GMAT Tip of the Week: Algebraic Repackaging (or, “How I Got Paid To Write About Last Night’s Episode Of Jersey Shore”)

If you’re in the demographic group “young professionals between 21 and 35” – and our market research suggests that you are – you’ve likely spent time today around the water cooler or coffee machine at work talking about last night’s season-premiere of Jersey Shore.  Maybe you were entertained by JWoww’s admission that she packed nine cans of bronzer for her trip, or by Snooki’s new workout routine.  Maybe you’ve watched the season preview trailer and can’t wait for Ronnie to deck the Situation, or you’re a hopeless romantic and want Ronnie and Sam to patch things up so that you can watch those two fight all over again.  Maybe, like your humble author, you can’t even find words to describe the entity that is Deena.

But regardless of your opinions, you’ve noticed a few striking differences this season.  The show has changed its face, planting the GTLiens in a fish-out-of-water situation in the quiet cultural hub of Florence, Italy.  And the characters have changed their faces, too:

-Vinny supposedly has a beard that everyone is talking about, but unless you’re watching in HD on a minimum 46-inch TV you’d never know

-Snooki has lost weight

-JWoww has lost significant amounts of weight and undergone a half-dozen or so plastic surgeries on her lips, eyebrows, etc.

-Sammi also appears to have gone under the knife, plus her Ronnie detachment procedure which looks to be taking

Consider the question:

999999^2 – 1 equals:

(A) (9^6)(11^6)

(B) (10^6)(10^5 – 2)

(C) (10^6)(10^6 – 2)

(D) (10^5)^2

(E) (10^6)^2

Here, the given information is in a quite-unusable form.  You have no interest in squaring 999999.  It’s a ridiculously large number, it will require an insanely long calculation, and most importantly it won’t look at all like the answer choices.  The work would all be for naught, as ultimately you’d have to repackage the number to look like one of the expressions in A-E.  Your mission here is not to calculate this number; as on many algebra-based problems, your mission is to repackage the given information as something much more useful.  Two things should lead you to this decision:

1) The number itself is incalculable by hand, so it’s not a calculation-based problem

2) The answer choices are in algebraic form, so you’re looking for an expression and not a number

Seeing this, you should recognize that your job is to take the statement given and reframe it as a restatement of the same fact…just a more useful form.  Restatements can come in several ways:

-Factor common terms to turn addition/subtraction into multiplication

-Multiply a fraction by the same numerator and denominator (so it equals 1) to give it a new expression

-Take an equation and do the same thing to both sides to change the look of the expression

Here, we can use arguably the most powerful repackaging tool in all of algebra; the Difference of Squares rule.  This rule states that x^2 – y^2 = (x + y)(x – y).  And since we already have 999999^2 – 1^2 (remember: 1 is the same as 1^2), we can change it to (999999 + 1)(999999 – 1).  Why?  because now we have 1000000 on the left, and that can be repackaged in exponent form as 10^6, which matches the notation in the answer choices.  We needed something with an exponent, and transforming this expression as we did allowed us to do that.  So we have:

(10^6)(999998)

And it’s our job now to repackage the term on the right to match an answer choice.  This can be done by stating 999998 as (10^6 – 2), giving us:

(10^6)(10^6 – 2) –> answer choice C.

What’s important to recognize here is that many algebra-based problems will hinge on your ability to take what you’re given and repackage it as something more useful.  In this situation, know your assets.  Tools like Difference of Squares can make repackaging algebra quite transformative.  Seeing the answer choices as a guide is also instrumental to many of these problems as the choices give you a blueprint of what the algebra ultimately needs to look like.  Repackaging is a huge component of the business world, as you can see with MTV’s juggernaut Jersey Shore and the reinvention of its format and its characters.  Use the same strategy on the GMAT, and you’ll be doing GTL at the GSB in no time (seriously…Stanford GSB’s new facilities are amazing, although we cannot confirm the presence of tanning beds.  But it’s California…it will be sunny.)