GMAT Tip of the Week: GMAT Math the Gob Bluth Way

GMAT PrepThere 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, rendering the company leader-less…well, that’s certainly the road less traveled, but for Arrested Development character George Oscar (Gob) Bluth, that made all the difference.

The lovably dimwitted magician, softball star, and ventriloquist may be most-beloved beloved for his rendition of the chicken dance, but he nonetheless reached a high position in corporate America as president of the fictional Bluth Company, however unorthodox in his path to that success.  More importantly for you, the aspiring corporate president, he left behind some words of wisdom that can help you conquer the GMAT, an important step on the more-traditional path to such business success:

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 ultimately they tend to be fairly 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’ll need to understand that you’re often going to need to match wits with smarter people.  The authors and overseers of the GMAT are not only sharp, but this is also their full-time job; you should assume that part of that full-time 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 posted in this space 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 question like that in the post, which simply asks you to find the number of factors of one particular number, the trick 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, so we’d then:

- Break off the exponents (2 and 2)

- Add one to each (3, 3)

- Then 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, knowing that such a trick exists, 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 that 54 has:

54 = 3^3 * 2^1

Break off exponents: 3, 1

Add 1: 4, 2

Multiply: 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.  Prime factorization is a strategy – the first step of the trick is crucial.  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, 18 (itself and 1)

2, 3 (the prime factors)

2*3 = 6

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 more importantly 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, as concepts and strategies, we always say, are the most important things as you attempt to succeed on the GMAT. Well, that, and breakfast.

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2 Responses

  1. Anshu Mishra says:

    Nice Article ! Totally agree that shortcuts are not a substitute for understanding.

    I would have again used the trick to calculate the common set of factors once we have calculated the overlapping set i.e. 3*3*2

    3^2*2^1, So number of common factors = (2+1)(1+1) = 6

    Thanks

  2. Brian Galvin says:

    Great point, Anshu – you can use that trick again once you get to the overlapping factors. And what’s most important is knowing that concept behind it all – all composite integers can be broken into prime factors, which makes that whole process possible!

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