Pop quiz: 1) Your restaurant bill came to exactly $64.00 and you want to leave a 20% tip. How much do you leave? 2) You’re running a charity half-marathon and your fundraising goal is $6000. You’ve raised $3300. What percent of your goal have you reached? 3) Your $20,000 investment is now worth $35,000. By what percent has your investment increased in value?
[Answers: $12.80; 55%; 75%]
If that was easy for you, good. It better have been. After all, you’re applying to graduate school and that’s maybe 6th grade math in three real-life contexts. Percents are not hard! But percent problems can be. And that’s what savvy GMAT test-takers need to learn:
On the GMAT, percent problems aren’t hard because of the numbers. They’re hard because of the words.
Consider two situations:
1) A band sells concert t-shirts online for $20 each, and in California, web-based sales are subject to a 10% sales tax. How much does a California-based purchaser pay in sales tax after buying a t-shirt?
2) At a concert in California, a band wants to sell t-shirts for $20. For simplicity’s sake at a cash-only kiosk, the band wants patrons to be able to pay $20 even – hopefully paying with a single $20 bill – rather than having to pay sales tax on top. If t-shirts are subject to a 10% tax on the sale price, and the shirts are priced so that the after-tax price comes to $20, how much will a patron pay in sales tax after buying a t-shirt?
So what are the answers?
The first, quite clearly, should be $2. Take 10% of the $20 price and there’s your answer. And taking 10% is easy – just divide by 10, which functionally means moving the decimal point one place to the left and keeping the digits the same.
The second is not $2, however, and the reason is critical to your preparation for percent questions above the 600 level on the GMAT: the percent has to be taken OF the proper value. Patrons will pay 10% OF the before-tax price, not 10% of the after-tax price. $20 is the after-tax price (just as $22 is the after-tax price in the first example…note that there you definitely did not take the 10% of the $22 after-tax price!). So the proper calculation is:
Price + 10% of the Price = $20
1.1(P) = 20
P = 20/1.1 = 18.18
So the price comes out to $18.18, meaning that $1.82 is the amount paid in tax.
While the calculation of 20/1.1 may have been annoying, it’s not “clever” or “hard” – the reason that many people will just say $2.00 to both isn’t that they screwed up dividing $20 by 1.1, but instead because they saw a percent problem with two numbers (10% and $20) and just “calculated a percent.” That’s what makes the majority of GMAT percent problems tricky – they require an attention to detail, to precision in wording, for examinees to ensure that the (generally pretty darned easy) percent calculations are taking the percent of the proper value.
They’re logic puzzles that require a bit of of arithmetic, not simple arithmetic problems that just test your ability to divide by 10 absent critical thought. So as you approach GMAT percent problems, remember that the math should be the easy part. GMAT percent problems are often more about reading comprehension and logic than they are about multiplication and division.
By Brian Galvin.