Mental Math: Percents

Can you find ten percent of a number? Can you add? If so, I can show you a faster way to calculate percents.

With the possible exception of 50%, there's no percentage easier to calculate than 10. Just move the decimal place one to the left. 100 becomes 10, 55 becomes 5.5, and 0.8 becomes 0.08.

Of course, the GMAT usually doesn't ask you to come up with ten percent of things. However, ten percent (and, by extension, one percent) is the fundamental building block of all other percents. Let's start with a couple of simple examples.

Tipping

The classic example of mentally calculating percents is tipping. Many people use the "double the tax" method, which works nicely in states where the sales tax is near eight percent. When you compute a tip this way, here's the mathematical representation of what you're doing, where x stands for the total price of the meal:

16% * x = 2 * 8% * x

If you want to be more generous and tip 20%, you can use the same reasoning, just starting with 10% instead of 8%:

20% * x = 2 * 10% * x

In your head, you're calculating as follows: "The tab is $65, so ten percent of that is $6.50, which means my tip should be double that, which is $13.00." Percents, of course, can be more complicated than that, but that technique is the backbone of coming up with any percentage you may need on the GMAT.

Tens, Fives and Ones

Just like 20% is easy (once you have 10%), 5% and 1% are simple, as well. If you know that 10% = $6.50, you're one small step away from knowing that 5% = $3.25 and 1% = $0.65. So, if you wanted to calculate 16% (and the receipt didn't conveniently show 8% sales tax!), you could simply add the three:

$6.50 + $3.25 + $0.65 = $10.40.

That isn't the only way to get to 16%. You could start by finding 20% (remember, double 10%) and subtract 4% (in other words, one percent, four times), as follows:

($6.50)(2) – ($0.65)(4) = $13.00 - $2.60 = $10.40

Any number can be expressed as a combination of tens and ones. It may be easier to use fives, as well. Once you know that 45 = 10(4) + 5, or than 28 = 10(3) – 1(2), you're just a couple of easy steps away from calculating a percentage.

The Mental Math Mantra

Every time I introduce a new mental math tip, I have to say it again: you won't instantly see a huge improvement in speed. You might even slow down a bit. If you practice doing percentages this way, though, you will soon find that you're doing them much more quickly than you ever did before.

Not only will this approach end up being faster, it will result in fewer careless mistakes. I've watched so many students misplace decimal points or forget to carry digits when multiplying, I'm confident that any method that avoids those things will be to your benefit.

Remember: you don't have to be at your desk, working through GMAT problems to practice a tip like this one. Next time you leave a tip, ignore the tax and calculate it yourself. If something is on sale at the grocery store and the markdown is taken at the register, see how quickly you can come up with the sale price. The more you do that, the more comfortable you'll be with percents, and the more efficient you'll be on the GMAT.

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.

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