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Approximate Your Way to GMAT Math Success
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Approximation is a very powerful tool, one that most students do not take full advantage of on the GMAT. Watching people work through problems, I'm always amazed at how much useless work I see them do. To illustrate the point and show you some ways to cut down on the time you spend calculating, let's look a few examples.
Here's a classic approximation question, one where it's perfectly obvious what the GMAT expects you to do. This is from The Official Guide to Quantitative Review, p.67, #45:
61.24 * (0.998)^2
The answer choices are 1, 3, 4, 5, and 6, so when it says "approximately," it means what it says! Change 61.24 to 60, 0.998 to 1, and 403 to 400, and you have this:
60 * 1^2
Much simpler: the numerator is 60, the denominator is 20, and the answer is 3. If you didn't round those numbers off, you may never have gotten to answer. If you can calculate the square root of 403 on paper, more power to you, but you'd be wasting your time.
Let's turn to a question that isn't so obviously about rounding. It shows some of the more powerful approximation techniques that are available to you. This is #15 on p.22 of The Official Guide to GMAT Review:
The product of all the prime numbers less than 20 is closest to which of the following powers of 10?
Because this problem looks to be somewhat calculation-intensive, and because it includes the word "closest," you should notice immediately that it is essentially an approximation question. In addition, the GMAT usually doesn't expect you to round by much: if the answer turns out to be 10^6, it's more likely that the precise answer is something like 996,112 than 766,880.
The first step here is to line up all the numbers we need to multiply:
2, 3, 5, 7, 11, 13, 17, 19
Next, since we're ultimately looking for one very big round number (a power of ten), let's see which of these we can group into subsets that will multiply to round numbers:
2*5 = 10
3*7 = 20+ (actually: 21)
11*19 = 200+ (actually: 209)
13*17 = 200+ (actually: 221)
Note that, in approximating those results, I aggressively eliminated useless information, but kept the general outline. It doesn't matter whether 3*7 is 20 or 21, but it might be handy to know that I've rounded down for three of the four calculations. That's an indication that the eventual result will turn out low.
The approximate answer, then, is 10*20*200*200, or 8,000,000. Because we rounded three of the four components down a little, the precise answer will be higher than that, just enough to get it very close to 10,000,000": 10^7, choice (C). (If you're keeping score at home, the exact answer is 9,699,690.)
Applying These Tricks
There are several general guidelines you can take away from this example:
- More problems can be solved by approximation than you think.
- When you round up or down, make a note of which way you've adjusted.
- If you're multiplying two numbers that are each close to a round number, but differ from nearby round numbers in opposite directions (like 11 and 19, or 9 and 21), using the round numbers will get you very close.
- The answer choices are a major hint to whether approximation is appropriate. If the answer choices are spread out (as in the previous example), approximate away!
Like so many math tricks, it takes some practice to get comfortable with approximation. When you're working through sample problems, you have nothing to lose: if you approximate and end up not being able to pick between two answer choices, you've gotten some good practice, but you've also learned that a certain type of question may not be amenable to approximating. I strongly encourage trial and error, especially over the first few weeks of your GMAT preparation.
The most general rule--one that I've already repeated on this blog, and will doubtless bring up again and again--is that the GMAT is not designed to test your computation abilities. It tests your ability to think through problems and solve them quickly, and very often, old-fashioned computation is most certainly not the most efficient method.
About the author: Jeff Sackmann has written many GMAT preparation books, including the popular Total GMAT Math, Total GMAT Verbal, and GMAT 111. He has also created explanations for problems in The Official Guide, as well as 1,800 practice GMAT math questions.
|Total GMAT Math
The comprehensive guide to the GMAT Quant section. It's "far and away the best study material
available," including over 300 realistic practice questions and more than 500 exercises!