Academically, Stanford University in no way takes an ivory tower approach to education; the list of contributions to the world by those associated with this research university is long and impressive. Stanford claims 22 Nobel laureates, 5 Pulitzer Prize winners, 27 MacArthur Fellows, and over 700 other distinguished academic awards in its community of scholars. Seventeen astronauts and 30 billionaires are also affiliated with Stanford.

Faculty, students and alumni have long been a creative force in shaping the future. Some of the most notable cutting edge projects and high profile companies in the world have come out of Stanford. Silicon Valley has its roots in Stanford where one of the precursors to the Internet was developed. Yahoo!, Google, Nike, Coursera, and other companies have been founded by Stanford faculty and/or alumni.

Students applying for an elite Stanford education will experience the lowest acceptance rates in the country. Stanford offers 40 academic programs in three undergraduate schools – Humanities and Sciences, Earth Sciences, and Engineering, as well as robust graduate offerings. More than 18 independent laboratories, institutes, and centers are managed by Stanford. Student opportunities for significant research are unsurpassed, with over 5,000 externally sponsored research opportunities.

The school operates on a quarter system from September to June, where undergraduate students have an option of earning a bachelor’s degree, or a coterminal degree. Coterm degrees are where graduate school becomes an extension of a student’s undergraduate education leading to a master’s degree.

Student housing is guaranteed for all four years of undergraduate studies at Stanford, and one year of graduate study. Ninety-seven percent of undergrads live in campus housing. There is a thriving Greek life on campus with 16 fraternities and 14 sororities; ten of those offer student housing. According to Greek Rank, the most popular sororities are Kappa Alpha Theta, Delta Delta Delta, and Chi Omega. Favorite fraternities are Phi Kappa Psi, Kappa Alpha Order, and Alpha Epsilon Pi.

Stanford offers 630 recognized student organizations, 44 religious organizations, six cultural centers, and the Haas Center for Public Service, which supports student community service. Aggregated student satisfaction data at Students Review gives Stanford a 90% positive rating. The Stanford campus is actually its own town and filled with every activity imaginable. Some highlights are Café Nights; parties, parties, parties; Flicks campus movie theater; lounging at Arrillaga Alumni Center Fountain; hitting balls at the Stanford driving range; hiking the Dish at sunset; or stargazing at the courtyard near the clock tower. Don’t forget you’re 30 minutes from San Francisco for the ultimate urban scene, or three hours from Yosemite National Park for prime outdoor adventure.

Excellence is a theme at Stanford. The Stanford Cardinals have 36 NCAA Division I men’s and women’s varsity teams competing in the PAC-12 Conference. Cardinal teams have amassed 105 NCAA national titles, and student athletes have captured 0ver 45 individual national championships. Stanford athletes competing in the Olympics have won over 240 Olympic medals since 1912, of which more than 125 of them were gold. Approximately 300 athletic scholarships are awarded each year. For the less competitive who still love sports, Stanford offers 19 club sports and 37 intramural sports.

Stanford’s main football rival is Berkeley. Every year the “Big Game” is the culmination of a week’s worth of preparations. The 2013 Rose Bowl Champions get fired up for the game against the “hippies across the bay.” For all Cardinal games you’ll be expected to know the proper Stanford cheers down to the jangling of keys and pointing in the right sequence and direction depending on what’s happening on the field. When basketball season rolls around, you’ll have to learn a whole new set of cheer skills.

Stanford University is rich with tradition – some serious, some more frivolous. For a complete breakdown, check out the Stanford University Unofficial Guide online. A few favorites include the freshman tradition of Assassins, class and Greek formals, Midnight Breakfast and Primal Scream during Dead Week, fountain hopping the 25 Stanford fountains on campus, an annual ski trip, and Stanford’s version of the Amazing Race.

If you’re brilliant and competitive, a compulsively curious overachiever with a bona fide penchant for shenanigans, Stanford may be just the school for you.

Still need to take the SAT? We run a free online SAT prep seminar every few weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter! Also, take a look at our profiles for The University of Chicago, Pomona College, and Amherst College, and more to see if those schools are a good fit for you.

*By Colleen Hill*

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We know that basic concepts are twisted to make advanced questions. Our aim is to break down the question into two parts – ‘the basic concept’ and ‘the complexity’. You can either deal with the complexity first and then glide through the basic concept or you can glide through the basic concept first and then face the complexity. The method you use will depend on the question. If the question seems too complex at the outset, it means you will have to deal with the complexity first. If the question seems familiar but has some extra not-so-familiar elements, it means you should get the familiar out of the way first. Let’s take a question today to see how to do that.

Question: During a sale of 20% on everything in a store, a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 14 candies. The store still makes a profit of 12% on this sale. What is the mark up percentage on each candy?

(A) 100%

(B) 80%

(C) 75%

(D) 66+2/3%

(E) 55%

Solution:

This question can get very messy if you let it! We have seen people working on this question with multiple variables: C for cost price, S for sale price, M for marked price etc. That can get very confusing because there are two types of mark up – the actual mark up (the store marks up the price of every candy by this percentage and lists it on the candy) and the effective mark up (because the kid takes 6 extra candies, this is the effective mark up). So let’s not go the algebra way.

Instead, let’s focus on what we can do without much effort. As a first step, let’s do what we know already (and hope that the rest will work out!).

We already know the relation between mark-up, discount and profit. The problem is that this question has another aspect – the kid takes 20 candies but pays the price of only 14 candies (which is the price obtained by reducing the marked price by 20% of discount). But let’s worry about it later.

Let’s first deal with the mark-up, discount and profit aspect of the question.

We know that (1 + m/100)(1 – d/100) = (1 + p/100) (already discussed in detail in this post)

Since p is the effective profit that the store got, m must be the effective mark up here.

(1 + m/100)(1 – 20/100) = (1 + 12/100)

(1 + m/100) = (5/4)*(28/25)

(1 + m/100) = 7/5

m = 40

So effective mark up was 40% – i.e. 40% was the mark up in a situation where 14 articles were sold and charged for. This tells us this – effective mark up turned out to be 40% though his actual mark up must have been higher since he gave away 20 articles for the cost of 14.

Now what we already know is done. We get to the really tricky part – the thing that makes this question different – how do we find the actual mark up?

Let’s say the cost price of each of the 20 candies was $1. Then total cost price for the 20 candies was $20. This is the cost of the candies to the store. The effective markup was 40% i.e. the articles were effectively marked at 20 + (40/100)*20 = $28. The store gave a discount of 20% on this amount and made a profit of 12%. But this amount of $28 actually represents the mark up on 14 candies only. The cost price of 14 candies is $14 to the store. So the actual mark up percentage on the 14 candies is (28 – 14)/14 * 100 = 100%

Answer (A)

Obviously, there are many other ways of solving this question. See if you can figure out another one on your own!

*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 in Detroit, Michigan, and regularly participates in content development projects such as this blog!*

Derek Jeter’s final game at Yankee Stadium?

Sure…but also some of the hardest Data Sufficiency problems you’ll see on test day.

For those who didn’t see, Derek Jeter’s final game in a home Yankee uniform finished in fairy tale fashion last night. The Captain delighted the crowd early with a double, then reached base again on an error, and was set to ride off into the sunset (well, if it hadn’t rained and been dark out) a hero with one final Yankee win. The crowd chanting his name in the top of the 9th inning, he nearly teared up as he looked at his storybook finish, but then…uncharacteristically, Yankee closer David Robertson allowed two home runs to tie the game, perhaps dooming the win but in the end giving the clutch shortshop an even greater chance at glory. And Jeter delivered, batting in the winning run in his final at bat in pinstripes, on the last pitch he’d ever see at Yankee Stadium.

The GMAT relevance? It followed a blueprint for one of the hardest Data Sufficiency structures that the GMAT writes. That blueprint goes:

Step One: Somewhat difficult statement that takes some work but “satisfies your intellect” as the 650-and-up crowd finally realizes why it’s sufficient. (i.e. Jeter’s double and reached-base-on-error to set up a Yankee win)

Step Two: A much easier statement that seems a mere formality to deal with, but that for the truly elite (i.e. Jeter) provides an opportunity to really shine (i.e. the blown save in the top of the 9th)

Step Three: The chance for the hero to deliver.

Consider this problem:

What is the value of integer z?

(1) z is the remainder when positive integer x is divided by positive integer (x – 1)

(2) x is not a prime number

Now look at statement 1. There’s a lot to unpack – the concept of remainder, the definitions of “positive integer x and positive integer (x – 1)”, the fact that x then can’t be 1 (or x-1 would be 0 and therefore prohibited), the fact that the two values being divided are consecutive integers. So it’s not surprising that, on their way to the trap answer selected by nearly 60% of respondents in the Veritas Prep Question Bank, many feel the glory when they unravel the variables and processes and think:

“Ah, ok. 5/4 would work and that’s 1 remainder 1. 10/9 would work and that’s 1 remainder 1. 100 divided by 99 would work and that’s 1 remainder 1. I get it…remainder is always 1.”

After all that work, statement 2 is as much a formality as a 2 run lead with no baserunners in the 9th inning. Piece of cake. So people start to hear that crowd chanting their name a-la “De-rek-Jeeeet-er”, they pat themselves on the back for the accomplishment, and they pick A. Without ever seeing the opportunity that statement 2 really should provide them:

“Wait…that’s not the script I want – it shouldn’t be that easy.”

Those who know the GMAT well – those Jeterian scholars who have honed their craft through practice and determination to go with the natural talent – look at statement 2 and think “why does this matter? Why would the author write such a mundanely-irrelevant statement? The question is about z and the statement is about x? Come on…”

And in doing so, they’ll ask “Why would a prime number matter? And what kind of prime numbers might change things?” And when you’re talking prime numbers, just like when you’re talking Yankee lore, you have to bring up Number 2. 2 is the only even prime number and it’s the lowest prime number. If you see the definition “prime” and you don’t consider 2, you’re probably making a mistake. So statement 2 here should be your clue to test x = 2 and realize:

2/1 = 2 with no remainder. Based on statement 1 alone the answer is almost always “remainder 1″ but this one exception allows for a remainder of 0, proving that statement 1 is not sufficient. You need statement 2 to rule it out, making the answer C (for captain?).

The real takeaway here?

Even if you think you’ve “won” after statement 1, if statement 2 looks so much like a mere formality that it’s almost anti-climactic there’s a good chance it’s there as a clue. Ask yourself why statement 2 might matter – sometimes it will and sometimes it won’t, but it’s always worth checking in these cases – and you may find that the real “glory” you’re after requires you to take a step back from that “win” you thought you had earlier on.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

*By Brian Galvin*

Students routinely report that they end up in this exact situation multiple times on test day, particularly on Critical Reasoning questions in the verbal section. Sometimes, you can predict the correct answer before perusing the answer choices, and avoid this dilemma. However, inference questions frequently ask for the best implication of the sentence, and many correct possibilities could exist. This leads to considering two answer choices as accurate, when in fact only one of them is correct.

As a simple example, a question could indicate that Ron is taller than Tom, and then ask for inferences based on this conclusion. Valid inferences that can be drawn from this situation include “Tom is shorter than Ron”, “Ron and Tom are not the same height”, and even (my personal favorite) “Ron is taller than Tom”. Indeed the exact same idea could be inferred from the conclusion because it must logically be true. More generally, multiple conclusions can all be inferred from the same statement, from the mundane to the insightful.

The one element that must always be considered is that any statement that can be inferred must be true in all situations. Oftentimes when you’re stuck selecting between two choices, one must actually be true whereas the other simply seems to be true. Our brains are trained to complete incomplete data, such as filling in missing letters in words and assuming relevant context (this is a perfet exmple). The GMAT test takers know this about human nature, so we must be careful not to fall into their clever traps and consider fringe corner situations when selecting between two tempting choices.

Let’s look at an example and see how the test makers exploit subtle differences in the answer choices:

*SwiftCo recently remodeled its offices to comply with the Americans with Disabilities Act (ADA), which requires that certain businesses make their properties accessible to those with disabilities. Contractors built ramps where stairs had been, increased the number of handicapped parking spaces in the parking lot, lowered door knobs and cabinet handles, and installed adaptive computer equipment.*

*Which of the following is the most likely inference based on the statements above?*

*(A) **SwiftCo is now in compliance with ADA requirements.*

*(B) **SwiftCo has at least one employee or customer who uses a wheelchair.*

*(C) **Prior to the renovation, some doors and cabinets may have been out of reach for some employees.*

*(D) **The costs of renovation were less than what SwiftCo would have been liable for had it been sued for ADA violations.*

*(E) **Businesses without adaptive computer equipment are in violation of the ADA.*

The situation (not the abs guy from Jersey Shore) above describes a recent remodel to the SwiftCo offices in order for them to comply with ADA regulations. The changes are described in some detail, from ramps to parking spots to door knobs. The question then asks us about which statement below is the most likely inference, which really means which of these must be true whereas the other four don’t have to be. Let’s do an initial pass to eliminate obvious filler.

Answer choice A “SwiftCo is now in compliance with ADA requirements“ seems perfect. The changes were made due to ADA standards, so A seems like a great choice. Let’s keep going.

Answer choice B “SwiftCo has at least one employee or customer who uses a wheelchair” makes some semblance of sense, because otherwise why install the ramps? However this clearly doesn’t have to be true, SwiftCo can simply be acting proactively in order to comply with standards. Answer choice B does not have to be true, and can thus be rapidly eliminated.

Answer choice C “Prior to the renovation, some doors and cabinets may have been out of reach for some employees” seems like another great choice. After all, why remodel if everything was already handy. This could easily be correct as well. Let’s keep going.

Answer choice D “The costs of renovation were less than what SwiftCo would have been liable for had it been used for ADA violations” makes a completely unsupported claim. (As Harvey Specter would say: “Objection. Conjecture”.) We can quickly eliminate this unconfirmed option as it does not have to be true.

Answer choice E “Businesses without adaptive computer equipment are in violation of the ADA” makes a similar claim to answer choice D, but at least has a little bit more logic behind it. If the company is installing adaptive equipment, it might be in order to comply with ADA regulations; however it might also be another proactive practice put in place by management of their own volition. Answer choice E doesn’t have to be true, and thus can be eliminated.

And thus we’re left with two answer choices that both seem reasonable. And yet there can be only one (so says Connor MacLeod). How do we select between answers A and C? Quite simply, we must look at every possible scenario and see if each option must still hold. This can be an arduous process, but sometimes the evaluation of discarded answer choices helps to guide our approach.

In evaluating answer choice E, the issue of whether or not these changes were exactly aligned with ADA requirements came up. It’s entirely possible that adaptive computer equipment is not required by ADA guidelines; however it’s also possible that it is required. We simply don’t have enough information to make that decision with the information given. That same logic, taken in a broader context, hints that the changes made may or may not align SwiftCo with ADA regulations. Therefore, although answer choice A could be true, it does not necessarily have to be. Perhaps ADA regulations call for other changes that weren’t effectuated for whatever reason (budget, space, zombies).

Comparing with answer choice C, some doors and cabinets may have been out of reach for some employees. The phrase does not even give 100% certainty that the handles were out of reach, it merely states that it was a possibility. If the handles were lowered, it’s likely because some people couldn’t reach them, but it could also have been a practical improvement. No matter the situation, answer choice C must therefore be true.

Often when pitting two choices against each other, students report that they couldn’t find any differences and essentially flipped a coin. (Always pick Heads!) There will always be a difference between two answer choices, and the trick is to determine in which situations the two options actually differ. One will always work, whereas the other one will have one or two corner cases in which it doesn’t hold. If you master the art of correctly separating the last two options, your coin flip becomes a much more attractive proposition. Heads I win. Tails the GMAT loses.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

*Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam. After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.*

**Part Two – Take the Hard Way Out**

As I write this post, the “Ice Bucket Challenge” is dominating social media, and it seems we never tire of watching our friends and celebrities experience absolute shock when the cold water hits them. They’re clearly well outside of their comfort zones. But in our day-to-day lives, isn’t it often tempting to do what’s familiar, instead of challenging ourselves? We eat at the same restaurants, vacation in the same places, buy the same brand or color of clothing. Consistency makes the decision easier – “It worked last year/weekend/time, so let’s just do it again” – but it can also cause us to miss out on some really meaningful opportunities.

Business school works the same way. When you started your school research, you probably instinctively looked at schools that reflected your strengths. If you were a banker or accountant, maybe you focused on Wharton, Columbia, or Booth. If you came from consumer products, Kellogg might have been the first school to catch your eye. If you were an engineer, MIT and Stanford probably rose to the top of your list. Once you’re in school, it’s tempting to use the same approach for class selection. If you’re a “quant,” you’ll take lots of finance and accounting. If you’re a “poet,” you may gravitate towards management.

But is sticking with what’s safe and known really the best way to make the most of your once-in-a-lifetime opportunity at business school?

It’s not. Because business school isn’t just about making you better at the things you’re already good at – you don’t need to pay close to $200K to do that. It’s just as much- if not more – about filling skill gaps and, in the process, uncovering hidden talents and interests. You advertising gurus might discover an aptitude for statistics, or you might find you’re a CPA with a knack for branding. This approach isn’t risk-free: although your level of knowledge will increase, your grades might suffer. However, schools like Wharton and Columbia encourage academic risk-taking through grade non-disclosure policies.

A personal anecdote illustrates my point: when I was at Wharton, operations absolutely terrified me. And I do mean TERRIFIED. And the school required three courses in it, so I couldn’t hide under the desk, as much as I might have wanted to. I realized from Day One that I had two choices: give up and barely pass or jump in and conquer it. I chose the latter. I volunteered to do the homework assignments, sought out professors and TAs during office hours, did all the reading and then some, and pretty soon my teammates were coming to me for help.

I learned several important lessons – first, I loved operations! As a former journalist, I would never have known this if I hadn’t challenged myself. Second, I was good at it. Who knew? Although I’d never been exposed to the underlying theories, I had a natural affinity for efficiency and process improvement, so the content intuitively made sense. And finally, I appreciated the opportunity to help my classmates. Helping an engineer with Monte Carlo simulation remains one of my proudest b-school moments.

Whether you’re researching, applying to, or already enrolled in school, you have a similar decision to make. If you’re still investigating schools, don’t automatically pick the “safe” one – really think about which one will best fill your skill gaps and will test you to extend your limits. You might even seek out a school with a grade non-disclosure policy. Once school starts, choose courses that take you well outside of your comfort zone. Volunteer to do the work that’s hard for you. If you let the CPA on your team do all the accounting homework or give the finance assignments to the banker, you’re wasting a learning experience. Don’t do that. Step up, jump in, accept the challenge. You just might find a new talent or passion, no ice required.

Want to craft a strong application? Call us at 1-800-925-7737 and speak with an MBA admissions expert today. Click here to take our Free MBA Admissions Profile Evaluation! As always, be sure to find us on Facebook and Google+, and follow us on Twitter!

*Rachel is a Veritas Prep Head Consultant for The Wharton School at University of Pennsylvania, and Johnson Graduate School of Management at Cornell University. Her specialties include consulting, older and part-time applicants, and international candidates.*

*Taylor is making a bracelet. He Starts with 4 blue knots, 6 red knots, and 2 yellow knots, in that order, and repeats the pattern until there is no more string. If the last Knot is yellow which of the following could be the total number of knots on the bracelet.*

*A) 89*

*B) 90*

*C) 95*

*D) 97*

*E) 102*

At first glance, this may seem to be a listing problem. The question gives a repeating pattern that can be written out and it would be possible to keep listing the next knot in the pattern until one of the numbers listed in the answer choices was reached. This would be a long and laborious process and the SAT, a timed test, tends to favor methods which conserve time.

So what is this problem really asking? The problem gives a pattern, so the problem is probably asking us to use the pattern to help us derive the answer more quickly. With many pattern problems, it is useful to think about the question as a *division and remainder* problem. Imagine you have a four unit repeating pattern and you want to figure out which number in the repetition is represented on the 7^{th} unit of the total pattern. If we divide the measure of one repetition, in this case four, by the total units we are examining, we get 1 with a remainder of 3. Think of this as if one full pattern fits into the whole number but only three of the remaining units of the pattern can also fit in the total. This implies that we stop on the third unit of the repetition. We can check this by writing out seven units: 1-2-3-4-1-2-**3**. This is the same technique that can be used to solve the above problem!

In total in the problem above, there are 4 blue + 6 red + 2 yellow or 12 units in the repetition. The yellow units are the 11^{th} and 12^{th} units of the repetition, which means that if we divide the total units of the bracelet by 12, we should get a remainder of 11 (for the 11^{th} unit) or 0 (if it is on the 12^{th} unit it will be a full repetition and will give no remainder). So all that is left to do now is to divide the answer choices by twelve and check the remainders:

A) 89 / 12 = 7 R5 X

B) 90 / 12 = 7 R6 X

C) 95 / 12 = 7 R11 ←

D) 97 / 12 = 8 R1 X

E) 102 / 12 = 8 R6 X

As this problem shows, the actual thing being tested is the students ability to find the right method for solving the problem. There are a number of problems like this on the SAT, but if a student is prepared to look for what is really being asked, he or she will have no problem finding the true question.

Plan on taking the SAT soon? We run a free online SAT prep seminar every few weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

*David Greenslade** is a Veritas Prep SAT instructor based in New York. His passion for education began while tutoring students in underrepresented areas during his time at the University of North Carolina. After receiving a degree in Biology, he studied language in China and then moved to New York where he teaches SAT prep and participates in improv comedy. Read more of his articles here, including How I Scored in the 99th Percentile and How to Effectively Study for the SAT.*

*When should I submit my finished application?*

There is probably no more heart-pounding moment in the application process than clicking that little “submit now” button on your computer. On the one hand, it’s thrilling to be finished, but on the other hand, you’re asking yourself if it’s good enough. Hopefully you have had the help of a qualified professional to guide you along the way and to look over everything, which can certainly make the submission a bit less stressful, but if you do find yourself in the coveted position of being done well before the actual deadline, do you submit now or wait?

For those wondering if there is some sort of strategic advantage to getting it in early, you should know that for schools with a hard deadline (as opposed to a rolling deadline), this doesn’t exist. Schools do not begin their process of vetting out applications until after they are all in the door. This of course makes for a very busy week following the admission deadline, especially since most people wait until the last minute anyway (thanks to human nature), but for those who are up at 11:59 desperately hoping their computer doesn’t crash so they can avoid missing the cutoff, rest assured, you will not be penalized.

There is, however some advantages to submitting early for schools with a **rolling deadline**. These admissions committees actually fill seats as applications come it, so the earlier you are in the door, the more seats are available and the more likely it will be to get one of them since you are not being compared to the entire application pool. In short, if they like you, you get an offer. Keep this in mind as you are pulling your application together.

One reason you might want to put off submitting to **hard-deadline** schools (non-rolling admissions) is because you might just think of that one extra bit of information you could add to make your application better. I always recommend putting finished applications “on the shelf” at least while you work on your other schools, just in case those schools draw out something you might have regretted not putting into another application. Just be sure you don’t literally wait until the last minute, as there have been nightmare scenarios of server crashes and overloading, which is stress you simply do not need. A good rule of thumb is to submit when you feel the application is at its best, and hopefully at least a day or two before the actual deadline!

Good luck!

Learn about top MBA programs by downloading our Essential Guides! Call us at 1-800-925-7737 and speak with an MBA admissions expert today, or click here to take our Free MBA Admissions Profile Evaluation! As always, be sure to find us on Facebook and Google+, and follow us on Twitter.

*Bryant Michaels has over 25 years of professional post undergraduate experience in the entertainment industry as well as on Wall Street with Goldman Sachs. He served on the admissions committee at the Fuqua School of Business where he received his MBA and now works part time in retirement for a top tier business school. He has been consulting with Veritas Prep clients for the past six admissions seasons. See more of his articles here.*

Incoming freshmen can choose from three undergraduate schools, Columbia College – a liberal arts school offering B.A. degrees, the Fu Foundation School of Engineering and Applied Sciences offering B.S. degrees, or the School of General Studies for non-traditional students who can earn either B.A. or B.S. degrees. All schools operate on a two-semester academic calendar. Columbia offers 67 majors in 21 areas of study. The top majors by enrollment are social sciences, engineering, health professions, history, and visual and performing arts. Students can expect nearly 80% of their classes to have fewer than 20 students, and a student-faculty ratio of approximately 6:1.

Students can participate in research alongside some of the top researchers in their fields. Nine current faculty members are Nobel laureates. Departmental research sites include Arts and Sciences, Earth Institute, Engineering, Medical Center, Social Work, Business, and International and Public Affairs facilities. A student graduating from Columbia University will be in the company of many other notable people; three U.S. Presidents, 26 Heads of State, 43 Nobel Prize winners, nine Supreme Court Justices, 123 Pulitzer Prize winners, and 39 Academy Award winners, among many more distinguished alumni.

At Columbia, 94% of students live in campus housing. Through the Faculty-in-Residence program, faculty members and their families live in the residence halls of East Campus, West Campus, and First Year Area. Incoming freshmen make this choice to establish long-term mentoring relationships. Freshmen may also opt to live in more traditional residences of the Living Learning Center, Furnald, John Jay, or Carman. Sophomores, juniors, and seniors may choose special interest residential communities where students live and learn together around their commonalities such as sustainability, jazz, writing, LGBT, and more.

There are also over 500 student organizations where students can find their place at Columbia. Students are encouraged to become fully involved in campus life and support each other’s interests. Choices range from Alternative Break, where students form service groups and carry out projects over break to the Davis Project for Peace summer program. Live at Lerner presents entertainment events as well as academic and cultural events for students throughout the year. Urban New York provides students with an opportunity to attend NYC events with free tickets; past trips and events have included Broadway musicals, New York Knicks and New York Yankees games, a brunch cruise, a night at the Apollo Theater, a performance at the Metropolitan Opera, and many more.

The NCAA Division I Columbia University Lions compete in the Ivy League Conference on 14 men’s and 15 women’s sports teams. Columbia has seen some success in various sports throughout their history. Columbia athletes were the first to ever win the English Henley Royal Regatta in crew. Columbia also had a female runner set an Olympic world record in track, made the NCAA finals in men’s soccer, and produced Hall of Famers in baseball and football. Their primary rival has long been Princeton University, although a new tradition began in 2002 with Fordham University. Columbia and Fordham play an annual football game for the right to hold the Liberty Cup until the next year’s game.

Columbia University offers students 38 club sports from ballroom dance to Moy Yee Kung Fu. Students can participate in six intramural league sports: flag football, soccer, volleyball, basketball, team handball, or dodgeball. Squash is the only individual intramural sport. If you don’t want to make a long-term commitment, there are one-day tournaments in various intramural sports each semester. For those looking to stay fit, but aren’t interested in competitive sports, there are group fitness classes at Dodge Fitness Center.

Many Columbia University traditions have evolved over its 260-year existence. The first tradition new students are likely to engage in is First Year March, where they will be ushered out the back of Lerner Hall together to re-enter through the main campus gates and officially become students of Columbia University. Also specific to freshmen, the first to find the owl hidden in the Alma Mater statue is thought to become valedictorian. Varsity Show is another long-standing tradition, where students write a musical for Columbia students. Rodgers and Hammerstein participating as student writer/directors at one time. Other traditions include Take Back the Night, Tree-Lighting and Yule Log Ceremonies, Primal Scream, Orgo Night, and more.

If you are looking for a challenging academic experience in one of the most exciting cities in the world, Columbia University may be just what you’re looking for in a school.

Still need to take the SAT? We run a free online SAT prep seminar every few weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter! Also, take a look at our profiles for The University of Chicago, Pomona College, and Amherst College, and more to see if those schools are a good fit for you.

*By Colleen Hill*

Let’s discuss one such trick today – a trick in which you need to realize that the situation calls for a complete U-turn of the usual.

Let’s take an example:

**Question**: Two cars run in opposite directions on a circular track. Car A travels at a rate of 6π miles per hour and Car B runs at a rate of 8π miles per hour. If the track has a radius of 6 miles and the cars both start from Point S at the same time, how long, in hours, after the cars depart will they again meet at Point S?

(A) 6/7 hrs

(B) 12/7 hrs

(C) 4 hrs

(D) 6 hrs

(E) 12 hrs

**Solution**: What would we usually do in such a question? Two cars start from the same point and run in opposite directions – their speeds are given. This would remind us of relative speed. When two objects move in opposite directions, their relative speed is the sum of their speeds. So we might be tempted to do something like this:

Perimeter of the circle = 2πr = 2π*6 = 12π miles

Time taken to meet = Distance/Relative Speed = 12π/(6π + 8π) = 6/7 hrs

But take a step back and think – what does 6/7 hrs give us? It gives us the time taken by the two of them to complete one circle together. In this much time, they will meet somewhere on the circle but not at the starting point. So this is definitely not our answer.

The actual time taken to meet at point S will be given by 12π/(8π – 6π) = 6 hrs

This is what we mean by unexpected! The relative speed should be the sum of their speeds. Why did we divide the distance by the difference of their speeds? Here is why:

For the two objects to meet again at the starting point, obviously they both must be at the starting point. So the faster object must complete at least one full round more than the slower object. In every hour, car B – the one that runs at a speed of 8π mph covers 2π miles more compared with the distance covered by car A in that time (which runs at a speed of 6π mph). We want car B to complete one full circle more than car A. In how much time will car B cover 12π miles (a full circle) more than car A? In 12π/2π hrs = 6 hrs.

Now we will keep the question the same but will change the figures a bit:

**Modified Question**: Two cars run in opposite directions on a circular track. Car A travels at a rate of 3π miles per hour and Car B runs at a rate of 5π miles per hour. If the track has a radius of 7.5 miles and the cars both start from Point S at the same time, how long, in hours, after the cars depart will they again meet at Point S?

So following the same logic as above,

Perimeter of the circle = 2πr = 2π*7.5 = 15π miles

The time taken to meet at point S will be given by 15π/(5π – 3π) = 7.5 hrs

But note that the two cars will not even be at the starting point, S, in 7.5 hrs. So this answer is wrong. Why? It has something to do with the word “at least” used in the explanation above i.e. “So the faster object must complete at least one full round more than the slower object. “

Try to put it all together.

Meanwhile, let’s give you **another method**. This will not fail you no matter what the figures.

**Using the original question**:

Time taken by car A to complete one full circle = 12π/6π = 2 hrs

Time taken by car B to complete one full circle 12π/8π = 1.5 hrs

So every 2 hrs car A is at S and every 1.5 hrs, car B is at S. When will they both be together at S?

Car A at S -> 2 hrs, 4 hrs, 6 hrs, 8 hrs …

Car B at S -> 1.5 hrs, 3 hrs, 4.5 hrs, 6 hrs …

In 6 hrs – the first common time, both cars will be at the point S together. So answer is 6 hours.

**Using the same method on the Modified Question**,

Time taken by car A to complete one full circle = 15π/3π = 5 hrs

Time taken by car B to complete one full circle = 15π/5π = 3 hrs

So every 5 hrs, car A is at S and every 3 hrs, car B is at S. When will they both be together at S?

Car A at S -> 5 hrs, 10 hrs, 15 hrs, 20 hrs

Car B at S -> 3 hrs, 6 hrs, 9 hrs, 12 hrs, 15 hrs

In 15 hrs – the first common time (LCM of 3 and 5), both cars will be at the point S together.

This all makes sense now.

*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!*

Through that lens, let’s discuss one of the most helpful “tricks” to avoid some of the most time-consuming types of problems on the GMAT, and we’ll lead with a problem:

*Whenever his favorite baseball team’s “closer” allows a hit, Sean becomes irate (just close out the game, Joe Nathan!). If the closer needs to get three outs to win the game, and each batter he will face has a .250 batting average (a 1/4 chance of getting a hit), what is the probability that he will give up at least one hit (assuming that there are no walks/errors/hit-batsmen)?
*

And for those not consumed with baseball, this question essentially asks “if outcome A has a 25% chance of occurring in any one event, what is the probability that outcome A will happen **at least once** during three consecutive events?”

Baseball makes for an excellent demonstration here, because if we take out the other “free base” situations, really only two things happen – a Hit or an Out. And since we need 3 Outs, we could have all kinds of sequences in which there is **at least one** hit:

Hit, Out, Out, Out

Out, Hit, Out, Out

Out, Out, Hit, Out

or episodes with multiple hits:

Out, Hit, Hit, Out, Out

Hit, Out, Hit, Out, Hit, Out

or even

Hit, Hit, Hit, Hit, Hit, Hit, Hit, Hit…(game called by mercy rule, Sean punches through his TV)

The GMAT-relevant point is this: when a problem asks you for the probability of “**at least one**” of a certain event occurring, there are usually several ways that **at least one** could occur. But look at it this way: the ONLY way that you don’t get “**at least one**” H is if all three Os come first. The opposite of “**at least one**” is “none.” And there’s only one way to get “none” – it’s “Not Event A” then “Not Event A” then “Not Event A”… as many times as it takes to finish out the number of events. In other words, in this baseball analogy, if there’s a 25% chance of a hit then there’s a 75% chance of “not a hit” or “Out”, allowing us to set up the ONLY sequence in which there isn’t at least one hit:

Out, Out, Out

Which has a probability of:

3/4 * 3/4 * 3/4

Do the math, and you’ll find that there’s a 27/64 probability of “not **at least one** hit” and you can then know that the other 37/64 outcomes are “**at least one** hit.”

To the baseball fan, that means “take it easy on your closer – .250 is a pretty lackluster batting average and that even takes out the chance of walks and errors, and even with *that* there’s a better-than-likely chance there will be baserunners in the 9th!”

To the GMAT student, this example means that when you see a probability question that asks for the probability of “at least one” you should almost always try to calculate it by taking the probability of “none” (which is just one sequence and not several) and subtract that from 1. So your process is:

1) Recognize that the problem is asking for the probability of “at least one” of event A.

2) Find the probability for “not A” in any one event

3) Calculate the probability of getting “not A” in all outcomes by multiplying the “not A” probability as many times as there are outcomes

4) Subtract that total from 1

(and #5 – make sure the problem doesn’t involve any unique probability-changing events like “if outcome A doesn’t happen in the first try then the probability increases to X% for the second try” – that kind of language is rare but does complicate things)

Probability factors into many autumn situations, so whether you’re a GMAT student or a baseball fan, if you know at least this one probability concept your autumn should be a lot less stressful!

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*By Brian Galvin*