“A rose by any other name would smell as sweet.” – Juliet / William Shakespeare

Carlos Danger is Anthony Weiner. And a creep by any other name would be just as creepy. This week the New York mayoral candidate, notorious for tweeting his last name all across the internet, put his campaign into his fake last name by doing the same thing under an alias. And in doing so, he taught many of you who aspire to live under his intended jurisdiction – as students at NYU-Stern or Columbia, or as bankers or marketers or hip-hop moguls after graduation – a valuable lesson about the GMAT:

Problems that look dangerous are often just the same old suspects in disguise.

Your job on the GMAT is often to see through the illusion of danger, to see the familiar amidst the unfamiliar, to know that the more unique a problem looks the more valuable it is to find something tried-and-true about it. Consider an example:

Let the superfactorial of a number n be denoted S[n] and represent the product of the first n factorial numbers. For example, S[4] = (4!)(3!)(2!)(1!) = (24)(6)(2)(1) = 288. Which of the following is equivalent to 11S[10} divided by S[11]?

(A) 1/10!
(B) 10/11
(C) 1
(D) S[10]
(E) S[11]

As with most function/sequence/awkward-notation problems, this problem is much more Anthony Weiner than Carlos Danger – it’s a fairly standard problem (it’s a factors/fractions problem in disguise) made up to look like something it’s not. Your clues? In large part it’s the answer choices, of which particularly A through C should give you insight – your job is to take a really complex fraction and reduce it to something simpler. And that typically comes from stacking the fraction and cancelling repetitive terms that multiply on both the top and bottom. So take a look:

Numerator: 11 * 10! * 9! * 8! * 7! * 6! * 5! * 4! * 3! * 2! * 1
Denominator: 11! * 10! * 9! * 8!… (you should see by now – all these factorials 10 and below will cancel)

So if you’re ready to cancel repetitive terms on top and bottom, this thing quickly simplifies to 11/11!. And so now what you really have is:

Numerator: 11
Denominator: 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 (or 11 * 10!)

So the 11s cancel, and you’re left with 1/10!, answer choice A.

The bigger takeaway? Even though this problem looked like a lot of exotic danger with the “superfactorial” definition, it was really a more common concept being tested. This question was all about reducing fractions, a pretty accessible skill just made to look a lot trickier by putting fancy names like “superfactorial” on top of it. Like the New York press, you’re smarter than that – you know that there’s usually a familiar suspect behind all that smoke, mirrors, and Carlos Danger. Keep that in mind, and your GMAT score report will be an image you’re proud to Twitpic to the world.

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By Brian Galvin