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Johan Cruyff is widely considered one of the greatest soccer players ever. As the star of the brilliant Holland teams of the 1970's (the 1978 team is regarded as the best team not to win the World Cup), he was part of a revolution called Total Football, initiated by the Dutch coach Rinus Michels. The concept was simple: as a player moves out of position, another player should be able to cover that area. Essentially, Total Football took soccer out of its traditional complex rigidity and led to a simpler, more fluid approach to the game. This adjustment led to some of the best soccer ever played, and elements of the philosophy are still used by teams such as Barcelona and Arsenal today. In the words of Cruyff, "football is simple, but the hardest thing is to play football in a simple way." For our purposes, we can paraphrase that as "the GMAT is simple, but the hardest thing is to attack the GMAT in a simple way." This approach is especially useful on the quantitative section.
For most students, studying for the GMAT is a daunting endeavor. The thickness of the Official Guide would seem to indicate that there are innumerable concepts that one must master in order to do well. Luckily for us, the opposite is true: the knowledge required to achieve a great score is a lot more basic than one would think. On the quant section, no knowledge beyond high school math is required; trigonometry, calculus, and advanced statistics are all gloriously absent. Simple quant problems test the same concepts as difficult ones; difficulty arises from how the concepts are layered on a given question. Johan Cruyff would tell us to approach even difficult problems in a simple way, looking for the basic concepts that we know how to apply and working through the problem from there. Percent problems are an especially good example of this:
In order to give his customers a 25 percent discount on the price and still net a 25 percent profit on the cost of an item, at what price should a merchant mark an item if it cost him $16.80?
Looking at this problem, we can see that we have to calculate two amounts based on percentages. Either one on its own would make a fairly simple GMAT problem, but having to interpret the information given and apply the percent change twice makes it far more difficult. So, how do we approach it? Again, Cruyff would tell us to look for simple steps. We know that the merchant wants a 25% profit on the item's cost of $16.80. For that, we simply multiply 16.80 by 1.25 to get $21.00. That's the price at which he should sell the item. We also know that he wants to give customers a 25% discount from the marked price. A common next step here is to multiply 21 by 1.25 to arrive at the marked price, but that's just the trap the GMAT writers expect you to fall into. How are discounts given on sale items? Typically, we subtract a percentage from the marked price. In this case, we know that $21.00 is the price AFTER the discount, so we want to set up our equation as .75(marked price)=21. From there, we can solve to find that the item should be marked at $28.00.
As we can see, simple concepts apply even on more difficult problems. These problems aren't monolithic chunks of complexity; rather, they can be broken down into basic steps and calculations that, when interpreted correctly, will lead to the right answer. The GMAT, like soccer, is simple; approaching it simply will yield the best results.
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