GMAT Tip of the Week: Whatever You Say I Am

It's Hip Hop Month on the Veritas Prep blog, and no discussion of contemporary rap would be complete without mention of Eminem, the controversial emcee who has earned Grammy award and platinum records at nearly the same pace as he has earned criticism and backlash for his honest, edgy lyrics and demeanor.

Like many great artists -- be they painters, poets, musicians, or filmmakers -- Eminem pours himself into his work, giving listeners an open, honest, and oftentimes eerie glimpse into the life that inspires him. Eschewing the trend for successful rappers to forego gritty portrayals of their innermost thoughts to focus on the glamour lifestyle of the rich and famous, Eminem continually derives his creativity from his strained relationships with his mother and ex-wife, his reluctant comfort with celebrity and wealth, and his introspective thoughts on his role and his art.

Eminem's unabashed honesty pervades each of his tracks, and even inspired a film, 8 Mile, that parallels his life. One of his first songs to offer an introspective look at his fame was The Way I Am; its lyrics detail the pressures that the artist felt from his fans and his record label after achieving success with his first album. In its chorus, Eminem attacks the celebrity culture that surrounds entertainers, with media outlets creating controversy and speculation around artists:

I am whatever you say I am. If I wasn't, then why would I say I am? ... I don't know, that's just the way I am.

In addition to serving as an anthem of frustration for one of the world's greatest entertainers, these lyrics may unlock for you a secret to success on the GMAT:

"I am whatever you say I am" can also be the anthem of any algebraic equation that the GMAT provides you on test day. That is, your success on math questions may depend on how you rephrase mathematical statements to serve your purposes (the same way that magazines reposition stories about Eminem to sell copies). As long as you "tell the truth" with an algebraic statement, you can rearrange it to fit your needs. Consider the question:

If x and y are nonzero integers, does x - y = y/x?

(1) y² = x²y – xy²

Looking at statement 1, it will be difficult to try combinations of numbers to prove anything about the question - combinations of x and y that satisfy the fact given in statement 1 will be somewhat tough to find, and then it requires effort transfering those values to the question to prove a trend of "yes" or "no". Accordingly, your goal should be to take statement 1 and rephrase it to see if you can match the question. The statement is "whatever you say it is", provided that you take the proper algebraic steps to make it match (it it wasn't, then why would the algebra say it is?). Taking that statement, you can start by dividing both sides by y, as there are no squared terms in the question:

y = x² – xy

Again, because there are no squared terms in the question, and because your goal is to equate x-y to y/x, you should recognize that factoring out an x from both terms on the right of the equation gets you closer to that goal:

y = x(x-y)

Then, if you divide both sides by x, you'll see that you've proven the answer to the question to be "yes":

y/x = x-y

This statement is exactly the same as the initial statement, just rephrased for our purposes. (To paraphrase Eminem, if it wasn't, then why would it say it was?) Because the question asks us to confirm an algebraic equality, our goal should be to take the algebraic facts that we're given and see if we can manipulate the algebra to get that confirmation. In these cases, two things are likely. Either:


1) You'll be able to rephrase the algebra to look exactly like the question, meaning that the statement is sufficient

or

2) You'll realize that you're one step off, meaning that the statement is probably insufficient (you should be able to find at least one set of values for which the answer would be "yes", but for most values the answer would be "no")

Overall, when GMAT quant questions provide you with algebraic equations for statements, your instinct should be to rephrase that algebra in a way that's more useful to you, as often the test will provide you with exactly the information you need, but just disguised as something that's a little less user-friendly than you'd like. In these cases, take a cue from Eminem and rephrase the statement you're given in a way that allows you to use it (the man did once rhyme "oranges" with "syringes" simply by pronouncing it a little different). On test day, the GMAT may just be asking if the real Slim Shady will please stand up.

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