Algebra the Vince Vaughn Way:

by on August 27th, 2010

vince-vaughnAdmit it.  In one way or another your goal of going to back to business school is related to your desire to be more like Vince Vaughn’s character from Old School: either you want to go back to school to live the good old college life again, or you want to build your own business empire to rival Speaker City (he was worth 3 and a half million dollars that the government knows about, after all…).

But even Vaughn’s character will tell you that he “built Speaker City from the ground up and I can barely read.”  How did he do it, and how will that philosophy help you on the GMAT?

He found a way to do what he did well and avoid the things that he didn’t, and you can use the same philosophy to achieve success on the GMAT.

Consider the question:

If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?

(A)   3
(B)   5
(C)   6
(D)   8.5
(E)    11.5

Like Vaughn’s Old School character might feel if he had to read War and Peace, you might look at this problem and think “impossible”, noting that you’re not that great at adding and subtracting exponential terms.  But when facing GMAT problems that seemingly ask to do something you don’t do well, look for opportunities to do what you do well!

Here, you can note that you do a few things quite well with exponential terms:

Break their bases down to primes to get common bases. Multiply them.

So when you see a problem like this, you should recognize your strengths with exponents and look to rearrange the algebra to take advantage of them.  Breaking the 4 terms down to prime factors (2), you get:

(2^2)^{2x} + 2^{4x} + (2^2)^{2x} + 2^{4x} = (2^2)^{24}

Then you can get back to multiplication to eliminate the parentheses:

2^{4x} + 2^{4x} + 2^{4x} + 2^{4x} = 2^48

Again, look for chances to do what you do well – and you know that if you can multiply the terms on the left instead of adding them, you’re then multiplying exponential terms with a common base…that’s your strength.  In this problem, you may recognize quickly that you have four of the same term, and can express it as:

4(2^{4x}) = 2^48

Were the problem slightly more difficult, or you didn’t make that recognition, you might need to factor out the common exponential term so that you can multiply it that way:

2^{4x}(1+1+1+1)=2^{48}

2^{4x}(4) = 2^{48}

Either way, you end up with the same multiplication, which is what’s most important – now you’re doing what you do well.

4(2^{4x}) = 2^{48}

One more step is to, again, break down different bases into primes so that you can again multiply exponents.  4 = 2^2, so you have:

2^2(2^{4x}) = 2^{48}

And because you’re pretty quick when multiplying exponents of the same base, you should recognize that that can be expressed as:

2^{4x+2} = 2^{48}

Now that the bases are the same and the terms are set equal, you can note that:

4x+2 = 48

4x = 46

x = 11.5, and the answer is E.

Most importantly, recognize that the GMAT will often ask you to do something that you don’t think you can do, but it will always allow you a way to convert the steps into something that you know you do well.  Know your strengths and look for opportunities to put them to use – multiplying exponential terms instead of adding or subtracting them is one great way to apply that ideology.  Apply these strategies toward success on GMAT algebra questions and you should be able to hear Vince Vaughn’s voice congratulating you with another epic quote from Old SchoolNice job, Frank.  Way to work it through.

9 comments

  • Props to Brian for successfully weaving in 'Old School' references in a serious GMAT math lesson. I never thought this day would come! :)

  • I felt easier converting all terms in the form of 4's exponent rather than in 2's exponent.

  • Thanks, Eric - we may transition in that Six-Degrees-of-Kevin-Bacon style to hinge on Jeremy Piven and get some Entourage or PCU references in the next one!

    Sudhanshu - definitely a smart way to do it, too - the key with exponents is to find a common base, so if you can do it at 4 and not at 2, you'll accomplish the same thing. As a decent rule-of-thumb, if you're looking for prime factors it's more often than not the fastest way, but there are always exceptions or matters of preference.

    • If you can ever make an article using Battlestar Galactica references, I'll send you a Beat The GMAT t-shirt!

  • Challenge accepted! Coming soon to a BTG article near you...

  • Eric - how can we get a T-Shirt? :)

    • Working on it. :)

  • This is a good practice question, and I needed it. Thanks!

  • Excellent article, although I was hoping for an "Ear muffs!" reference...

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