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Welcome to the third installment of our Fast Math series. (Miss the earlier installments? Start here.)
Here’s the basic premise: I’m always on the lookout for ways to get out of doing tedious paper calculations on the GMAT.
The awesome part: the test writers actually set this up for me! They know we’re not going to have to do a bunch of paper math in b-school or the real world, so they construct problems that allow us to take advantage of all sorts of shortcuts…if we’re paying attention.
Principle #3: Use benchmarks to find percents.
Some GMAT problems appear to involve tedious percent calculations, but they’re really not all that tedious if you take a step back and use benchmarks.
What are benchmarks? First, let’s start with a number—say, 140. Now, let’s say that the problem calls for 18% of 140. You could set up a couple of fractions and then simplify numerators and denominators…but ugh.
Here’s how to use benchmarks instead:
The starting number, 140, is 100%.
10% of 140 is 14. Therefore, 20% is twice that, or 28.
We’re trying to get to 18%, which is 2% less then 20%.
We already know that 20% = 28. Therefore, 2% = 2.8.
20% − 2% = 18%, so 28 − 2.8 = 25.2.
That’s it! The answer is 25.2
Any percentage can be calculated using some combination of “benchmark” percentages that are easier to find. The easiest-to-find benchmarks are 100%, 50%, 10%, and 1%. From 50%, you can move the decimal left once to get 5%. Using these 5 benchmarks, you can calculate anything, because you can “add up” percents.
For example, find 63% of 86.
63% = 50% + 10% + 3(1%)
50% of 86 is 43
10% of 86 is 8.6
1% of 86 is 0.86 (and we need 3%, so it’s really 3 × 0.86)
Around about now, I’d be glancing at the answer choices to see whether I can estimate from here, because adding that up is annoying. This is the GMAT, so it might just be enough to estimate low 50s. If I’m really pressed, I might go as far as, “It’s 51.6 plus a little less than 3, so around 54.” On the GMAT, that’ll be enough for me to get to the answer.
Practice that benchmarking until you can do it in your sleep (well, until you can do it at the restaurant table while estimating an 18% tip). And join us next time, when we’ll cover Principle #4! 📝
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Stacey Koprince is a Manhattan Prep instructor based in Montreal, Canada and Los Angeles, California. Stacey has been teaching the GMAT, GRE, and LSAT for more than 15 years and is one of the most well-known instructors in the industry. Stacey loves to teach and is absolutely fascinated by standardized tests. Check out Stacey’s upcoming GMAT courses here.