITY OF NO YELLOW, FIRST DRAW: 10 non-yellow / 18 total
PROBABILITY OF NO YELLOW, SECOND DRAW: 9 remaining non-yellow / 17 remaining total

10/18 * 9/17 reduces to 10/2 * 1/17 = 5/17. Now here’s the only tricky part of using this technique: 5/17 is the probability of what you DON’T want, so you need to subtract that from 1 to get the probability you do want. So the answer then is 12/17, or B.

More important than this problem is the lesson: when you see an “at least one” probability problem, recognize that the probability of “at least one” equals 100% minus the probability of “none.” Since “none” is always a single calculation, you’ll always be able to save time with this technique. Had the question asked about three marbles, the number of favorable sequences for “at least one yellow” would be:

Yellow Yellow Yellow
Yellow Not-Yellow Not-Yellow
Yellow Not-Yellow Yellow
Yellow Yellow Not-Yellow
Not-Yellow Yellow Yellow

(And note here – this list is not yet exhaustive, so under time pressure you may very well forget one sequence entirely and then still get the problem wrong even if you’ve done the math right.)

Whereas the probability of No Yellow is much more straightforward: Not-Yellow, Not-Yellow, Not-Yellow would be 10/18 * 9/17 * 8/16 (and look how nicely that last fraction slots in, reducing quickly to 1/2). What would otherwise be a terrifying slog, the “long way” becomes quite quick the shorter way.

So, remember, when you see “at least one” probability on the GMAT, employ the “100% minus probability of none” strategy and you’ll save valuable time on at least one Quant problem on test day.

By Brian Galvin.

# Everything You Need to Know About GMAC’s New Common Letter of Recommendation

Letters of recommendation are the one key part of the MBA application process that most applicants have little to no control over. Of course you can influence the quality of your recommendation through your performance leading up to the ultimate request, but the actual delivery is totally out of your control.

What further complicates the recommendation process for many is the fact that applicants also have to deal with two, three and sometimes four recommenders for an application season, or even for a single application. For some the process can be simple, but for others it is more difficult, especially with recommendations often coming from busy senior management members.

The level of anxiety MBA candidates have over letters of recommendation is often through the roof! But fear not – the Graduate Management Admission Council (GMAC) has heard your pleas. GMAC, better known as the organization that administers the GMAT exam, has recently introduced a Common Letter of Recommendation (LOR).

The main goal of this new initiative is to save recommenders and applicants time during application season. The Common LOR will offer recommenders a single recommendation form with a common set of questions. GMAC also offers an application system that houses these LOR responses for each participating school so each recommendation is in one central location, making updates or edits a breeze.

The Common LOR assessment grid is based on 16 leadership competencies which are grouped in five categories: Achievement, Influence, People, Personal Qualities, and Cognitive Abilities.  The form also includes three more qualitative and open-ended recommendation questions that are very similar to other independent LOR questions asked by MBA programs in the past. These questions are based on the applicant’s overall performance, comparative performance, and required development in an organization.

There are currently only a handful of schools that are part of the common LOR form, with some business schools (like Michigan Ross, Cornell Johnson, and Columbia) using the entire form, and other schools (such as Stanford, NYU Stern, Darden, and Berkeley Haas) using just the recommendation questions. GMAC is still trying to evangelize the Common LOR to the remaining MBA community, which will take some time as the form has not been available for long.

As more business schools begin to utilize the GMAC’s Common LOR form, make sure you stay abreast of the latest and greatest information, as this form can certainly save all those who are involved in the recommendation process tons of time.

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.

# ACT Registration Checklist and Testing Dates

Completing the ACT registration process is the first step toward sitting down to take the test. Having a checklist of things to do can help you to organize the process.

Learn about the steps you need to take, as well as some important things to consider, before you sit down to register for the ACT.

Create a Student Account Online
ACT registration can be accomplished very easily by visiting their official website, ACT.org. After creating an account, it takes about 40 minutes to complete the registration forms. There is a test fee that you can pay with a credit card via a secure payment system. Also, you must upload a photo of yourself during ACT test registration. This photo is used for identification purposes and will be put onto the ticket that you’ll take with you to the testing center.

Special Accommodations for the Test
If you have a disability, it’s possible to get special accommodations for the ACT. For instance, if you’re visually impaired, you may be able to arrange for a magnifying device or a reader. During the registration process, you have the chance to express the need for special accommodations. After registration is complete, you will receive an email explaining how to request testing accommodations. You must then work with the officials at your school to secure accommodations for the ACT. You will have to submit proof of a disability along with other documentation. Your school must submit the actual request for accommodations to ACT testing officials.

The Writing Test
The writing test on the ACT is optional. During registration, you can specify whether you want to take it. If you change your mind later about taking the writing test, you can log onto the website and make this adjustment. Keep in mind that you must make the change before the late registration deadline connected with your test date. There is an additional fee for the writing test.

Choose a Test Date and Location
You’ll have the opportunity to choose a test date as well as a testing center located near you. On the website, there is a chart that displays upcoming test dates as well as corresponding ACT registration dates. The ACT registration dates are the deadlines for anyone who wants to take the test on a particular day. It’s possible to register for the test after the deadline passes, but the ACT charges a late fee for that service. The test center locator on the website makes it simple for you to find a location that is convenient. Your test date and location will be confirmed after you finish the ACT test registration process.

Arranging for the Delivery of Score Reports
As part of your testing fee, the ACT sends your score report to four colleges. You can specify these colleges during test registration. You have the option of sending your score report to more than four colleges, but there is a fee for each additional request.

Preparing for the Test
After going through the process of ACT registration, your next step is to prep for the test! That’s where we can help. At Veritas Prep, our talented instructors can provide you with tools that enable you to highlight your skills on the ACT. We’ll guide you through taking a practice ACT to reveal both your strengths and weaknesses when it comes to the material on this test. In addition, we’ll pair you with an instructor who knows how to convey lessons with your learning style in mind. We’ll help you improve your test performance by giving you strategies to use on every section of the ACT.

When you sign up with Veritas Prep, you get to study with an instructor who scored in the 99th percentile on the test, so the study tips you receive are coming from someone who has taken and conquered the ACT! Our team is proud to provide quality ACT tutoring both online and in person. We use proven study resources in our classes so you know you’re getting practical information you can use on the test.

If you’re looking for the best in ACT prep, send us an email or give us a call today. Let Veritas Prep play a part in your victory on the ACT!

Still need to take the ACT? We run a free online ACT prep seminar every few weeks. And be sure to find us on Facebook, YouTube, Google+ and Twitter!

# Solving GMAT Geometry Problems That Involve Infinite Figures

Sometimes, we come across GMAT geometry questions that involve figures inscribed inside other figures. One shape inside of another shape may not be difficult to work with, but how do we handle problems that involve infinite figures inscribed inside one another? Such questions can unsettle even the most seasoned test takers. Let’s take a look at one of them today:

A square is drawn by joining the midpoints of the sides of a given square. A third square is drawn inside the second square in this way and this process is continued indefinitely. If a side of the first square is 4 cm. Determine the sum of areas of all squares?

(A) 18
(B) 32
(C) 36
(D) 64
(E) None

Now the first thing that might come to our mind is this – how do we mathematically, in the time limit of approximately 2 minutes, calculate areas of infinite squares?

There has to be a formula for this. Recall that we do, in fact, have a formula that calculates the sum of infinite terms – the geometric progression formula! Let’s see if we can use that to find the areas of the squares mentioned in this problem.

First, we’ll see if we can find a pattern in the areas of the squares:

Say the side of the outermost square is “s“. The area of the outermost square will be s^2 and half of the side will be s/2. The side of the next square inside this outermost square (the second square) forms the hypotenuse of a right triangle with legs of length s/2 each. Using the Pythagorean Theorem:

Hypotenuse^2 = (s/2)^2 + (s/2)^2 = s^2/2
Hypotenuse = s/√(2)

So now we know the sides of the second square will each equal s/√(2), and the area of the second square will be s^2/2.

Our calculations will be far easier if we note that the diagonal of the second square will be the same length as the side of the outer square. We know that area of a square given diagonal d is d^2/2, so that would directly bring us to s^2/2 as the area of the second square.

The second square and the square inscribed further inside it (the third square) will have the same relation. The area of the third square will be (s^2/2)*(1/2) = s^2/4.

Now we know the area of every subsequent square will be half the area of the outside square. So the total area of all squares = s^2 + s^2/2 + s^2/4 + s^2/8 + …Each term is half the previous term.

Therefore, the sum of an infinite Geometric Progression where the common ratio is less than 1 is:

Total Sum = a/(1-r)
a: First Term
r: Common Ratio

Sum of areas of all squares = s^2 + s^2/2 + s^2/4 + s^2/8 + …
Sum of areas of all squares = s^2/(1 – 1/2)
Sum of areas of all squares = 2s^2

Since s is the length of the side of the outermost square, and s = 4 (this fact is given to us by the questions stem), the sum of the areas of all the squares = 2*4^2 = 32 cm^2. Therefore, our answer is B.

We hope you understand how we have used the geometric progression formula to get to our answer. To recap, the sum of an infinite geometric progression is a/(1 – r).

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!

# How to Find the Maximum Distance Between Points on a 3D Object

How do we find the the two farthest points on a 3D object? For example, we know that on a circle, any two points that are diametrically opposite will be the farthest from each other than from any other points on the circle. Which two points will be the farthest from each other on a square? The diagonally opposite vertices. Now here is a trickier question – which two points are farthest from each other on a rectangular solid? Again, they will be diagonally opposite, but the question is, which diagonal?

A rectangular box is 10 inches wide, 10 inches long, and 5 inches high. What is the greatest possible (straight-line) distance, in inches, between any two points on the box?

(A) 15
(B) 20
(C) 25
(D) 10 * √(2)
(E) 10 * √(3)

There are various different diagonals in a rectangular solid. Look at the given figure:

BE is a diagonal, BG is a diagonal, GE is a diagonal, and BH is a diagonal. So which two points are farthest from each other? B and E, G and E, B and G, or B and H?

The inside diagonal BH can be seen as the hypotenuse of the right triangle BEH. So both BE and EH will be shorter in length than BH.

The inside diagonal BH can also be seen as the hypotenuse of the right triangle BHG. So both HG and BG will also be shorter in length than BH.

The inside diagonal BH can also be seen as the hypotenuse of the right triangle BDH. So both BD and DH will also be shorter in length than BH.

Thus, we see that BH will be longer than all other diagonals, meaning B and H are the points that are the farthest from each other. Solving for the exact value of BH then should not be difficult.

In our question we know that:

l = 10 inches
w = 10 inches
h = 5 inches

Let’s consider the right triangle DHB. DH is the length, so it is 10 inches.

DB is the diagonal of the right triangle DBC. If DC = w = 10 and BC = h = 5, then we can solve for DB^2 using the Pythagorian Theorem:

DB^2 = DC^2 + BC^2
DB^2 = 10^2 + 5^2 = 125

Going back to triangle DHB, we can now say that:

BH^2 = HD^2 + DB^2
BH^2 = 10^2 + 125
BH = √(225) = 15

Thus, our answer to this question is A.

Similarly, which two points on a cylinder will be the farthest from each other? Let’s examine the following practice GMAT question to find out:

The radius of cylinder C is 5 inches, and the height of cylinder C is 5 inches. What is the greatest possible straight line distance, in inches, between any two points on a cylinder C?

(A) 5 * √2
(B) 5 * √3
(C) 5 * √5
(D) 10
(E) 15

Look at where the farthest points will lie – diametrically opposite from each other and also at the opposite sides of the length of the cylinder:

The diameter, the height and the distance between the points forms a right triangle. Using the given measurements, we can now solve for the distance between the two points:

Diameter^2 + Height^2 = Distance^2
10^2 + 5^2 = Distance^2
Distance = 5 * √5

In both cases, if we start from one extreme point and traverse every length once, we reach the farthest point. For example, in case of the rectangular solid, say we start from H, cover length l and reach D – from D, we cover length w and reach C, and from C, we cover length h and reach B. These two are the farthest points.

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!

# What Subjects Are on the GRE Exam?

What subjects are on the GRE? Many students are aware of the standard Graduate Record Examination, or GRE, but may not know as much about the GRE subject tests. These tests reveal a student’s skills and knowledge in a specific subject. Here, you can discover more about the seven GRE subject tests offered to students who plan to apply to graduate school, as well as what subjects you can expect to find on each test.

Mathematics
About 50 percent of the mathematics test consists of calculus questions. The questions cover both integral and differential calculus. A student must be prepared to apply calculus concepts when completing this section. Students will also encounter basic, linear, and abstract algebra questions. They must understand systems of linear equations, characteristic polynomials, group theory, and number theory among other concepts. Other test topics include geometry, statistics, probability, and algorithms.

There are a total of 66 multiple-choice questions on this test. Students preparing for the mathematics test can benefit from the knowledge and experience of our professional instructors at Veritas Prep. In our online courses, we teach students effective test-taking strategies and tips that help them approach the GRE subject tests with confidence.

Physics
This test challenges a student’s understanding and application of the principles of physics. There are 100 multiple-choice questions on the physics test. A student’s prep work should include studying topics such as electromagnetism, classical mechanics, atomic physics, quantum mechanics, and special relativity. Knowledge of calculus, coordinate systems, partial differential equations, and vector algebra is also helpful when completing questions on the physics test.

Biology
Questions on cellular and molecular biology make up the first section of the biology test. Cell structure, cell function, genetics, DNA, and plant and animal viruses are all topics in this section. The second section on this test is all about organismal biology. Many of the questions concern animal and plant reproduction and development. Other questions relate to the instincts of animals and how plants and animals interact with their environment. There are also questions on fungi and its life cycle.

The third section on the biology test contains questions about ecology and evolution. Students are tested on behavioral ecology and ecosystems, as well as evolutionary processes. The instructors who teach our GRE subject test prep classes at Veritas Prep use high-quality resources to guide students as they study the various topics covered on the biology test.

Chemistry
The 130 questions on this test focus on a variety of chemistry skills. The test covers analytical, organic, inorganic and physical chemistry. Some physical chemistry questions focus on the three laws of thermodynamics. There are organic chemistry questions that test a student’s skills with organometallics and various functional groups. Questions on physical chemistry and organic chemistry make up the bulk of this test. Veritas Prep’s instructors help students practice for all of the topics on this challenging test.

Biochemistry
Questions on biochemistry, cell biology, molecular biology, and genetics are all a part of this subject test. Students use their problem-solving skills to answer many of the 170 questions on this test. They are presented with diagrams and experimental results and must choose the correct multiple-choice option based on the data they are given. Thermodynamics, kinetics, the cell cycle, chromosomes, and genome maintenance are some of the topics that students can expect to encounter on the biochemistry test.

English
The English test gives students an opportunity to display their knowledge of great works of literature. The 230 questions on this test challenge students to identify literary movements or may ask what time period a particular short story, novel, or poem belongs to. Some of the questions are factual while others are analytical. Students should be skilled at analyzing works of literature to identify genre or references made within a piece of writing. In addition, they should be knowledgeable about literary criticism.

Psychology
There are 205 multiple-choice questions on the psychology test. The questions are designed to test a student’s ability to analyze relationships, apply psychological principles and draw conclusions based on research data. Some of the topics found on the psychology test include memory, perception, behavioral neuroscience, abnormal psychology and the history of psychology.

Our helpful staff is glad to supply additional information to students who want to know what subjects are on the GRE. They are welcome to contact Veritas Prep regarding our GRE subject test prep courses. There are also on our frequently asked questions page. We are proud to give students the tools they need to find success on these critical tests!

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 options. And as always, be sure to follow us on Facebook, YouTube, Google+ and Twitter!