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Today’s GMAT challenge question comes from our friends at ManhattanGMAT.  To help you with your GMAT studying, try to solve the problem on your own, and then read on for the explanation of its solution:

Problem

The sum of the first n positive perfect squares, where n is a positive integer, is given by the formula n3/3 + cn2 + n/6, where c is a constant. What is the sum of the first 15 positive perfect squares?

(A) 1,010
(B) 1,164
(C) 1,240
(D) 1,316
(E) 1,476

Solution

The brute-force way to solve this problem is literally to add up the first 15 positive perfect squares, from 1 to 225, inclusive. This is not necessarily completely out of bounds, given that we only have to sum up 15 numbers, all of which we should know already, and several of which are small. However, we should look for a shortcut using the formula.

Unfortunately, there is an unknown constant in the formula, but by using a small test number, we can solve for this constant. You can certainly pick n = 1, since it is a positive integer:
12 = 13/3 + c12 + 1/6
1 = 1/3 + c + 1/6
1/2 = c

If you feel uncomfortable picking n = 1, you can pick n = 2 and come to the same result almost as quickly.

Now, we plug n = 15 into the formula and solve:

12 + 22 + … + 152 = 153/3 + 152/2 + 15/6
= 15×15×15/3 + 15×15/2 + 15/6
= 15×15×5 + 15×15/2 + 5/2
= 225×5 + 225/2 + 5/2
= 1,125 + 230/2
= 1,125 + 115
= 1,240

The correct answer is (C).

For more information on ManhattanGMAT, download Clear Admit’s independent guide to the leading test preparation companies here.  This FREE guide includes coupons for discounts on test prep services at nine different firms!

The Tuck School of Business at Dartmouth this week announced the creation of a new leadership center to build upon existing leadership initiatives at the school. Founded by Tuck professor Pino Audia, the innovative center will focus on students themselves rather than using case studies to analyze how others lead.

The new Tuck Center for Leadership will provide a range of leadership development activities for students that expand upon the initiatives of the Cohen Leadership Development Program, which was established in 2003. With the launch of the new center, every Tuck student will now be required to complete leadership training as part of the MBA course, as well as fulfill a new ethics and social responsibility credit requirement.

The center also will support ongoing research in leadership topics and serve as a place where business leaders and scholars can gather to share and promote best practices and research findings.

“The creation of the center shows Tuck’s continuing commitment to provide the best business leadership education in the world,” Audia said in a statement announcing the center’s creation.

Rather than dissecting case studies to understand how others lead, students at the center will take part in a 360-degree feedback diagnostic, working in small groups and giving feedback to one another about their leadership styles, strengths and weaknesses. Professors, second-year students and consultants will serve as coaches, leading first-year students through the leadership exercises.

“The idea is that effective leadership requires not only knowledge about how organizations are run but also knowledge about oneself,” Audia said. “This second type of knowledge is surprisingly difficult to acquire due to biases that render people’s perceptions of themselves inaccurate.”

There also will be collaboration between the new center and Tuck’s Career Development Office. Richard McNulty, executive director of the Career Development Office, has been appointed to serve as the new center’s executive director as well. 

“Our goal on the career planning side is to help students be even more informed about the decisions they make,” McNulty said in a statement. “To choose a path where their strengths are aligned with what it takes to maximize their success.”

Welcome to the latest edition of Clear Admit’s Fridays From The Frontline! Every week we take a tour through the many blogs of those hoping to gain entry into an MBA program, and current students, whose application process is thankfully behind them. This week many MBA hopefuls were taking a collective breath as the last of round one deadlines passed. Students continue to be engaging in all sorts of activity, from watching classmates sing for a marketing competition to accepting  job offers, current MBA bloggers are certainly a busy bunch.

Madalogue shared some of her favorite passages from a recent article by Tim Berry about the value of an MBA to an entrepreneur.  Steve felt strangely empty without applications to work on, but found an MBA-oriented site that he encouraged other applicants to check out. ArdentMeerkat submitted her first application (Cornell) and found that seeing an end in sight helped her focus on her GMAT prep. A Beautiful Mind enjoyed Rotman’s class video, had plans to celebrate a few family birthdays and looked back on his set of applications.  Procrastinator turned in his last round one application (Fuqua) and hoped his recommenders wouldn’t mind four more schools over the coming months. XLick asked his readers for suggestions for round two schools, and expressed his thanks and thoughts on the advice he was given. LBiggs spoke with a few Sloan alumni about how the application process works, and shared their overview with his readers. Rocky Balboa received zap news from Wharton, but felt great about finishing up his Babson application.

Kellogg ‘11 Orlando shared a video of him practicing for the AT Kearney competition and hoped to look back at it in two years’ time and see improvement. Boston ‘11 Felish enjoyed the Net Impact conference she and fellow classmates attended in Ithaca, but continued to be very busy. Kellogg ‘11 Windsor appreciated fellow classmates’ video for the Kellogg Marketing Competition. Chicago Booth ‘11 GlobThink thought that a recent lecture by Professor Sapra was one of the best he ever attended. Kellogg ‘11 Shobhit found that, once in b-school, rankings were not as central to the experience as one might think. Stanford ‘11 Sunnyside Up’s laptop had a scary run-in with 12 ounces of water, which has led to her decision to back up her computer each and every night.   Goizueta ‘11 Ahembeea wished he turn his blog into a photoblog in order to properly explain how much he was enjoying his b-school classes and community. LBS ‘11 Alex wanted to hear his readers’ thoughts on his concept of ‘excitement management.’

Darden ‘10 July Dream didn’t feel that her blog was in any way censored by the school, and explained why. Marshall ‘10 Andrew explained what made his Leadership and Executive Development course one of his favorites. McCombs ‘10 Paragon2Pieces made butternut squash soup and became compulsive about her reading. Harvard ‘10 Inside HBS accepted a full-time position and wrote about Harvard’s recruiting regulations.  McCombs ‘10 Metal played a good tennis match and had his own phrase included in a group project’s slides. Darden ‘10 Sameer wrote about the effort it took to start the Darden South Asia Club.

And that concludes this fresh Fridays From The Frontline. We hope that all applicants are taking a moment to regather their strength before more interview invites and final decisions come out, and that current students are making the most of their MBA experience. Keep blogging and have a great weekend!

Chinese undergraduates are enrolling at American universities in record numbers and may soon outpace Indian students, who for the past eight years have come to the United States in greater numbers than any others, according to a recent article in the New York Times. Overall, international enrollment at U.S. schools was the highest ever in 2008-9 and showed the largest percentage increase year over year in more than 25 years.

These and other figures were released as part of the annual Open Doors 2009 Report, published by the Institute of International Education with support from the State Department. Citing the report, the Times article revealed that China last year sent 98,510 undergraduates to study at American universities, a 21 percent increase over the year before. India, which sent 103,260 students, saw only a 9 percent increase over the previous year.

“I think we’re going to be seeing 100,000 students from each for years to come, with an increasing share of them being undergraduates,” Peggy Blumenthal, executive vice president of the Institute of International Education, told the Times.

The upward shift is most notable in China, according to the Times. China sent 26,275 undergraduates and 57,451 graduate students to the United States last year, up from 8,034 undergraduates and 50,976 graduate students five years earlier.

Blumenthal told the Times that the increase among undergraduates coming from China promises to alter the face of Chinese students’ presence in the United States more widely.

“It used to be that they were all in the graduate science departments, but now, with the one-child policy, more and more Chinese parents are taking their considerable wealth and investing it in that one child getting an American college education,” she said, adding that a book explaining liberal arts education is receiving considerable attention in China right now.

The book, A True Liberal Arts Education, explains the concept of liberal arts and describes the education available at small liberal arts colleges, both of which were previously unfamiliar to most Chinese. It was written by three Chinese undergraduates from Bowdoin College, Franklin & Marshall College and Bucknell University.

Overall, broken out by field of study, more international students come to the United States to study business and management than any other subject, according to the Open Door 2009 report. In 2008-9, 137,495 international students pursued business and management courses, representing a 25 percent increase over the year before (higher than any other field) and 21 percent of international students overall.

To read the Times article, click here. To access the Open Doors 2009 Report, click here.

Welcome to another installment of Twitter Thursdays, a weekly column in which we highlight the updates of the top MBA programs on Twitter!  If you’re not following Clear Admit already, be sure to check us out on Twitter for updates, special prizes, admissions tips and breaking news.   We’ve also created a list of MBA programs to ease your daily access to breaking news from the top MBA programs, as reported by admissions committee members themselves.

UCLA / Anderson’s Dean, Judy Olian, recounted her weekend Q & A session with 60 prospective students visiting UCLA’s campus for its Embracing Diversity weekend. Rich Lyons, the Dean of the Haas School of Business, announced the school’s new vision statement: where innovative leaders thrive.  MBA Admissions Coordinator at Judge Business School, James Barker, announced a few Cambridge information sessions in Johannesburg and Zurich.  Associate Dean for Student Recruitment and Admissions at Chicago Booth, Rose Martinelli, brought together some first-year students for a live, online chat to share some insight into life at Booth.

Meanwhile, the Haas School is gearing up for its fifth annual entrepreneurship challenge, a competition for new technology business ideas.  Back in Boston, MIT Sloan will be hosting a slew of CFOs in its annual CFO Summit this week.  Duke / Fuqua’s Global Entrepreneurship Network demonstrated that it knows how to live up to its name – at networking Happy Hours in various cities throughout the world.  The Kellogg School of Management welcomed Federal Reserve Vice Chairman Donald Kohn to campus for a lecture on federal policy.

That wraps up Twitter Thursdays this week!  If you’re on Twitter, let us know; direct message us on Twitter or e-mail wiki@clearadmit.com with your user name and status as an MBA applicant, student or admissions officer so we can add you to the appropriate Twitter list.  Happy “tweeting” and we’ll see you next week with some more Twitter updates!

We return to this week’s Campus Chronicles with a perusal of Wharton’s student newspaper, The Wharton Journal, to learn about the latest events on Wharton’s campus.  Our hope is that this summary of the latest happenings at Huntsman Hall is helpful for Wharton applicants in the midst of R1 interviews as well as for candidates targeting R2!

With the culmination of the six-week Jay H. Baker Retailing Initiative Speaker Series, this fall offered ample opportunities for Wharton students to learn about the fashion and retail business.  Wharton’s campus was visited by three top executives in the field: Millard Drexler, the chief executive of J. Crew, Terry Lundgren, Macy’s CEO, President, Director, and Chairman of the Board, and Martha Stewart.  Students who participated in the Fashion & Luxury Club treks also met with industry executives during their trips to firms including J. Crew, Gilt Group, Li & Fung, and Bonobos.  Executives at these events cited creativity, mixed media, and catering to customers as integral to success, especially due to the recent economic challenges.  Despite these challenges, upcoming Wharton graduates were informed of the broad opportunities for job placements in this industry: Macy’s, for example, is looking to hire 200 MBA students this year.  Wharton treks occurring later this year include a visit to Polo Ralph Lauren as well as a week-long trip to Europe over spring break.

This past weekend Wharton students had the chance to attend the Wharton Africa Business Conference and learn about the business opportunities available throughout the continent.  Panels focused on the traditional topics of capital markets and private equity as well as the growth of African businesses, a topic previous uninvestigated.  Thierry Tanoh, International Finance Corporations’ Vice President for Sub-Saharan Africa, Western Europe for the Global Manufacturing Industry Cluster, was the keynote speaker in the morning session.  Citing the 200,000 bank accounts held in Congo despite its 60 million citizens, he emphasized the opportunities available in this country.  During the “Panel on the Brain Gain,” Zemedenen Negatu, an MD at Ernst & Young, and Kunbi Oguneye, the Head of Strategy at Nigeria’s Oceanic Bank, discussed the importance of African countries providing incentives for its citizens to return to Africa and use their education and experience to contribute to the country’s growth.  Others speakers included Louisa Mojela, founder of WIPHOLD, the first all-women’s investment fund in Africa as well as Anna Getaneh, a former model who recently founded her own couture African fashion line.  Both Mojela and Getaneh discussed overcoming the challenges of being a woman in the business world, both in Africa and internationally.

November has been a winning month for Wharton students engaged in business competitions.  Wharton won first place at the Cornell-Fidelity MBA Stock Pitch Competition, thanks to the efforts of first-years Victor Bonilla, Nikhil Gadia, and Joe O’Donnell.  In this 12-team tournament, each team had 12 hours to determine buy, sell, or hold recommendations on three stocks and then present their decisions to a judging panel of investment management experts.  Not only is this year the first time Wharton has won top prize, it comes off last year’s second place win, which was the first time Wharton placed in the competition.  Wharton also took the top prize at the Sixth Annual American Bankruptcy Institute (“ABI”) Corporate Restructuring Competition.  Participants in this competition have one week to use their knowledge on bankruptcy topics to solve a real-world restructuring case problem, this year prepared by Houlihan Lokey.  Teams prepared an operational and financial plan to solve the issue, ultimately presenting before a plan of judges acting as management, the board of directors, and bondholders.  Three of the 12 participating teams advanced to the final round, and Wharton’s Amit Gupta (WG ’10), Howard Levine (WG ’10), Colin McGinnis (WG ’11) and Adam Piekarski (WG ’11) ultimately won first place.  McGinnis cites his team’s ability to please the three different groups represented in the judging panel as a substantial reason for his team’s success.

Today’s GMAT tip comes from the test prep firm ManhattanGMAT. In this article, ManhattanGMAT instructor Stacey Koprince analyzes an example of a GMATPrep® Sentence Correction (SC) question:

First, set your timer for 1 minute and 15 seconds and try the problem!

“The Achaemenid empire of Persia reached the Indus Valley in the fifth century B.C., bringing the Aramaic script with it, from which was derived both northern and southern Indian alphabets.
“A) the Aramaic script with it, from which was derived both northern and
“B) the Aramaic script with it, and from which deriving both the northern and the
“C) with it the Aramaic script, from which derive both the northern and the
“D) with it the Aramaic script, from which derives both northern and
“E) with it the Aramaic script, and deriving from it both the northern and”

Okay, have you got your answer? Now, let’s dive into this thing! Was everything okay in the original sentence or do you want to examine anything further?

On this one, perhaps the “, from which” in the original sentence caught your eye. This marker signifies a noun modifier. Noun modifiers are supposed to modify the closest main noun; in this case, that means the noun before the comma. That noun is the pronoun “it.” So, what is “it” referring to?

“It” is referring to the empire. So the noun modifier is telling us “the empire, from which was derived .” Can an alphabet be derived from an empire? Figuratively, perhaps, but not literally. Literally, one alphabet is derived from another alphabet – so the sentence should convey that meaning.

So, we’ve found an error in the original sentence, and we can immediately cross off choice A. Next, let’s scan the remaining answers to see whether we can reuse our new-found knowledge. Do any of the other choices repeat the error that we just found?

Answers C and D have “script, from which,” so they both fix that problem. Answers B and E change things up a bit – they introduce an “and” after the comma, so we no longer have a straight noun modifier marker.

Now, each person has to make a choice: do you want to try to figure out what’s happening with these new “and” markers in B and E? Or do you want to try to find something else? There isn’t one right answer to this question; it just depends upon your strengths and weaknesses. In this case, let’s examine B and E further.

B says “it, and from which deriving…” The “and” is a parallelism marker: X and Y. If this choice is correct, then, it should have some X and Y components that can be made parallel. Right after the “and,” we have the “from which” modifier marker, so this is the start of the Y component of the “X and Y” parallelism structure. What is the X? Ah, there’s the problem! We don’t have a parallel noun-modifier X component before the “and.” Eliminate B.

We know already that E also introduced an “and” at this point in the sentence, so let’s see if we can reuse our work from B on E. This time, we have “script, and deriving…” The word “deriving” is the start of our Y component; what is the parallel X component? Perhaps it’s the word “bringing” from the non-underlined portion? Let’s test it out.

“The empire reached the Valley, bringing with it , and deriving from it .” These “comma –ing” structures are adverbial modifiers, which modify the preceding clause (subject and verb). In addition, the parallelism sets up certain expectations; for instance, when using the same pronoun in the same position in two parallel structures, the expectation is that the pronoun refers to the same noun both times. What does the first “it” refer to? Does the second “it” refer to the same noun?

For more information on ManhattanGMAT, download Clear Admit’s independent guide to the leading test preparation companies here.  This FREE guide includes coupons for discounts on test prep services at nine different firms!

With a number of top schools currently rolling out interview invitations – from Berkeley / Haas to Harvard Business School, Columbia Business School and Michigan / Ross to Yale School of Management – we wanted to take a moment today to point readers to the Clear Admit Wiki as a free source of breaking interview invitation news and extensive information on the interview process at each program. For those who aren’t familiar, the Wiki is a collaborative resource for the MBA applicant community where applicants can (anonymously or otherwise) post reports about their interviews, campus visits and application experiences at the top business schools, and read about those of others. Our hope is that the sum of these individual firsthand accounts is a representative picture of the culture and processes at each program.

For the next few weeks, we’ll be awarding a $10 iTunes gift certificate to every fifth applicant who contributes content to the Wiki.  To be eligible for the prize, simply send your contribution to wiki@clearadmit.com; we’ll post it to the Wiki and notify the winners by e-mail.

The most helpful and informative reports usually include the following information:

1. Date/Admissions Round
2. Description of visit and/or interview atmosphere
3. Type of interview (alum vs. adcom, blind vs. application-based)
4. List of interview questions
5. Commentary (What did you think of the interview? What surprised you? What didn’t surprise you? What might you conclude about the school based on this experience?)

Applicants who would like to supplement the information available on the Wiki can check out our Clear Admit Interview Guides, which provide school-specific insight and strategic advice to help applicants with their admissions interviews.

As always, we wish the best of luck to Round 1 applicants who have submitted their materials and are now eagerly awaiting good news from their target schools! Stay tuned to this blog for an array of interview tips in the coming weeks, and keep an eye out for upcoming editions of Wiki Wednesdays, a column highlighting especially insightful and informative contributions to the Clear Admit Wiki.

Times Higher Education (THE), a London-based weekly newspaper that publishes the annual World University Rankings, has dropped its long-time research partner QS and instead will use research data specialist Thomson Reuters for rankings data, according to a recent report in University World News (UWN).

THE drew significant criticism for the methodology it employed during its six-year collaboration with QS. Because the methodology called for factoring in the results of reputational surveys of academics and leading employers, opponents argue that it perpetuated out-of-date perceptions of universities. Also problematic was the fact that QS, in addition to its research function, offered consultancy services to participating universities to help them improve their position in the rankings, UWN reports.

QS, which is headed by Wharton MBA graduate Nunzio Quacquarelli, has run into trouble before, UWN reports. In February 2007, the associate dean at UNC’s Kenan-Flagler Business School described the research methods used by QS to compile an MBA ranking in Fortune Magazine as “shoddy, inaccurate and inappropriate.” Fortune was forced to remove the rankings from its website, according to UWN.

Quacquarelli shrugged off being dropped by Times Higher Education. “The partnership with THE may be at an end but QS will continue its commitment to providing rankings for a growing number of geographical and disciplinary contexts,” he told UWN.

Thomson Reuters, THE’s new research partner, is planning a range of improvements for the new World University Rankings, according to Jonathan Adams, director of research evaluation for the research data specialist firm. Though the rankings will continue to use reputational data, THE and Thomson Reuters will work closely with the academic community to reduce the “reputational hangover” effect, Adams said.

The 2010 World University Rankings will look different and include more information about the methodology, Adams told UWN. He expects even more changes, improvements and refinements in coming years, he added. “We are aiming for something that people will be able to pick up and say ‘Yes, that makes a lot of sense – this probably agrees with what I see of the landscape around me,’” he told UWN.

The revamped World University Rankings will still rank the top 200 universities worldwide, with separate rankings by subject area.

To read the UWN report, click here.

We are pleased to report that The Clear Admit Guide to GMAT Preparation Companies, our free publication, now includes coupons on services from the firms outlined in the guide.  The discounts offered in this guide are worth several hundred dollars and have been made exclusively for those who download the publication!

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To obtain your free copy and to see what discounts the test prep centers have made available to you, simply visit the Clear Admit shop. Click on the corresponding link to be guided through a brief ordering process, after which you will receive an email with a password that lets you download, save, print or read your own copy of The Clear Admit Guide to GMAT Preparation Companies.

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