This is the first in a series of  posts from our friends at Accepted.com. Stay tuned for inside tips on the law school and B-school admissions process.

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What are the most boring, non-starters for your personal statement? Openings that use wording from the question, or in the case of general questions, are so common that they will have a narcotic effect on any admissions reader wading through mounds of files.

Recently, Accepted editors discussed a client’s response to the question, “How have you experienced culture shock?” The applicant began her response with “I experienced culture shock when…” How many applicants responding to this question start similarly? Too many. However, if the applicant from the first word contrasted the culture she comes from with the one that engendered the shock, she would be immediately painting a picture of the situation, differentiating herself from her competition, and making maximal use of each word in an essay with a tight word count.

Another common opening: “I want to be a lawyer because…” or “I was born in…” or “I come from…” Start with an opening that portrays your vision for the future, reveals your preparation for your chosen path, or depicts an illustrative and impressive experience from your background. Then swing back and tie this opening to your desire for a legal education or the theme of your personal statement.

Your opening needs to immediately grab your reader’s attention, introduce your topic, and make effective use of the space. You all have word or page limits. Your readers have limited attention spans and a pile of other applications staring at them. Don’t bore them from the get-go. Begin with an opening that engages and grabs attention. Start your essays with an anecdote, a description of a scene, a startling statistic, or an appropriate quote.

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Accepted.com’s staff has been checking clients’ work for the essentials of great law school personal statements since 1994. Visit accepted.com/law for professional advising and editing services as well as sample law school personal statements, tips, free ecourses, webinars, and more.

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Rich Zwelling is one of the expert teachers in Knewton’s GMAT course. “Combinatorics” is  a word he throws around casually.

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I was recently discussing a particular GMAT problem with a friend, and as so often happens with standardized-test nerds, the discussion turned into an extended analysis.  We can’t help ourselves, I suppose.

The question went something like this:

Jim and John are workers in a department that has a total of six employees.  Their boss decides that two workers from the department will be picked at random to participate in a company interview.  What is the probability that both Jim and John are chosen?

Now, with many GMAT problems, there are multiple ways to skin a cat.  As it turns out, my friend and I chose completely different strategies that arrived at the same answer.  But interestingly enough, our different strategies got us to hit upon some key distinctions between probability and combinatorics.

1. My friend chose to go strictly with probability:

There is a 1/6 chance that Jim will be selected first.  Then, there are 5 workers left, so the probability that John is chosen next is 1/5.  Therefore, the probability of Jim being chosen first, then John being chosen second is simply 1/6 * 1/5 = 1/30.

However, we also have to consider the possibility that John is chosen first and Jim second.  That still leads to the same number:  1/6 * 1/5 = 1/30.

So, because we are interested in each of these possibilities (and nothing else), we must add the two probabilities to get the final answer:

1/30 + 1/30 = 1/15.

2. I chose to bring combinatorics into the picture:

There are 15 possible combinations of 2 people that you can choose from a group of 6.  You can find this using the combination formula:

n! / [k! * (n-k)!]

In this case, n = 6, since there are six people total, and k = 2, since we’re finding a subgroup of two.  Therefore:

6! / (2! * 4!) = 6 * 5 / 2 = 15 total combinations.

Now, out of those 15 combinations, we are interested in only one — Jim and John.   And recall that this is a combination (where order does not matter), as opposed to a permutation (where order does matter).  Jim and John is the same combination as John and Jim, since the same two people are involved.

(For clarification, it would be a permutation if, say, John and Jim were running a race, and we awarded different prizes for 1st and 2nd.  In that case, Jim finishing first is different from John finishing first.  But in our problem, we’re not concerned with who is picked first; we only care about who’s in the group of two).

Back to the problem:  We’re interested in only one combination (Jim and John) out of a total of 15.  Therefore, the final answer is 1/15.

“But wait,” said my friend, “It’s a combination, so that means order shouldn’t matter.  Jim and John is the same combination as John and Jim.  So how come in my solution, we added two different probabilities for Jim-John and John-Jim?  Order shouldn’t matter, but in my solution, it did.”

What we realized is that order mattered in my friend’s solution because he was considering two different events, not two different combinations.  Jim and John is the same combination as John and Jim, so if we were restricting ourselves to finding information solely about combinations, then order would not matter.

However, we were not only finding information about combinations; we were also interested in probability.  The situation of Jim and John being chosen first and second, respectively,  is a distinct event from that of John and Jim being chosen first and second, respectively.  So even though both events involve the same combination of people, the events themselves are different.

What makes problems like this a little bit tricky is that they can involve both probability and combinatorics, and it might be easy to confuse the two.  But always remember, combinatorics on their own deal solely with finding the number of combinations or permutations in a given set of data, while probability deals with finding the likelihood that an event or events will occur.

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Photo by John-Morgan on Flickr.

The scales are tipped in one direction

A big, old-school test preparation company (Kaplan Inc.) recently released a statement claiming that its online GMAT course had “the most comprehensive guarantee in the industry.” The terms of its guarantee were as follows: Students who do not feel ready to take the GMAT, or who aren’t satisfied with their score improvement may retake the course for free. And students who don’t score higher on the GMAT may prep again for free or get their money back.

Jess Nepom is one of the expert GMAT prep and SAT prep teachers at Knewton. She loves helping students navigate the college admissions process; this is the first post of a series that will lay out the timeline of that process step by step. Stay tuned!

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The college admissions process can be intimidating. For many students (and parents!), the hardest part is keeping track of what they should be doing to get ready and when they should be doing it.

The good news is, there are concrete steps you can take to make sure you’re putting together the best application possible. College apps should be exciting! This college admissions guide will help you break down every part of the process—from junior year to senior year—so you can relax and enjoy the experience.

First step: junior year, when most students take the SAT. Here’s what else you should keep in mind.

10 things to do during your junior year

1. Make contacts. Get to know your college counselors. You’ll work together a lot in the next year or so. The better they know you, the more useful your  meetings will be.
2. Get involved. Now’s the time to dive into extracurriculars. By junior year, you should know the one or two that you are most passionate about – focus on those. It’s better to have a leadership role in one activity than to be a member of 12 different clubs and not do anything in any of them.  Start taking on more important responsibilities in whatever you do.
3. Get good grades. Obviously. All your grades matter, and colleges do look at them. If you were hit or miss in your freshman and sophomore years, now’s the time to buckle down.
4. Take challenging courses. Even if your grades aren’t all As, taking AP or advanced classes shows admissions committees that you push yourself. If you take a foreign language, work toward the highest level you can. You might be able to test out of language courses in college if you do well.
5. Read as much as you can, not just for school.
6. Do your research. What kind of school appeals to you? Big? Small? State? Private? If you live near a college or travel somewhere near one, stop by and take a tour or wander around the campus. If you’re far away from the schools that interest you, check them out via the magic of the Internet.
7. Plan some visits. If you have an older friend/sibling/relative in college, go visit! See the dorms, ask what students do for fun, and see what they do and don’t like about their school.
8. Think about what makes you special. Is it a musical instrument? A sport? An academic subject? Your involvement in community service? Focus on the aspects of your life that make you unique so your future application will stand out.
9. Think about your weaknesses. Assess yourself as a candidate. Any bad grades in the past? Disciplinary problems? No activities? You still have time to make up for past mistakes and plan now to do something about them.
10. Know your financial situation. Will you need to apply to scholarships? Financial aid? Do you not have to worry about it? Talk to your parents early in the process so you know how much aid (if any) you might need down the line.

That’s your general junior year college admissions guide. Next up we’ll take you through a month-by-month approach to make sure you’re on track as you go!

Amy McDowell is the VP, Web Marketing at Knewton and an MBA student at Columbia. She loves thinking of ways to spread the word about Knewton’s GMAT course and LSAT course.

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As a current full-time student in Columbia Business School’s executive MBA program and a full-time online marketing maverick for Knewton.com, I often get asked this question: Are you completely nuts? How can you balance the demands of school and a career without sacrificing one for the other?

I usually make a bevy of random excuses: “Insanity runs in my family,” “Masochism is a hobby of mine,” or my personal fav, “The Columbia executive program provides hot catered meals and free Red Bulls.”  But in all seriousness, going to business school while working for Knewton has actually been one of the best decisions of my life.

At Knewton, I work with some of the most talented, intelligent people I have met in my career.  Their passion for bringing top-notch education to the laptops of students all over the world is incredible, and their drive and dedication keeps me inspired and energized each day.

At school, top business leaders from all around the world are my classmates and friends. The highly distinguished Columbia faculty serves as my mentors and role models. Being surrounded by innovative, creative people in both facets of my life has definitely reshaped my professional (and personal) outlook, and I am thankful and humbled by both experiences. I work at a fast-paced, rapidly growing start-up that helps bring the industry’s best GMAT prep and LSAT prep to students everywhere. I also get to study in a top academic institution like Columbia and hone my skills so I can build value for consumers and corporations alike.

So at the end of the day, when I’m asked why I am pursuing both work and school, the answer is easy:  How could I not?

As for that pesky question of whether one can truly excel in both areas, I can happily report that Knewton.com has seen tremendous success over the past year. Students from all over the world tell us wonderful stories about their score increases and how they got into the schools of their dreams. And maybe not so coincidentally, I’ve also made the Columbia Business School Dean’s list each semester since I’ve joined Knewton – so yes, this girl can have her cake and eat it too!

Rich is one of the stellar teachers in Knewton’s GMAT course, in whch he loves helping students rock the Quantitative section.

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In any GMAT prep course, one of the first things taught about the Data Sufficiency section is that the two statements are true and do not contradict one another.  It’s a point that’s easy to gloss over and completely overlook during the hustle and bustle of your test prep.

But this supposedly self-evident point gets many students into trouble when dealing with YES/NO questions, because they mistakenly try to prove or disprove the statements rather than the prompt.

I’ll explain:  Recall that a YES/NO question is one in which the answer will be “Yes” or “No.”  For example, “Is x even?” or “Are the distances equal?”  This is in contrast to VALUE questions, for which you must come up with one particular value (e.g. “What is x?”, “What is the average of a and b?”).

If a statement produces both a YES and a NO, then it is insufficient.  If the statement (or combination of statements) always produces a YES or always produces a NO, then it is sufficient.  (Remember, a NO is not the same thing as INSUFFICIENT; so if you’re asked “Is x even?” and a statement lets you know that x is always odd, then that is SUFFICIENT, because you can answer NO with certainty.)

Basic example:

Is x odd?

(1)  x is a multiple of 3.

(2)  x is a multiple of 5.

For Statement (1), x could be 3, which would lead to a YES, but x could also be 6, which would lead to a NO.  Insufficient.

For Statement (2), x could be 5, which would lead to a YES, but x could also be 10, which would lead to a NO.  Also insufficient.

Combining the statements, we see that x could be 15, which would lead to a YES, but x could also be 30, which would lead to a NO.   Final answer, E: the statements together are not sufficient to answer the question.

This is a simple example that would not likely appear on the GMAT, but it’s great for illustrating a basic mistake students make: trying to disprove the statements.

It might be tempting to look at Statement (1) and try to find a YES or a NO to the statement itself, rather than the prompt.  So you try to prove/disprove “x is a multiple of 3″, rather than prove/disprove the real question, “Is x odd?”

This would result in you picking, let’s say, x = 3, because it answers YES to “x is a multiple of 3″.  Then you might pick x = 5, because it answers NO to “x is a multiple of 3.”

But of course, both 3 and 5 answer YES to the question in the prompt, and you may erroneously conclude that Statement (1) is sufficient, when in actuality, it is not.

Obviously, this approach can get you into trouble, because you may get an incorrect answer.  But there’s an even more basic error behind this mistake:  You’re wasting valuable time trying to prove/disprove something that is already known to be true!

And thus I return to that basic maxim of Data Sufficiency questions:

The statements are always true and never contradict one another.  Again, it seems like a trivial point, but as the aforementioned example demonstrates, you’d be surprised how forgetting the basics can lead to unnecessary wasted time!

So, in conclusion, recognize that the statements are true, and use their information to address what really matters:  the question in the prompt.

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It’s great to learn about new companies that cut against the grain, so we were excited when Joanna (a stellar Knewton TA) told us about Encountour. Josh Egan is the co-founder; last week we tracked him down to answer a few questions.

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What’s the goal of Encountour? What kind of work do you do?

We provide Alternative Spring Break opportunities for college students. Our mission is to provide travel experiences that broaden global perspectives and directly aid the efforts of local non-profits in Latin America; the spring break program is a great opportunity for college students to dip their feet into the field of social activism. The trips are affordable, the sign-up process is easy, and the work is pre-screened for safety and to ensure that there’s a strong community impact. We do everything from house construction and community development to reforestation projects and agricultural fieldwork.

We’re always curious about start-ups. What motivated you to start the organization, and how did you go about it?

We’re trying to prove that socially conscious companies can do just as much good as non-profit organizations while still turning a profit (we’re still working on the second part!). My co-founder, Andrew Steinberg, and I realized the value of international volunteer work the first time we visited Guatemala as part of our own Alternative Spring Break trip. Working with children in a local education center was an amazing experience, and we wanted to ensure that college students across North America had access to similar opportunities.

Today, Encountour is a team comprised of eight passionate, fun-loving individuals, who realize that their daily responsibilities are more than just a means to an end. Whether we’re developing new relations with a local community that needs our support, promoting the benefits of international travel to a student that’s never left home, or watching one of our volunteer groups present a newly constructed house to grateful family, we are constantly shaping lives. This overall sense of meaning motivates us in a way that I think is different from most companies out there.

What kind of volunteers are you looking for, and how should they apply?

We’re looking for students who want to experience more when they travel. Instead of visiting a country and acting as a bystander, we encourage you to take part in an active personal and cultural exchange.

This year we’re sending volunteer groups to Costa Rica and Guatemala. To learn more, visit us at encountour.com. You can also send us an email (contact@encountour.com) or give us a ring (800-899-3789). We’d love to hear from you.

A: The Snuggies come out.

Sara, cold coding.