Admit it — as much fun as the World Cup has been, you’re looking forward to the return of sports in which American superathletes dominate. Landon Donovan’s 91st minute goal to win the pool was great, but nil-nil ties and inferiority to both -guays (Para- and Uru-) isn’t the kind of thing Americans can really get behind.

What we can get behind are big wins, big personalities, and big history, and this weekend, as we celebrate the very existence of America itself, we get to watch one of the biggest winners that the U.S. has ever produced compete on a big stage: Lance Armstrong rides again.

Nicknamed “Mellow Johnny” in an intentional Americanization of the phrase “maillot jaune” (French for “yellow jersey,” the shirt worn by the leader and eventual winner of the Tour de France), Armstrong is typically far from mellow in his intense approach to training, competing, and life in general. But lately he’s been more relaxed in interviews, eluding to things in life that are more important to him than winning. He’s a full-time cancer crusader and part-time cyclist, and admits that his return to cycling the last two years has had more to do with the platform it’s given him to raise awareness about cancer than with his zeal for winning. Embedded within that is an important GMAT lesson for you:

As you attempt to solve large-scale problems, find opportunities to do what you do best.

For Armstrong, fighting cancer has been made easier by cycling, as that’s what he does best. For you on the GMAT, it will be extremely helpful for you to approach problems by remembering the things that you do well and finding chances to apply those, and in doing so not allowing yourself to be trapped into performing calculations or using concepts that are time-consuming on a path to nowhere.

Consider the case of exponents. The rules that you know for exponents all relate to multiplication:

x^a * x^b = x^(a+b)

(x^y)^z = x^(yz)

etc.

By the time you take the GMAT, you should be very good at manipulating exponents when multiplication is present. But, on the other hand, we’re awful at using exponents when we’re adding and subtracting terms. Consider the following question:

What is 3^8 + 3^7 – 3^6 – 3^5?

(A) (3^5)(2^4)

(B) (3^5)(2^6)

(C) (3^6)(2^5)

(D) 6^5

(E) None of the above

Again, because we’re not that great when it comes to adding and subtracting exponents, we need to find a way to do what we do well, which is multiplying. With that in mind, if we factor the original equation, we can start that multiplication process. Factor out a 3^5 from each term to get:

(3^5) (3^3 + 3^2 – 3 – 1)

Because the parenthetical term on the right deals with numbers that we can calculate pretty easily, and because we know from the answer choices that we’ll likely need to get that term in terms of the number 2, let’s calculate that out:

(3^5) (27 + 9 – 3 – 1)

(3^5) (32)

(3^5) (2^5)

Now, we have our algebra in the same terms as the answer choices, but it doesn’t match those terms A, B, or C. Again, though, think about what we’re good at — we’re good at multiplying exponents! If we rephrase our expression, we can manipulate it a bit to get:

(3^5)(2^5)

(3*2)^5

6^5

And the correct answer is D.

With problems that look complicated, it’s helpful to find the scope of what needs to be done and then ask yourself what in that realm you do well. Your “core competencies” on the GMAT will be your guiding lights as you approach all kinds of questions, so keep in mind that, among other things, you’re great at multiplying exponents, breaking down numbers into prime factors, performing using calculations using fractions, etc. Just like Lance Armstrong is much better at riding a bike than he is at public speaking or fundraising (no knock on those abilities — he’s just the world’s greatest on a bike!), you’re much better at the above skills than at many others, so look for opportunities to put them to use!

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