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A recurring question from many students who are preparing for GMAT is this: When should one use the permutation formula and when should one use the combination formula?

People have tried to answer this question in various ways, but some students still remain unsure. So we will give you a rule of thumb to follow in all permutation/combination questions:

You never NEED to use the permutation formula! You can always use the combination formula quite conveniently. First let’s look at what these formulas do:

Permutation: nPr = n!/(n-r)!

Out of n items, select r and arrange them in r! ways.

Combination: nCr = n!/[(n-r)!*r!]

Out of n items, select r.

So the only difference between the two formulas is that nCr has an additional r! in the denominator (that is the number of ways in which you can arrange r elements in a row). So you can very well use the combinations formula in place of the permutation formula like this:

nPr = nCr * r!

The nCr formula is far more versatile than nPr, so if the two formulas confuse you, just forget about nPr.

Whenever you need to “select,” “pick,” or “choose” r things/people/letters… out of n, it’s straightaway nCr. What you do next depends on what the question asks of you. Do you need to arrange the r people in a row? Multiply by r!. Do you need to arrange them in a circle? Multiply by (r-1)!. Do you need to distribute them among m groups? Do that! You don’t need to think about whether it is a permutation problem or a combination problem at all. Let’s look at this concept more in depth with the use of a few examples.

There are 8 teachers in a school of which 3 need to give a presentation each. In how many ways can the presenters be chosen?

In this question, you simply have to choose 3 of the 8 teachers, and you know that you can do that in 8C3 ways. That is all that is required.

8C3 = 8*7*6/3*2*1 = 56 ways

Not too bad, right? Let’s look at another question:

There are 8 teachers in a school of which 3 need to give a presentation each. In how many ways can all three presentations be done?

This question is a little different. You need to find the ways in which the presentations can be done. Here the presentations will be different if the same three teachers give presentations in different order. Say Teacher 1 presents, then Teacher 2 and finally Teacher 3 — this will be different from Teacher 2 presenting first, then Teacher 3 and finally Teacher 1. So, not only do we need to select the three teachers, but we also need to arrange them in an order. Select 3 teachers out of 8 in 8C3 ways and then arrange them in 3! ways:

We get 8C3 * 3! = 56 * 6 = 336 ways

Let’s try another one:

Alex took a trip with his three best friends and there he clicked 7 photographs. He wants to put 3 of the 7 photographs on Facebook. How many groups of photographs are possible?

For this problem, out of 7 photographs, we just have to select 3 to make a group. This can be done in 7C3 ways:

7C3 = 7*6*5/3*2*1 = 35 ways

Here’s another variation:

Alex took a trip with his three best friends and there he clicked 7 photographs. He wants to put 3 of the 7 photographs on Facebook, 1 each on the walls of his three best friends. In how many ways can he do that?

Here, out of 7 photographs, we have to first select 3 photographs. This can be done in 7C3 ways. Thereafter, we need to put the photographs on the walls of his three chosen friends. In how many ways can he do that? Now there are three distinct spots in which he will put up the photographs, so basically, he needs to arrange the 3 photographs in 3 distinct spots, which that can be done in 3! ways:

Total number of ways = 7C3 * 3! = (7*6*5/3*2*1) * 6= 35 * 6 = 210 ways

Finally, our last problem:

12 athletes will run in a race. In how many ways can the gold, silver and bronze medals be awarded at the end of the race?

We will start with selecting 3 of the 12 athletes who will win some position in the race. This can be done in 12C3 ways. But just selecting 3 athletes is not enough — they will be awarded 3 distinct medals of gold, silver, and bronze. Athlete 1 getting gold, Athlete 2 getting silver, and Athlete 3 getting bronze is not the same as Athlete 1 getting silver, Athlete 2 getting gold and Athlete 3 getting bronze. So, the three athletes need to be arranged in 3 distinct spots (first, second and third) in 3! ways:

Total number of ways = 12C3 * 3! ways

Note that some of the questions above were permutation questions and some were combination questions, but remember, we don’t need to worry about which is which. All we need to think about is how to solve the question, which is usually by starting with nCr and then doing any other required steps. Break the question down — select people and then arrange if required. This will help you get rid of the “permutation or combination” puzzle once and for 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!

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In college, you can get busy. Like really busy. Like how-did-I-ever-think-I-was-busy-in-high-school-I-don’t-think-I-even-know-what-busy-even-meant busy. Don’t worry, college is still really fun and exciting, but the workload and responsibilities can get overwhelming at times.

It’s easy to fall into the mindset of thinking you should be doing something all the time. Reading now, essay later, dinner with friends at night, club meeting afterward, problem set before bed… With so much on your plate and a seemingly endless supply of homework, taking a break from working can seem like a dangerous idea.

I’m here to say that breaks are good. Breaks are great! I think breaks have so much value that I’d go so far as to advocate taking a full day off from schoolwork once per week, every week. That’s right, I said it: take an entire day off! Don’t worry about finishing your project or getting ahead on your textbook reading. Spending a day without doing any homework is a great idea, and here are a few reasons why:

1) A day off allows you to relax and recharge.

The demands of college life can really add up, so a whole day on the schedule devoid of school responsibilities is just what a student needs to stay relaxed and mentally healthy. It’s wonderful to wake up knowing that you could spend all day in bed and still not feel behind in school. Burnout is a real problem among college students – what better way to make sure that you aren’t working too hard than to make one day entirely work-free.

2) A day off gives you time to do things you enjoy.

The things you do in college will often be fun, but it’s common to not have time in your schedule to do things you used to like. (For me, it was reading for pleasure and playing the piano). When you have a whole day in front of you with no schoolwork responsibilities, you won’t feel to make time for those things. Instead of being so sick of reading textbooks and articles for school that you can’t bear the thought of reading any more, you will feel rejuvenated and free enough to cozy up with your favorite novel!

3) A day off makes you extra organized the other 6 days of the week.

When you know you only have 6 days to get all your work done, you will really learn to make those 6 days count. Setting aside a day for free time will challenge you to be organized and responsible the other days of the week so that you can reap the benefits of your day off.

College is a time where you get to set your own schedule. Take full advantage of that by making one day on your schedule a relaxation day. If you really can’t afford to give yourself a full day off every work, remember that the value of taking breaks still exists even if the time period is shorter than a whole day. Working all the time is unhealthy and counterproductive; be sure to remember to step back, relax, and a take a break. You’ll have earned it!

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One common complaint I get from students is that their algebra skills aren’t where they need to be to excel on the GMAT. This complaint, invariably, is followed by a request for additional algebra drills.

If you’ve followed this blog for any length of time, you know that one of the themes we stress is that Quantitative Reasoning is not, primarily, a math test. Though math is certainly involved – How could it not be? – logic and reasoning are far more important factors than conventional mathematical facility. I stress this in every class I teach. So why the misconception that we need to hone our algebra chops?

I suspect that the culprit here is the explanations that often accompany official GMAC questions. On the whole, they tend to be biased in favor of purely algebraic solutions. They’re always technically correct, but often suboptimal for the test-taker who needs to arrive at a solution within two minutes. Consequently, many students, after reviewing these solutions and arriving at the conclusion that they would not have been capable of the hairy algebra proffered in the official solution, think they need to work on this aspect of their prep. And for the most part it isn’t true.

Here’s a good example:

If x, y, and k are positive numbers such that [x/(x+y)]*10 + [y/(x+y)]*20 = k and if x < y, which of the following could be the value of k?

A) 10

B) 12

C) 15

D) 18

E) 30

A large percentage of test-takers see this question, rub their hands together, and dive into the algebra. The solution offered in the Official Guide does the same – it is about fifteen steps, few of them intuitive. If you were fortunate enough to possess the algebraic virtuosity to solve the question in this manner, you’d likely chew up 5 or 6 minutes, a disastrous scenario on a test that requires you to average 2 minutes per problem.

The upshot is that it’s important for test-takers, when they peruse the official solution, not to arrive at the conclusion that they need to solve this question the same way the solution-writer did. Instead, we can use the same simple strategies we’re always preaching on this blog: pick some simple numbers.

We’re told that x<y, but for my first set of numbers, I like to make x and y the same value – this way, I can see what effect the restriction has on the problem. So let’s say x = 1 and y = 1. Plugging those values into the equation, we get:

(1/2) * 10 + (1/2) * 20 = k

5 + 10 = k

15 = k

Well, we know this isn’t the answer, because x should be less than y. So scratch off C. And now let’s see what the effect is when x is, in fact, less than y. Say x = 1 and y = 2. Now we get:

(1/3) * 10 + (2/3) * 20 = k

10/3 + 40/3 = k

50/3 = k

50/3 is about 17. So when we honor the restriction, k becomes larger than 15. The answer therefore must be D or E. Now we could pick another set of numbers and pay attention to the trend, or we can employ a bit of logic and common sense. The first term in the equation x/(x+y)*10 is some fraction multiplied by 10. So this term, logically, is some value that’s less than 10.

The second term in the equation is y/(x+y)*20, is some fraction multiplied by 20, this term must be less than 20. If we add a number that’s less than 10 to a number that’s less than 20, we’re pretty clearly not going to get a sum of 30. That leaves us with an answer of 18, or D.

(Note that if you’re really savvy, you’ll recognize that the equation is a weighted average. The coefficients in the weighted average are 10 and 20. If x and y were equal, we’d end up at the midway point, 15. Because 20 is multiplied by y, and y is greater than x, we’ll be pulled towards the high end of the range, leading to a k that must fall between 15 and 20 – only 18 is in that range.)

Takeaway: Never take a formal solution to a problem at face value. All you’re seeing is one way to solve a given question. If that approach doesn’t resonate for you, or seems so challenging that your conclusion is that you must purchase a host of textbooks in order to improve your formal math skills, then you haven’t absorbed what the GMAT is really about. Often, the relevant question isn’t, “Can you do the math?” It’s, “Can you reason your way to the answer without actually doing the math?”

*Official Guide question courtesy of the Graduate Management Admissions Council.

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Recently, Facebook COO Sheryl Sandberg made a fairly bold post on Quora saying that a business school degree does not really matter in the tech industry. “While I got great value from my experience, MBAs are not necessary at Facebook and I don’t believe they are important for working in the tech industry,” Sandberg wrote.

She did admit that her MBA helped give her a foundational understanding of business, which might be important “for some people and in some situations,” but did not think that the training would help at a company like Facebook. “I believe—and at Facebook we believe—that degrees are always secondary to skills. In hiring at Facebook we care what people can build and do,” she continued.

It’s certainly a valid opinion, but how accurate is it? Maybe it would be smart move to ask hiring managers in the tech industry if they agree. After all, they are very often the first line when it comes to screening candidates for their company and through years of experience, know exactly what they are looking for in candidates. Well, a startup called Tapwage tried to do something similar.

Tapwage is a “job discovery” startup that takes a unique approach to the classic job board of old. They analyzed “over 50,000 job listings for major tech companies and another 50,000 listings at companies outside of tech.” What they found might surprise many folks out there, including Sheryl: Facebook is not only looking to hire business school students, but they actually want to hire more than a company like Goldman Sachs! According to Tapwage, “As it turns out, Facebook looks for more MBAs than Goldman Sachs. In fact, three times as many job postings by Facebook state a preference (and sometimes a “strong preference”) for an MBA compared to Goldman, both in absolute number of jobs, and in the jobs as calculated as a percentage of their total job listings.”

So what does this mean for current and prospective business school students? Well Sheryl’s point is a valid one, if we could restate it a bit. What is more likely to be true is that a business school degree is not the “only” thing you need to find a great job and be successful in it.

Tech companies (and probably all companies) value people who can execute, people with experience, and smart people with passion, regardless of your graduate degree. Whether you have a degree from business school or not could just be icing on the cake for some, or depending on how much skill and experience a student had acquired before school, a prerequisite for getting that dream job. However, it is clearly not a prerequisite for each and every tech job. You will have to decide if the two year investment of time and money is a good one, or if it is a better use of your time to go out and get the kinds of experience an executive like Sheryl Sandberg believes you need for a tech company.

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

ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

When you get to college, the vast array of courses available to you can be incredibly exciting. If you’re like many students whose high schools had limited course offerings, you might be tempted to take a bunch of classes in college in a subject you love that your high school didn’t offer.

This makes sense. You’ve been stuck taking the same math, science, and history classes the last 12 years – maybe now you really want to spend your tuition money studying what you actually enjoy, like architecture or astronomy. Or maybe you really liked history but disliked math and science, so only plan to take social studies courses.

In both of those cases, I’d urge you to reconsider. While I know from personal experience that it’s really easy to just take subjects you know you already like, it’s really important to branch out and be balanced. I think there are 2 primary reasons why taking a broad mix of classes is good for your academic and personal development.

The first reason is that taking different subjects forces you to think in different ways and develop different skills. Each discipline pushes you in different directions intellectually: math will hone your numerical analysis; history will hone your critical thinking; philosophy will hone your argument analysis; science will hone your command of data; architecture will hone your spatial reasoning… I think you get the point by now.

What I’m really trying to say, is that working with a variety of subjects broadens your horizons as a thinker. The more you’re challenged to develop a mental capacity outside your comfort zone, the more able you’ll be to think on your feet and synthesize diverse information successfully.

The second reason is that branching out allows you to find other things that interest you aside from what you already thought you liked. The academic world is filled with fascinating subjects. You won’t discover most of them if you stick to what you know. We’re teenage college students (or soon-to-be college students) – our desires are fickle and change all the time. To really maximize our intellectual enjoyment, it’s crucial to explore the unknown.

Of course, the hardest part of this will be actually finding courses to branch out with. How are you supposed to know what you will like among the things you don’t think you’ll like? It seems like a tough predicament, but the solutions are pretty simple. One good way is to search for courses in a department you’ve never even heard of, like, say, Egyptology. Then just pick the class that sounds the most random and go for it. Think of all the cocktail party trivia you will learn! The other way is to look around for great professors. The best professors will get you to fall in love with subjects you never thought you enjoyed, making any class you choose a good one.

College is a time where you’ll be exposed to the most new information you’ll have ever seen in your life. Take full advantage of that opportunity by learning about as many different subjects as you can. Trust me – your future self will thank you for making yourself smarter and more interested.

ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

The SAT is a major source of worry for a lot of students, and this worry can affect their scores in a negative way. When even thinking about the test fills a student with anxiety and dread, he will be unconfident and unable to achieve his potential.

In order to overcome that worry, we first need to understand where it comes from. Students tend to make the SAT a bigger deal than it is – they think it is the measure of how smart they are, they think it will completely determine where they go to college, and on the extreme end, they make it out to be the biggest moment of their lives, acting as if doing poorly on the SAT will ruin their futures forever.

To these students, or any students who worry about the SAT, here’s what I say: the SAT does not define you. It doesn’t tell you how smart you are. It is not the only thing (not even close) that matters for getting into college. It certainly doesn’t tell you whether you’re a good person, or even a good student. All the SAT does is tell you how good you are at playing the game of the SAT.

Of course the SAT is an important test – if it wasn’t, nobody would take it and this whole blog wouldn’t exist. But even though the SAT is important in itself, it’s even more important to put the test in perspective. Does the SAT help you get into the colleges you want to go to? Yes, so you should definitely try to do your best. The SAT can be one aspect of a well-rounded college application that will help you reach your higher education goals. Is taking the SAT the biggest moment of your life? Does your score dictate your future happiness and tell you what job you will have in 10 years? No, no, and no! The SAT is a college admissions test – it’s crucial to stop pretending that it’s more than that.

Here’s the advice that I give my SAT classes when I’m teaching: treat the SAT like anything else you want to do well on. Study hard and try to do the best you can, but always keep the bigger picture in mind. I like to think of the SAT as a win-neutral test – if you do well, great! Your application will look that much better. If you don’t do so well, that’s also fine. You can always try again, and there will still be plenty of great colleges that want you to be a member of their communities. When you’re getting stressed out about the SAT, take a deep breath, step back, and remind yourself that you’ll still be you, no matter how many points you get on the test.

The best part about having a healthy perspective on the SAT is that it can even help you score higher. The more you understand just how the SAT matters and what it shows about you, the more relaxed and level-headed you’ll be. With those qualities, your score can do nothing but improve.

When you finally realize what role the SAT should really play in your life and start to see that you have all the tools necessary to crush it, you’ll be well on your way to a good attitude and a good score.

ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

It is common knowledge that “going green” has a host of benefits for the companies that employ these practices. Improving corporate environmental operations has been known to increase brand value and strengthen the public’s trust. Doing business in a sustainable manner also exempts companies from numerous fines and fees, and occasionally qualifies them for certain tax credits.

As this positive trend continues, it has also branched out into other sectors that were previously unaffected. Traditionally, businesses were able to attract recent MBA graduates using salary as their main incentive, however this practice is rapidly undergoing extinction. Today’s students are growing increasingly likely to gravitate toward companies that realize the threat of climate change and utilize sustainable practices.

According to a recent global study, recruiting top talent is quickly becoming more dependent on factors other than salary alone. This study was conducted by Yale University, in collaboration with the World Business Council for Sustainable Development and the Global Network for Advanced Management, and it surveyed over 3,700 students at 29 of the world’s top business schools. What might be very surprising, is the fact that the results showed that 44% of business school students are willing to accept a lower wage to work for an organization with admirable environmental practices. Additionally, 19% said they refuse to work for a company with poor standards, regardless of pay.

Today’s business students want to work for companies that have developed committed and responsible leadership in the search for solutions to environmental issues. 92% of students stated that they believe climate change is already happening, and 64% said that they do not think modern corporations are doing enough to address the problem.

Those beliefs are not the only factor behind the recent push for more aggressive action in preventing climate change. 71% of business school students believe that environmentally-friendly companies see improved market competitiveness, and even more (80% – an overwhelming majority) consider environmental action extremely profitable, providing economic growth and job creation.

Overall, business school students desire to work for companies that do not delegate sustainability to a separate department. They want sustainability to be incorporated throughout the company as a whole – 86% agree that the reporting of financial and sustainability metrics should be integrated. Many also believe that both the positive and negative impacts of an organization’s activities should be measured and analyzed.

The companies that will be most successful at attracting new talent in the form of recently graduated MBAs will have aggressive approaches to thwarting climate change and will address issues through industry-wide collaboration. A resounding 90% of the surveyed students claimed that board-level action on environmental and sustainability issues should be instigated.

As time goes on, this trend is predicted to have relatively steady growth, according to the Yale study. Today’s business students want to work for companies with transparent and progressive environmental standards – this means more than just using recycled coffee cups in the break room. In order to attract top talent, businesses will need to take action and stay competitive with the responsibilities they take for preventing climate change.

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

ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

You’ve made it through the admissions process, completed your interview, and think you have a good shot at being admitted. Instead, you get that discouraging letter that you aren’t in – at least, not yet. There is good news and bad news when it comes to being put on the waitlist for the business school of your dreams. The bad news is that you’ll have to wait a bit longer to get in. The good news is that the waitlist is not the death of your MBA admissions campaign.

Think of it as a new beginning, another chance to prove to the admissions committee why you are deserving of admittance to their school. Remember, business schools only put people on the waitlist who they think are good candidates and have the chance to be admitted. Very often it simply becomes a numbers game, and schools have to wait and see how students from your demographic are accepting or not accepting their admission offers. If you do end up on the waitlist, here are some tips for how you can help improve your situation:

Read the Waitlist Letter and Follow Its Instructions

Some schools will want you to follow up your waitlist letter with additional information, such as a new recommender, update on your job, or a progress report on classes you might be taking. However, some schools make it clear that they will reach out to you when the time comes, and do not want any further materials sent to them. Whatever they say, do it. Don’t think you’ll be able to get on the good side of the committee by reaching out to the admissions director with a “question” about your status. Follow the instructions that are given to you.

Asked for Additional Information?

If the waitlist letter does give you the chance to provide additional information, consider the following:

Providing an update on recent projects at work or sharing a recent promotion or achievement award.

Making clear how passionate you are about the school.

Showing how you have, or are addressing, shortfalls in your application. For example, do you know you have a low Quant score on the GMAT? Make sure you are taking some stats classes at your local community college to supplement this aspect of your application.

Have a Backup Plan

Now is the time to build a backup plan and put it into action. Whether that is applying to more schools, retaking the GMAT, or staying at your job for another year, you never want to leave yourself with no options.

Be Patient

No one likes being told “no,” and our first instinct is to make that person change his or her mind. However, Admissions Committees have been reviewing thousands of candidates for a long time – they know what they are looking for. Now is not the time to panic and risk embarrassing yourself with constant calls to the admissions office. Instead, focus on other applications you might be working on, maintain a high work output, and try to remain positive. Worst case scenario, you will be able to reapply next year.

Good luck, and if it’s meant to be, don’t hold the fact that you were put on the waitlist against the school. Just remember, your future MBA diploma won’t say anything about your previous waitlist status.

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

ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

This week, the internet exploded with a massive Twitter feud between rappers Kanye West and Wiz Khalifa, with help from their significant others and exes. For days now, hashtags unpublishable for an education blog have topped the trending lists, all as a result of the epic social media confrontation. And all of THAT originated from a classic GMAT mistake from the Louis Vuitton Don – a man who so loves his hometown Kellogg School of Management that he essentially named his daughter Northwestern – himself:

Kanye didn’t consider all the possibilities when he saw variables.

A brief history of the beef: there was musical origin, as Wiz wanted a bit of credit for his young/wild/free friends for the term “Wave,” as Kanye changed his upcoming album title from Swish to Waves. But where things escalated quickly all stemmed from Wiz’s use of variables in the following tweet:

Hit this kk and become yourself.

Kanye, whose wife bears those exact initials, K.K., immediately interpreted those variables as a reference to Kim and lost his mind. But Wiz had intended those variables kk to mean something entirely different, a reference to his favorite drug of choice. And then…well let’s just say that things got out of hand.

So back to the GMAT: Kanye’s main mistake was that he didn’t consider alternate possibilities for the variables he saw in the tweet, and quickly built in some incorrect assumptions that led to disastrous results. Do not let this happen to you on the GMAT! Here’s how it could happen:

1) Forgetting about not-obvious numbers.

If a problem, for example, defines k as 10 < k < 12, you can’t just think “k = 11” because you don’t know that k has to be an integer. 11.9 or 10.1 are also possibilities. Similarly if k^2 = 121, you have to consider that k could be -11 as well as it could be 11.

Ultimately, that was Yeezy’s mistake: he saw KK and with tunnel vision saw the most obvious possibility. But why couldn’t “KK” have been Krispy Kreme or Kyle Korver or Kato Kaelin? Before you leap to conclusions on a GMAT variable, see if there’s anything else it could be.

2) Assuming that each variable must represent a different number.

This one is a bit more nuanced. Suppose you were asked:

For positive integers a and b, is the product ab > 1?

(1) a = 1

With that statement, you might start thinking, “Well if a is 1, b has to be something else…” but all the variable b really means is “a number we don’t know.” Just because a problem assigns two different variables does not mean that they represent two different numbers! B could also be 1…we just don’t know yet.

Where this manifests itself as a problem most often is on function problems. When people see the setup, for example:

The function f is defined for all values x as f(x) = x^2 – x – 1

They’ll often be confused when that’s paired with a question like, “Is f(a) > 1?” and a statement like:

(1) -2 < a < 2

“I know about f(x) but I don’t know anything about f(a),” they might say, but the way these variables work, f(x) means “the function of any number…we just don’t know which number” so when you then see f(a), a becomes that number you don’t know. You’ll do the same thing for a: f(a) = a^2 – a – 1. What goes in the parentheses is just “the number you perform the function on” – the function doesn’t just apply to the variable in the definition, but to any number, variable, or combination that is then put in the parentheses.

The real lesson here is this: variables on the GMAT are a lot like variables in Wiz Khalifa’s Twitter feed. You might think you know what they mean, but before you stake your reputation (or score) on your response to those variables, consider all the options. Hit this GMAT and become yourself.

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In our “Quarter Wit, Quarter Wisdom” series, we have seen how to solve various rates questions – the basic ones as well as the complicated ones. But we haven’t considered critical reasoning questions involving rates, yet. In fact, the concept of rates makes these problems very difficult to both understand and explain. First, let’s look at what “rate” is.

Say my average driving speed is 60 miles/hr. Does it matter whether I drive for 2 hours or 4 hours? Will my average speed change if I drive more (theoretically speaking)? No, right? When I drive for more hours, the distance I cover is more. When I drive for fewer hours, the distance I cover is less. If I travel for a longer time, does it mean my average speed has decreased? No. For that, I need to know what happened to the distance covered. If the distance covered is the same while time taken has increased, only then can I say that my speed was reduced.

Now we will look at an official question and hopefully convince you of the right answer:

The faster a car is traveling, the less time the driver has to avoid a potential accident, and if a car does crash, higher speeds increase the risk of a fatality. Between 1995 and 2000, average highway speeds increased significantly in the United States, yet, over that time, there was a drop in the number of car-crash fatalities per highway mile driven by cars.

Which of the following, if true about the United States between 1995 and 2000, most helps to explain why the fatality rate decreased in spite of the increase in average highway speeds?

(A) The average number of passengers per car on highways increased.

(B) There were increases in both the proportion of people who wore seat belts and the proportion of cars that were equipped with airbags as safety devices.

(C) The increase in average highway speeds occurred as legal speed limits were raised on one highway after another.

(D) The average mileage driven on highways per car increased.

(E) In most locations on the highways, the density of vehicles on the highway did not decrease, although individual vehicles, on average, made their trips more quickly.

Let’s break down the given argument:

The faster a car, the higher the risk of fatality.

In a span of 5 years, the average highway speed has increased.

In the same time, the number of car crash fatalities per highway mile driven by cars has reduced.

This is a paradox question. In last 5 years, the average highway speed has increased. This would have increased the risk of fatality, so we would expect the number of car crash fatalities per highway mile to go up. Instead, it actually goes down. We need to find an answer choice that explains why this happened.

(A) The average number of passengers per car on highways increased.

If there are more people in each car, the risk of fatality increases, if anything. More people are exposed to the possibility of a crash, and if a vehicle is in fact involved in an accident, more people are at risk. It certainly doesn’t explain why the rate of fatality actually decreases.

(B) There were increases in both the proportion of people who wore seat belts and the proportion of cars that were equipped with airbags as safety devices.

This option tells us that the safety features in the cars have been enhanced. That certainly explains why the fatality rate has gone down. If the cars are safer now, the risk of fatality would have reduced, hence this option does help us in explaining the paradox. This is the answer, but let’s double-check by looking at the other options too.

(C) The increase in average highway speeds occurred as legal speed limits were raised on one highway after another.

This option is irrelevant – why the average speed increased is not our concern at all. Our only concern is that average speed has, in fact, increased. This should logically increase the risk of fatality, and hence, our paradox still stands.

(D) The average mileage driven on highways per car increased.

This is the answer choice that troubles us the most. The rate we are concerned about is number of fatalities/highway mile driven, and this option tells us that mileage driven by cars has increased.

Now, let’s consider the parallel with our previous distance-rate-time example:

Rate = Distance/Time

We know that if I drive for more time, it doesn’t mean that my rate changes. Here, however:

Rate = Number of fatalities/highway mile driven

In this case, if more highway miles are driven, it doesn’t mean that the rate will change. It actually has no impact on the rate; we would need to know what happened to the number of fatalities to find out what happened to the rate. Hence this option does not explain the paradox.

(E) In most locations on the highways, the density of vehicles on the highway did not decrease, although individual vehicles, on average, made their trips more quickly.

This answer choice tells us that on average, the trips were made more quickly, i.e. the speed increased. The given argument already tells us that, so this option does not help resolve the paradox.

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

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The ancient Greeks were, to put it mildly, really neat. They created or helped to create the foundations of philosophy, theater, science, democracy, and mathematics – no small accomplishment for a small war-torn civilization from over two millennia ago. Many of our contemporary ideas, beliefs, and traditions are rooted in contributions made by Greek thinkers, and the GMAT is no exception.

When I first encountered this problem I couldn’t help but wonder what kind of mad scientist question-writer engineered it. Where would such an idea even come from? It turns out, it wasn’t a GMAC employee at all, but Archimedes, the famous Greek geometer and coiner of the phrase “Eureka!”

The question is based on his attempt to trisect an angle with only a straight edge and a compass. (Alas, Archimedes’ work, though ingenious, was not technically a correct solution to the problem, as it provides only an approximation.) The reader is hereby invited to contemplate the kind of person who encounters a proof by Archimedes and instinctively thinks, “This would make an excellent Data Sufficiency question on the GMAT!” We’d like to believe that the good folks at GMAC are just like you and me, but perhaps not.

So this got me thinking: what other interesting Greek contributions to mathematics might be helpful in analyzing GMAT questions? In Euclid’s work Elements, he offers a simple and elegant proof for why there is no largest prime number. The proof proceeds by positing a hypothetical largest prime number “p.” We can then construct a product that consists of every prime number 2*3*5*7….*p. We’ll call this product “q.”

The next consecutive number will be q + 1. Now, we know that “q” contains 2 as a factor, as “q,” supposedly, contains every prime as a factor. Therefore q +1 will not contain 2 as a factor. (The next number to contain 2 as a factor will be q + 2.) We know that “q” contains 3 as a factor. Therefore q + 1 will not contain 3 as a factor. (The next number to contain 3 as a factor will be q + 3.)

Uh oh. If “p” really is the largest prime number, we’ve got a problem, because q + 1 will not contain any of the primes between 2 and p as factors. So either q + 1 is itself prime, or there is some prime greater than p and less than q + 1 that we’ve failed to consider. Either way, we’ve proven that p can’t be the largest prime number – I told you the Greeks were neat.

One axiom that’s worth internalizing from Euclid’s proof is the notion that two consecutive numbers cannot have any factors in common aside from 1. When q contains every prime from 2 to p as a factor, q + 1 contains none of those primes. How would this be helpful on the GMAT? Glad you asked. Check out this question:

x is the product of all even numbers from 2 to 50, inclusive. The smallest prime factor of x + 1 must be:

(A) Between 1 and 10

(B) Between 11 and 15

(C) Between 15 and 20

(D) Between 20 and 25

(E) Greater than 25

We’re given information about x, and we’re asked about x + 1. If x is the product of all even numbers from 2 to 50, we can write x = 2 * 4 * 6 …* 50. This is the same as (1*2) * (2*2) * (3*2)… (25*2), which means the product consists of all the integers from 1 to 25, inclusive, and a bunch of 2’s.

So now we know that every prime number between 2 and 25 will be a factor of x. What about x + 1? (Paging Euclid!) We know that 2 is not a factor of x + 1, as 2 is a factor of x, and so the next multiple of 2 would be x + 2. We know that 3 is also not a factor of x + 1, as 3 is a factor of x, and so the next multiple of 3 would be x + 3. And once we’ve internalized that two consecutive numbers cannot have any factors in common aside from 1, we know that if all the primes between 2 and 25 are factors of x, none of those primes can be factors of x + 1, meaning that the smallest prime of x, whatever is, will be greater than 25. The answer, therefore, is E.

Takeaway: One of the beautiful things about mathematics is that fundamental truths do not change over time. What worked for the Greeks will work for us. The same axioms that allowed ancient mathematicians to grapple with problems two millennia ago will allow us to unravel the toughest GMAT questions. Learning a few of these axioms is not only interesting – though I’d caution against bringing up Archimedes’ trisection proof at a dinner party – but also helpful on the GMAT.

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Looking for colleges can seem like just a senior year activity, but it’s actually helpful to start early and be consistent. Spreading out the search for colleges over all 4 years of high school decreases stress and increases the likelihood of finding schools you really love. So, it’s a good idea develop a general plan for how your process is going to work, and go do it! (And of course, a little preparedness always helps to get the parents off your back, and that’s never a bad thing.)

There are lots of ways to approach looking for colleges, but here is a guide to some helpful strategies for each year of high school to put you in command of your college future:

Freshman Year

– Think about purchasing a college guide (such as the Fiske Guide to Colleges) and flip it open once in a while – it’s a no stress way to introduce yourself to the college landscape.

– Talk to older friends and siblings about where they are going or considering going to school. This will introduce you to different schools, and might even land you some free tidbits of college application wisdom.

– Don’t get too anxious! Getting acclimated to high school and doing well academically are more important than freaking out over which college you’ll go to.

Sophomore Year

– Stay focused on doing well in school, and don’t get nervous if you hear peers talking about college; you still have plenty of time to figure things out.

– Take the PSAT (or ACT Aspire) this year to help you figure out an appropriate range of schools to start looking at.

– Tour a local college, or any school you happen to be passing by.

– Keep flipping open those college books! Start asking yourself some questions about what you want from a school, and start building a basic list of schools that sound good. You can easily use websites like Naviance, Niche or countless others to help refine your search.

Junior Year

– Start to compile a real list! The list doesn’t have to be perfect; it’s okay if it’s really big or really small. Try to get a group of friends together to talk about schools you’re considering – often your friends’ choices can help inspire you to consider new possibilities.

– Be sure to take advantage of the college resources your high school provides. If there are college seminars or information days, don’t be afraid to check them out. If you can’t seem to find anything, talk to your counselors; they’ll be happy to work with you to help you find great colleges and alleviate your stress.

– Tighten up your search criteria – figure out the things you really want in a college (such as size, majors, academic structure, social scene, etc.) and find colleges that have them. Once you find some schools that match your criteria, make the time to go on some tours. Pick some schools you are really interested in and see if your family has time to check them out.

– Take the SAT or ACT to open up opportunities for yourself! Doing well on these tests in junior year will make your senior year much more stress-free.

– Over the summer, start to work on your application and essays. You don’t want to be that person scrambling to send in applications right at the schools’ deadlines. I know it sounds awful to start the Common App during your summer vacation, but trust me when I say that you’ll be glad to not have it hanging over your head as senior year rolls around.

Senior Year

– Congratulations! You’re almost at the finish line! It’s time to finally narrow down that list of schools you made last year. Most students typically apply to anywhere from 1-25 schools, but a healthy number is around 6-12. This may seem like obvious advice, but be sure you only apply to schools you actually want to go to. There is no point in wasting an application fee on a school there’s no chance you’ll attend.

– If you have the time, re-visit the schools you’re applying to. Often, you can get a more in-depth feel for a school when you’re there for the second time. If a college still has that “it” factor even though you’ve already seen it, that’s a very good sign.

– Once you’ve sent in all your applications, take a well-deserved break, and bond with your classmates who just went through the same process. Senior year will be a fun time – it’s important to take in the excitement of your last months in high school without getting caught up in the worries of where you’ll go to college.

Remember that each person goes at his or her own pace, and there is no one right way to approach searching for a college. Keep in mind, the key to finding the school that is right for you is fit. Personal fit, academic fit, and social fit are the three broad criteria you should make sure a college fulfills for you.

Above all, the best way you can complete your college search process is to get excited and get into it. Finding schools can be fun! There is a world of possibilities out there that will reveal themselves to you when you open your mind and dive in.

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Most high school seniors recognize the importance of doing their best on the SAT because they know that good SAT scores can help them get into the college of their choice. But what they may not know is that many colleges actually offer scholarships for SAT scores that are above average.

Students who achieve high SAT scores can qualify for a number of different scholarships that can help them pay for tuition, basic college supplies, and more while they are working towards their degrees. This makes it all the more critical for students to showcase their skills on this exam. Consider some facts about the SAT and how you can earn scholarships as a result of your hard work on this challenging test:

A Closer Look at SAT Scores for Scholarships

There are many colleges that offer scholarships for students who excel on the SAT, however, the specific requirements of these scholarships differ from school to school. For instance, one college may have a scholarship that’s open to students who score between 1330 and 1600 on the SAT, while another college may have a scholarship that requires students to have a minimum score of 1440 on the SAT. In many cases, both a student’s SAT scores and GPA are taken into account in examining their scholarship applications, as schools want as much information as possible about the academic work of a student before awarding them a coveted scholarship.

In addition to varying in value, these scholarships can also differ in the number of semesters they cover. In applying for these scholarships, you will want to check with the schools themselves to ensure you know exactly what terms their scholarships have before actually submitting your applications for them.

Why Do Colleges Offer Scholarships Based on SAT Scores?

Not surprisingly, colleges want to accept students who are going to succeed in their intellectual endeavors and add value to their programs, and typically, students who earn high SAT scores are likely to excel in their future college courses.

But an impressive SAT score is just one indication that a student is going to flourish at a particular school. Other indications of a promising student include a high GPA, dedication to extracurricular activities, and even volunteer work, which is why scholarship requirements will vary so much from school to school and include some of these other factors. All colleges want to accept students who will be excellent representatives of their school, and offering scholarships is one way to do that.

How to Find Colleges That Offer Scholarships for High SAT Scores

One way you can locate scholarships awarded for high SAT scores is to just do a basic online search – it should be relatively easy for you to find information about any scholarship on the web. If you have an interest in attending a particular college, it may be wise to also search the school’s official website for details of the scholarships it awards for high SAT scores. Talking to your high school counselor is another way to learn about college scholarships related to performance on the SAT, as your counselor should have access to many helpful resources you can utilize in your search.

How to Earn a High Score on the SAT

The first step toward winning this type of scholarship is to earn a high score on the SAT! Scholarships have deadlines just as college applications do, so it’s a good idea to research the cutoff dates for the scholarships that interest you. Scholarships are well within the reach of well-prepared students who approach the SAT with confidence, so taking a practice test will be a good place to start to build this confidence and help you determine what subjects to focus on in preparing for this test. Through this proper preparation and research, you’ll be well on your way to earning your own SAT scholarship.

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The Graduate Management Admission Council (GMAC) released their 2015 Global Management Education Graduate Survey. The GMAC has been conducting this survey since 2000 and this year’s survey covered over three thousand students from 112 universities and 29 different countries across the globe.

One statistic that stood out the most in this study was just how happy students were with their decision to attend business school. Nine out of ten respondents from the class of 2015 said that the value of their business degree was “good to outstanding,” and another 88% would recommend their program to others looking for a graduate degree. A very strong job market is also present in the survey results. Since so much of students’ satisfaction is based on their employment outcomes, let’s dive deeper into those numbers and see how they compare for various types of programs:

First, full-time MBA students had a pretty good year for job offers: 63% of full-time, two-year MBA graduates had a job offer by graduation, compared to only 40% in 2010. Other graduate programs showed similar increases – for example, 89% of students earning a Masters in Accounting had a job offer compared to 66% in 2010. The biggest growth in this area was for students pursuing a Masters in Management where 59% of students had a job offer by graduation, more than double the amount in 2010.

Part-time MBA programs also showed significant gains in employment outcomes. In 2010, only 22% of job seekers in part-time programs had a job offer by graduation, but this statistic has more than tripled this year to 68%. This is very interesting since in the past, part-time programs were targeted to students who planned on staying at their current employer and recruiters treated them so, largely focusing their recruiting efforts on full-time program students, instead.

Recruiters are now starting to see the value in part-time students and programs, however – they see that part-time students tend to have more experience and, unlike their full-time counterparts, continue to gain work experience during school. Recruiters are responding by shifting some of their resources to recruiting these students alongside more traditional full-time students.

Perhaps the one bit of bad news in this survey is for European business schools and their students: the MBA is the only type of program ata these schools that has seen a drop in job offers by graduation. In 2013, 57% of students at European MBA programs had an offer by graduation, however, the following year, that number dropped slightly to 56%, and in 2016, the number of students dropped even further to only 41%.

What can European programs do to help turn the tide and improve their job placement results? Most importantly, these schools can try to develop stronger relationships with employers outside of Europe. Since many students either don’t come from Europe or would find it hard to stay for work, the schools need to do a better job opening up recruiting channels outside of Europe.

Overall 2015 was a very good year – one of the best years ever – for both students and business schools when it came to finding post-MBA jobs for students. Keep this information in mind as you consider pursuing your own MBA.

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

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Every year, the world’s top business schools become more and more expensive. There are various ways to pay for one’s MBA education, and for domestic students, the process is pretty straightforward. Many students will utilize loans as one of their primary forms of payments, others will pay out of pocket or enjoy the benefits of an employee sponsorship.

One of the most coveted forms of paying for an MBA is the scholarship, because it usually comes with no attached financial commitment to repay the money one is given. Now, these lucrative scholarships do not come easy, especially for international students. Free money is difficult to come by as is, but for international students, there are a few complicating factors.

The biggest challenge international students face with this process is the origin of the scholarship money – most scholarships that are applicable to MBAs at business schools in the United States usually come from domestic donors, and for this reason, the money is largely earmarked for domestic students. This leaves very little available money for international students. If you are an international student, make sure you use this information to research scholarships that are open to, or specifically target, international students.

Keep in mind, if you are applying from an over-represented group, this process may be even more competitive for you. With so many students applying for so little available money, attempting to secure a scholarship can be daunting, which makes it even more important to put your best foot forward in the application process (of course for admission purposes, but also for the limited available money). Candidates with top-notch profiles will obviously stand out in this phase of the process, as many scholarships are administered based on career potential and available scores and grades.

Do not limit your scholarship search simply to those provided by your school. Publicly available scholarships are certainly out there, and if your profile or career trajectory align with the requirements of the organization offering the scholarship, you may be “in the money.” Conducting a basic online search is a good way to find out what scholarships are available, and applicable, to you.

The best advice I can give to international students here is to try and get into the best and most reputed school possible – this will afford you the best career options and highest potential future income level, scholarship or not. Know the realities of the scholarship search and the unique challenges for international students, and set yourself up for success in securing financial support for your education.

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

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

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As we head into Super Bowl weekend, the most popular conversation topic in the world is the Carolina Panthers’ quarterback, Cam Newton. Many questions surround him: is he the QB to whom the Brady/Manning “Greatest of All Time” torch will be passed? Is this the beginning of a new dynasty? Why do people like/dislike him so much? What the heck is the Dab, anyway? And most commonly:

Why is Cam dancing and smiling so much?

The answer? Because smiling may very well be the secret to success, both in the Super Bowl and on the GMAT.

Note: this won’t be the most mathematically tactical GMAT tip post you read, and it’s not something you’ll really be able to practice on Sunday afternoon while you hit the Official Guide for GMAT Review before your Super Bowl party starts. But it may very well be the tip that most impacts your score on test day, because managing stress and optimizing performance are major keys for GMAT examinees. And smiling is a great way to do that.

First, there’s science: the act of smiling itself is known to release endorphins, relaxing your mind and giving you a more positive outlook. And this happens regardless of whether you’re actually happy or optimistic – you can literally “fake it till you make it” by smiling through a stressful or unpleasant experience.

(Plus there’s the fact that smiling puts OTHER people in a better mood, too, which won’t really help you on the GMAT since it’s you against a computer, but for your b-school and job interviews, a smile can go a long way toward an upbeat experience for both you and the interviewer.)

There are plenty of ways to force yourself to smile. One is the obvious: just do it. Write it down on the top of your noteboard in all caps: SMILE! And force yourself to do it, even when it doesn’t feel natural.

But you can also laugh/smile at yourself more naturally: when Question 1 is a permutations problem and you were dreading the idea of a permutations problem, you can laugh at your bad luck but also at the fact that at least you’re getting it over with while you still have plenty of time to recover. When you blank on a rule and have to test small numbers to prove it, you can laugh at the fact that had you not been so fascinated with the video games on your calculator in middle school you’d know that cold. You can smile when you see a friend’s name in a word problem or a Sentence Correction reference to a place you want to visit someday.

And the tactical rationale there: when you can smile in relation to the subject matter on the test, you can remind yourself that, at least on some level, you enjoy learning and problem-solving and striving for achievement. The biggest difference between “good test takers” and “good students, but bad test takers” is in the way that each approaches problems: the latter group says, “I don’t know,” and feels doubt, while the former says, “I don’t know…yet,” and starts from a position of confidence and strength. Then when you apply that confidence and figure out a problem that for a second had you totally stumped, you’ve earned that next smile and the positive energy snowballs.

As you watch Cam Newton on Sunday (For you brand management hopefuls, he’ll be playing football between those commercials you’re so excited to see!), pay attention to that megawatt smile that’s been the topic of so much talk radio controversy the last few weeks. Cam smiles because he’s having fun out there, and then that smile leads to big plays, which is even more fun, and then he’s smiling again. Apply that Cam Newton “smile your way to success” philosophy on test day and maybe you’ll be the next one getting paid hundreds of thousands of dollars to go to school for two years… (We kid, Cam – we kid!)

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Today we will discuss a pretty advanced GMAT question, because we can still use our basic GMAT concepts to find the answer. It may seem like we will need trigonometry to handle this question, but that is not so. In fact, the question will look familiar at first, but will present unforeseen problems later on.

While going through this exercise, we will learn a few tips and tricks which will be useful in our mainstream GMAT questions, hence, it will add value to our GMAT repertoire (especially in elimination techniques). Let’s go on to the question now:

In triangle ABC, if angle ABC is 30 degrees, AC = 2*sqrt(2) and AB = BC = X, what is the value of X?

(A) Sqrt(3) – 1

(B) Sqrt(3) + 2

(C) (Sqrt(3) – 1)/2

(D) (Sqrt(3) + 1)/2

(E) 2*(Sqrt(3) + 1)

What we see here is an isosceles triangle with one angle as 30 degrees and other two angles as (180 – 30)/2 = 75 degrees each.

The side opposite the 30 degrees angle is 2*sqrt(2). One simple observation is that X must be greater than 2*sqrt(2) because these sides are opposite the greater angles (75 degrees).

2*sqrt(2) is a bit less than 2*1.5 because Sqrt(2) = 1.414. So 2*sqrt(2) is a bit less than 3. Note that options (A), (C), and (D) are much smaller than 3, so these cannot be the value of X. We have already improved our chances of getting the correct answer by eliminating three options! Now we have to choose out of (B) and (E).

Here is what is given: Angle ABC = 30 degrees, and AC = 2*sqrt(2). We need to find the value of X. Now, our 30 degree angle reminds us of a 30-60-90 triangle in which we know the ratio of the sides – given one side, we can find the other two.

The problem is this: if we drop an altitude from angle B to AC, the angle 30 degrees will be split in half and we will actually get a 15-75-90 triangle, instead. We won’t have a 30-60-90 triangle anymore, so what do we do now? Let’s try to maintain the 30 degree angle as it is to get the 30-60-90 triangle, and drop an altitude from angle C to AB instead, calling it CE. Now we have a 30-60-90 triangle! Since BCE is a 30-60-90 triangle, its sides are in the ratio 1:sqrt(3):2. Side X corresponds to 2 on the ratio, so CE = x/2.

Area of triangle ABC = (1/2)*BD*AC = (1/2)*CE*AB

(1/2)*BD*2*sqrt(2) = (1/2)*(X/2)*X

BD = X^2/4*Sqrt(2)

Now DC = (1/2)AC = 2*sqrt(2)/2 = sqrt(2)

Let’s use the pythagorean theorem on triangle BDC:

BD^2 + DC^2 = BC^2

(X^2/4*Sqrt(2))^2 + (Sqrt(2))^2 = X^2

X^4/32 + 2 = X^2

X^4 – 32*X^2 + 64 = 0

X^4 – 16X^2 + 8^2 – 16X^2 = 0

(X^2 – 8)^2 – (4X)^2 = 0

(X^2 -8 + 4X) * (X^2 – 8 – 4X) = 0

Normally, this would require us to use the quadratic roots formula, but let’s not get that complicated. We can just plug in the the two shortlisted options and see if either of the factors is 0. If one of the factors becomes 0, the equation will be satisfied and we will have the root of the equation.

Since both options have both terms positive, it means the co-efficient corresponding to B in Ax^2 + Bx + C = 0 must be negative.

x = [-B +- Sqrt(B^2 – 4AC)]/2A

-B will give us a positive term if B is negative, so we will get the answer by plugging into (X^2 – 4X – 8):

Put X = Sqrt(3) + 2 in X^2 – 4X – 8 and you do not get 0.

Put X = 2*(Sqrt(3) + 1) in X^2 – 4X – 8 and you do get 0.

This means that X is 2*(Sqrt(3) + 1), so our answer must be (E).

To recap:

Tip 1: A greater side of a triangle is opposite a greater angle.

Tip 2: We can get the relation between sides and altitudes of a triangle by using the area of the triangle formula.

Tip 3: The quadratic formula can help identify the sign of the irrational roots.

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

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Business school is one of the few power graduate degree programs where age and work experience play a key role in the admissions process as well as quality of the overall student community. Graduate programs in law and medicine often admit students right out of undergraduate university with no expectation of work experience, but with business school, age, maturity, and work experience often play a critical role in the assessment process.

As a younger candidate applying to business school, it is important that you think critically about how age factors into your chances and whether you are old enough – from both an age and maturity perspective – to compete for a spot at the top schools in the world. Let’s explore some of the aspects that should factor into this determination:

Career Clarity:

Is your rationale for applying to business school at this moment sound? Why is this year the ideal year for you? Could next year make more sense? Oftentimes, candidates will have set in their mind that they need to go to business school on a set time-table, as soon as possible – make sure your rationale is focused instead on an authentic reasoning for applying. Younger candidates are put under additional scrutiny to ensure they have really thought through why business school is the ideal next step in their career, so make sure you have a good answer for the Admissions Committee when thinking through this key question.

Work Experience:

Have you cultivated the requisite amount of quality professional work experience to contribute to an MBA classroom? It is not enough to just have the right GPA, GMAT score, and pedigree to apply – your ability to add value to the student community for your classmates is another critical element that the Admissions Committee will evaluate you on. With the increase in team-based assignments in business schools around the world, your ability to contribute to group and classroom educational dynamics is critical to the experience of others. If you have no work experiences to share during classroom discussions, it will be difficult for admissions to see you as a viable candidate.

Class Profile:

Historically, certain schools such as Harvard and Stanford have been unafraid to lean a bit younger in targeting potential MBA students. Understanding the reputation of your target program and investigating how its class profile may factor into admissions decisions can help you better curate your list of potential programs. The question of whether you are qualified or not still remains the most important, but by evaluating trends in class composition at your target program, you can save yourself a lot of precious time in the application process.

Use the criteria above to evaluate whether right now is truly the best time for you to apply to business school, and use this evaluation to stress in your applications why your young age will not hinder you in pursuing an MBA at this time.

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

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

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When you’re taking the SAT, it’s easy to get lost in the moment concentrating on the test. You’re so focused on doing well, answering all the questions, double checking your work, and staying within the time limits that it’s easy to neglect thinking about the ways to actually be successful on the test.

One way I’ve found to make sure I don’t get distracted from my purpose is to consciously take a second to pause and remind myself that I know how this standardized test works. The SAT is standardized, which means it always operates in the same way; I “step back” to use that knowledge to my advantage.

Not really sure what I’m saying? Let me explain. So right now, as I’m writing this article, I am fully aware that there is always only one right answer on each SAT question. I’m aware that the answers to reading passages always have direct evidence from the text. I’m aware that all SAT math questions can be solved using uncomplicated math. But when I actually take a test, sometimes the pressure gets to me and I forget these vital tips. I’ll agonize over two different answers I think might be right, or I’ll find myself using calculus to try to solve a problem. When you’re desperate for points, things like this can happen.

To solve this problem, I need to consciously extricate myself from the pressures of the test and take a deep breath, remembering that the SAT has to follow certain rules every time. This is what I mean by “stepping back.” Once you “step back,” you’ll likely see a flaw in your thinking that was causing you to mess up on the problem in the first place. Maybe you’ll notice an assumption you were making about the passage, and now that you’re clearheaded and can remember that assumptions should not be made on the SAT, you’ll see that only one of the answers is justifiable in the passage.

It might seem scary to do this process, since taking a pause mid-test could cost you precious time. In reality, that is far from the truth – stepping back only takes a few seconds and will allow you to clear your mind, thereby eliminating time wasted agonizing over tough problems.

The SAT is not a test that you will do well on if you aren’t aware of what kind of test it is. The SAT is a standardized test that has to operate by certain rules and principles – it’s easy to forget this when your whole mind seems focused on how to fix a comma splice. Taking a moment to remember what you have to do is a valuable exercise that will help maintain a useful perspective on the test day.

ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

Most MBA applicants find this to be the most difficult question to answer.

As professionals and entrepreneurs, we are trained to put our best foot forward in order to sell our businesses and ourselves. We think and rehearse how to best present our strengths, while hardly spending any time considering our weaknesses. Understandably, addressing this question during one’s MBA application essay or interview usually proves to be quite a challenge.

Asked to identify his weaknesses, a typical MBA applicant will ask him or herself two questions:

1) What should I avoid mentioning?

Everyone worries about giving an answer that will reveal a fatal flaw to the admissions committee and hurt one’s chances at being admitted to an MBA program. Thus, a frequent mistake is to answer this question using a fake weakness – saying something like, “I am too smart,” or, “I work too effectively,” does not really answer the question and will just irritate your audience. Presenting yourself as unrealistically perfect will also diminish the genuine strengths you have, and create doubt in the accomplishments you have discussed throughout the essays or the interview, as it makes you appear incapable of an honest self-assessment.

Another similar no-no is to blame somebody else for your weakness. Do not attribute a weakness solely to your work environment, personal circumstances, or ethnicity – this comes across as a reckless generalization and will not add any value to your case. It will also only shift the conversation into a negative tone and counter the strong, optimistic vibe that you want to be associated with.

2) What exactly are they looking for?

Admissions committees are looking for applicants who will greatly benefit from attending their school’s MBA program, and who can contribute to the experience of other MBA participants. Using this as a guide, the weakness question should be used to demonstrate character traits of self-awareness, ability to learn from failures, and open-mindedness to effectively use feedback and criticism.

An applicant should identify specific skills and knowledge gaps that he or she will need to work on in order to reach her post MBA goals – ideally, specifics of the target MBA program in terms of courses, culture, or community should be matched to these potential growth areas.

Executing this answer properly will put forth an honest reflection that shows genuine interest in a school’s MBA program and convinces the admissions committee that the applicant has really researched the school’s offering. Effectively demonstrating your potential to gain from, and contribute to, an MBA program through your personal story will help convince the admission committee of your fit with their school. Filling in details of how you have addressed your identified weakness or how you are in the process of doing so will also help show how proactive you are, and how you will greatly benefit from this particular MBA program.

A final tip: whenever you are asked about strengths and weaknesses in one question, whether in an essay or an interview, you must allocate time and space as evenly as possible between talking about the two. Most applicants spend 2/3 or more of the space they are given for strengths leaving little room to develop the weakness portion of the answer. This type of answer will look like it was just glossed over, and that the question was not answered adequately – it will also not allow you to make a proper case as to why you will benefit from the program.

A good answer to the “weakness” question strengthens your case to be admitted to your target MBA program even as you identify a real weakness. Skillfully weaving stories of your personal experiences, self-reflection, and vision through discussion of this weakness will make your profile unique and compelling to the admissions committee.

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

Written by Edison Cu, a Veritas Prep Head Consultant for INSEAD.

ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors