Construct x[4]y in stages, working up from n = 1:
x[1]y = xy

Now, to figure out x[2]y, apply the second part of the definition, using n = 1 (odd):
x[2]y = (x[1]y)x = (xy)x = xyx

Be careful to apply the right part of the definition! Track carefully where n + 1 is and where n is.

Now keep going, using the third part of the definition (with n = 2, even):
x[3]y = (x[2]y)x = (xyx)x = xyxx

(We’ll avoid even tinier exponents by simply writing xx for x2.)

Finally, the x[4]y expression will add another y to the exponent:
x[4]y = (x[3]y)y = (xyxx)y = xyyxx

Now, we are told that y is ½ and that this crazy expression xyyxx equals 2.Substituting in y = ½, you get x^(x2/4) = 2, using the “caret” (^) to indicate exponentiation.

You should recognize at this point that it’s unlikely to be most efficient to try to solve directly for x—in fact, it may not even be possible within “GMAT math.” Rather, you should glance through the answer choices and see whether you can backsolve, eliminating obviously wrong answers.

(A) x = ¼ produces an expression in which you’re raising ¼ (a proper positive fraction) to a fractional power (taking a root), which will result in a number closer to 1, but certainly not 2.
(B) same problem as in (A).
(C) x = 1 produces 1^¼ = 1, not 2.
(D) x = 2 produces exactly what we want: 2^(22/4)=2^1 = 2.

We can stop there, but you can check 4 quickly: the expression becomes 44, which is not 2.

The correct answer is D.

Formal events are reportedly a big part of Harvard Business School social life. As the name suggests, Holidazzle is HBS’s annual holiday party, which takes place in early December. According to the HBS Students Association, it is the business school’s longest-running event, and starts with RC section dinners followed by drinks (open bar) and dancing. The Newport Ball is held each spring in tony Newport, Rhode Island, which is just a short drive from Boston. Students attending the ball enjoy dinner and dancing at a Newport mansion and typically decide to stay for the entire weekend, touring the city’s historically preserved estates, such as The Breakers, Rosecliff, and Marble House, built by titans of the gilded age.

For in-depth descriptions of social and community activities at HBS and 15 other top MBA programs, check out the mbaMission Insider’s Guides.

The expression x[n]y is defined for positive values of x and y and for positive integer values of n as follows:

• x[1]y = xy
• If n is odd, x[n+1]y = (x[n]y)x
• If n is even, x[n+1]y = (x[n]y)y

If y = ½ and x[4]y = 2, then x =

(A) ¼
(B) ½
(C) 1
(D) 2
(E) 4

Roberto Rigobon (“Applied Macro and International Economics,” “Sustainable Development and Social Entrepreneurship”) specializes in international economics, monetary economics and development economics. At an awards ceremony in 2005, Sloan students described him as someone who “epitomized the fine line between madness and genius.” Other award-related descriptions of Rigobon refer to him as “serious but hilarious,” “crazy and brilliant” and “high energy.” He teaches the wildly popular “Applied Macro and International Economics” course, which is often taken by up to 30% of Sloan students at a time. Rigobon handles as many as four sections (six hours) back to back, three days a week. He has won numerous teaching awards during his time at Sloan (including the school’s Excellence in Teaching Award in 2000, 2003, and 2005, and Teacher of the Year in 1999, 2002, and 2004) and is primarily recognized for his accessibility. As one second-year student blogged, “The door to his office was always open.”

For more information about the MIT Sloan School of Management and 15 other top-ranked MBA schools, check out the mbaMission Insider’s Guides.

MBA applicants who prefer the East Coast or who want to get in on the ground floor of the country’s hottest new tech hub might consider New York City as a home base. And the New York tech community is pretty easy to find. Many start-ups are located in close proximity to one another, with the offices of such companies as Tumblr, Shelby.tv and The Levo League located between Union Square and the Flatiron District in Manhattan. New York is even home to pioneering organizations such as Women Innovate Mobile, which is the first start-up accelerator designed for women-founded companies in mobile technology. It’s always worth the time for MBA hopefuls to go beyond the stereotypes of schools or regions to dig a little deeper and find a gem that might be a perfect fit for their needs.

When you are applying to business school, leave your parents out of the process! Although this MBA admission tip may seem obvious to most candidates, those who are a part of “Gen Y” or “The Millennials” may have parents who are accustomed to helping guide their children’s choices, having done so throughout the candidates’ high school and college years. These parents naturally want to be involved in the MBA admissions process as well and are now leaving many admissions officers across the country shaking their heads.

Of course, having a parent call to confirm whether an important document was received when an applicant is perhaps traveling/working abroad and/or cannot make such a call him- or herself during work hours is certainly not the same as having a parent call to ask why his/her son or daughter hasn’t gotten an interview invitation yet. Unless the matter at hand is an entirely practical one, candidates have nothing to gain by having their parents act as their agents. On the contrary, they have everything to lose. An aggressive parent can reflect badly on an applicant for a variety of reasons, the most obvious being that it suggests that the candidate lacks maturity and perhaps even the ability to make independent judgments and decisions.

Think very carefully before you involve your parents in any aspect of the application process except sitting at home and waiting for great news—successful applicants do it all the time!

The creative list is quite impressive—Andrew and Neil are in good company with Shaquille O’Neal, Wes Anderson and Aziz Ansari.

If you are interested in a free Ding Review, please send one complete application to info@mbamission.com. We will randomly select 20 applicants, and if you are chosen, we will contact you about your free session.

No clear rules exist as to what you should discuss, but as you consider ideas, “knowing your audience” is of the utmost importance. Never take risks by discussing an economic, political, social or cultural idea that you believe an “average person” might find extreme. Of course, “extreme” is open to interpretation, and this is why choosing the issue you will discuss requires so much careful consideration. As a general guideline, when you begin writing, keep in mind that you are not trying to win voters or recruit people to your cause, but are trying to show that you are engaged in the issues, can consider them in a balanced way and are able to articulate your ideas persuasively.

And on we go—this is the fifth entry in what began as a three-part series on the GMAT’s new Integrated Reasoning (IR) section. I can’t help it—they keep releasing new and important info—so we’ll just keep going until either we get sick of the topic or GMAC stops giving us new things to discuss.

GMATPrep 2.0 has been out for nearly a month now, and we’ve got some important details to share. First, if you haven’t heard already, the new software is Mac compatible (finally!). Second, I got a bit of a nasty surprise when I took my second GMATPrep—the IR questions were exactly the same ones I saw on the first test!

So here’s our first big tip for you: Save 12 official IR questions for your second GMATPrep: one Multi-Source Reasoning with three questions, and three each of the other three types. (Note: this is not the exact guaranteed mix on the real test, but it’s one of the possible mixes.) You can get these questions from within the practice section of the GMATPrep software or from the OG13 IR question bank.

You can also just skip the IR section on the second test, but the problem is that this might give you an artificial advantage on the quant and verbal portions (because you won’t be as mentally fatigued as you’d normally be). As such, we strongly recommend that you save 12 questions to make the second GMATPrep experience as much like the real test as possible.

An “updates available” feature is built into GMATPrep 2.0. If you see that icon pop up, click on it. Eventually, I’m sure they’ll add a second “real” IR section to the test, so you want to get that update when it’s available!

Finally, a little OG news. The Official Guide for GMAT Review, 13th edition, (OG13) has a code for an online question bank consisting of 50 IR questions. Your access is good for six months from the date of activation, so don’t activate the set until you’re ready to do your first OG IR problem.

Also, if you’ve already bought OG12 but are planning to take the new test, good news: you can purchase access to just the online IR question bank for $10. This option will be available until June 5; after that, the 50-question IR bank will be available only with the purchase of OG13.