GMAT Math the Gob Bluth Way

by on December 28th, 2010

There are many paths to becoming president of a major real estate company.  A failed career as a magician that leads to your wealthy father’s arrest for SEC violations, followed by his embroilment in a treason scandal that prompts him to install you as a figurehead president so that your more responsible brother does not take the fall, for instance. Well, that’s certainly the road less traveled, but for Arrested Development character George Oscar (Gob) Bluth, that was a path that worked.

As the aspiring corporate president in the hit TV series, Bluth left behind some words of wisdom that can help you conquer the GMAT.  Whenever asked to perform magic tricks, Bluth is famous for always replying, “I do illusions; tricks are for…” Well, let’s just call them “the kinds of people who turn tricks”.

On the GMAT, tricks can seem like godsends, but they ultimately tend to be limited in scope.  Sure, you can find a trick that nicely solves a difficult problem from the Official Guide.  But, much like Gob Bluth,   you should understand that you are often going to need to match wits with smarter people.  The authors and overseers of the GMAT are not only sharp;   this is also their full-time job!  You should assume that part of that  job is to stay one step ahead of the common trick that easily solves difficult Official Guide problems.

As an example, let’s revisit a trick that we actually wrote about a year ago:  “A Trick That Might Factor In”.

(Notice we used the word “might” in the title… This trick might factor in, but it’s not a sure thing!)

On a question like the one in that post, which asks you to find the number of factors of one particular number, the trick we discuss works perfectly.  For example, if the question were

How many factors does 36 have?

We could answer by first noting that 36 can be  broken down into 2^2 * 3^2.  Knowing this, we’d then:

  • Break off the exponents: (2 and 2)
  • Add one to each: (3, 3)
  • Multiply the exponents: (3*3 = 9)

Pretty neat trick, right? But as Gob Bluth might say, tricks are for lower-level employees… CEOs need strategies.  Because the authors of the GMAT  know that such a trick exists, they might change the question slightly to add difficulty:

How many factors are common to both 36 and 54?

Here, it’s not quite as easy as finding that 36 has 9 factors (as we proved above), and applying the same trick to 54:

54 = 3^3 * 2^1

  • Break off the exponents: 3, 1
  • Add one to each: 4, 2
  • Multiply the exponents: 4 * 2 = 8 factors for 54

Without a way to determine which factors are which, how do we use this trick to solve this factor problem?  We can’t! It’s the knowledge behind the trick that’s important, because that knowledge allows us to be flexible.

The trick’s first step, prime factorization, is crucial.  Prime factorization is a strategy, not a trick.  We know that:

54 = 3 *3 * 3*2

and

36 = 3 * 3 * 2 * 2

Because of that, the common set of factors to both numbers is the overlapping 3*3*2 -  that common set of prime factors is what will lead us to the entire set of common factors.  The greatest common factor of each number is 18, so the common factors are:

1 and 18 (itself and 1)

2 and  3 (the prime factors)

2* 3 = 6, and

3*3 = 9

There are a total of 6 unique factors in common between 36 and 54.

Note that the factor “trick” can be used once you get to the greatest common factor of 18, but the GMAT will typically make you think before it allows you to simply plug in a trick.  Therefore, this example should serve as a reminder that tricks and shortcuts are not a substitute for understanding and strategy . Know and appreciate the tricks that come naturally and seem useful to you, but  teach yourself to look for the underlying reasons why the tricks work, and for the core concepts that the tricks rely upon.  Flexible knowledge will allow you to solve the many varieties of questions that the GMAT can dream up. Rigid, plug-and-chug knowledge is actually something that the authors of the GMAT are specifically trying to punish (or at least not reward).

To rise to the corporate heights of a Gob Bluth, you may need to incorporate the wisdom (and the patience) of Gob.  Tricks…well, they may not be what we want to be known for.  Concepts and strategies are the most important things to help you succeed on the GMAT. Well, that and breakfast.

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