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Brian Galvin is the Director of Academic Programs at Veritas Prep, where he oversees all of the company’s GMAT preparation courses.
At any given time, the Forbes magazine list of the richest people in the world will include multiple members of the Walton family, with money coming from family patriarch Sam Walton’s Wal-Mart fortune. For one person to become a billionaire is an unthinkable feat; for a man to ensure that each of his children will not only be a billionaire, but rank highly on the list of the world’s richest people, is an unbelievable feat. And Sam Walton owes much of it to a concept that will serve you well on the GMAT: the mathematical concept of “greater than” (represented as >) includes numbers just a tiny fraction above that limit.
Walton’s competitive advantage in his first retail stores was that he was willing to accept a smaller markup on his items in order to attract more customers with a low price. He knew that “> $3.00” included, for example, $3.01, and not merely rounder (and more profitable) numbers like $3.50 and $4.00. Content with a modest profit-per-item if it eventually brought him a massive number of items sold, Walton built an empire on fractional profits – billions of dollars a penny at a time.
On the GMAT, you can employ this same ideology – after all, business schools love a business model that leads to billions of dollars – to conquer difficult Data Sufficiency problems. Inequality problems often require this concept. Consider the question:
If x > 0, is x > 6?
(1) x2 > 35
(2) x3 > 217
Statement 1 may look pretty tempting, as if x2 is greater than 35, you might think that it must be 36 or higher, making x at the very least 6. But x2 can be 35.01, in which case x would be just slightly less than 6. Because of this, statement 1 is not sufficient. Statement 2 is, indeed, sufficient. If x3 were 216, x would be 6; since we know that x3 is greater than 216, then x must be greater than 6.
Particularly when dealing with exponents and roots, using fractions and decimals may seem cumbersome, or may not even occur to you. But in cases like the above, it’s crucial that you consider the potential for those small, fractional shifts off of the value in the inequality, as the GMAT loves to test your ability to recognize those Waltonesque marginal changes. You don’t need to fully calculate these minute values if, like Walton, you simply consider what would happen if you took the “obvious” value and shaved it by a mere fraction. Calculate the value for the integer, and then move the decimal slightly to see what the change would be. As Walton found, those tiny insights can lead to your posting huge numbers.
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