If it’s the autumn of an even-numbered year, change is in the air, or at least in the hot air of the politicians seeking election in November. Noting, evidently, that most people are unhappy, politicians repeat the word change more than any other (with the exception of John McCain, who in 2008 used the word “Petraeus” slightly more than he used “change”, but it was close!). Browse the political ads and stump speeches on YouTube and you won’t get too specific an idea of what each candidate promises, but, by George, they’ll certainly repeat the word “change” until you want to change the channel.
If you’ve clicked off of the Brown-vs.-Whitman or O’Donnell-vs.-sanity ads long enough to view this post, you’re probably looking to change your GMAT score and your MBA candidacy. If so, you’re in luck, because if there’s one thing you can be sure of on the GMAT, it’s change. Ratios, mixtures, proportions — they’re all GMAT problem types that focus on change.
And if you focus on that change in each problem, the change becomes the key to unlocking the entire problem – literally change you can believe in and should depend on. And, with a nod to Hillary Clinton, yes, this change post is one you can certainly Xerox if you’d like to. We don’t mind.
How can an emphasis on change improve your GMAT score?
Consider the question:
The average of 5 numbers is 6.8. If one of the numbers is multiplied by a factor of 3, the average of the numbers increases to 9.2. What number is multiplied by 3?
As with any problem, you should start with what you know. You know that, if the average of 5 numbers is 6.8, then the sum of those numbers is 5*6.8 or 34. Similarly for the new total, if the average is 9.2, then the sum of those five numbers is 5*9.2 or 46.
So we have:
Old total: 34
New total: 46
When problems involve a change – ratio problems in which a certain number is added or subtracted and the ratio changes; mixture problems in which something is added to or subtracted from the solution and the mixture changes, etc. – the key to solving them is typically the change itself. Almost always, the change is expressed in two ways:
x is added and the new ratio becomes…
one of the numbers is multiplied by 3 and the average becomes…
When you’re given two ways to mathematically express that change, use those two ways to set up an equation – you can then solve for a variable that links the past to the present (or the present to the proposed future, depending on how the question is asked) and that solution will allow you to fill in the entire puzzle.
In this case, we know that “multiplying one number by 3” also “increases the sum by 12”. Since the only number that changes is that number that is multiplied by 3, we know that the multiplying by 3 is the same as adding 12 to that number. So, mathematically, we can say that:
3x = x + 12
2x = 12
x = 6
Therefore, the number in question – that which is multiplied by 3 and in doing so is also added to 12 – is 6, and the correct answer is E.
Use change as your “anchor” in problems that emphasize a change in ratios, proportions, or any other elements of a mixture. By expressing the change in two ways, you’ll have an equation that will translate to both the initial and the final mixtures, and therefore will be able to answer any question that the GMAT asks about any part of the relationship. If politicians can use change as their platform to try to get to Washington, you can certainly use change as your springboard to Boston, Palo Alto, Evanston, or the other b-school campus of your choice.