GMAT Quantitative Section: Stacking Percents
September 15, 2012
The Wrentham Village Premium Outlets are a great place to stop for cheap brand-name clothes, and they’re a popular tourist destination for visitors to Massachusetts. Like all tourist/retail locations, they need to get people in the door. They’ve tried lot of things, but their latest gimmick has interesting implications for GMAT students. They’ve started stacking discounts.
Nearly every store in the mall has signs that say something like, “65% off, PLUS take an additional 20% off!” Moreover, a coupon book gives additional discounts—the particular store with that sign also offered 15% off purchases over a certain value.
To the unenlightened, this seems too good to be true. After all, 65% + 20% + 15% = 100%. Are we seriously to believe that the outlet store is giving away things for free?
Well, that might be a trap answer on the GMAT—and it’s a trap answer for the unwary consumer as well. But because we have been practicing GMAT quant, we know better. Even though the signs say “additional” and “plus,” we’re not really adding. 65% off means that the baseline price 35% of the retail value, and a further 20% off means we pay 80% of that discounted value. When translating from English to Math, the word “of” means “times.” So, when we take a percentage “of” a percent, we multiply; the results of the previous example are as follows:
(1 – 0.65)(1 – 0.2)(1 – 0.15) = (0.35)(0.8)(0.85) = 0.238
We end up with a 76.2% discount all told; that’s a pretty good deal, but hardly the 100% sale that some might have mistakenly expected!
When stacking percentage increases or decreases on the GMAT, you need to multiply—or, you can pick 100 and plug it into the equation. But however you solve, you cannot just add the numbers together; and you can quickly rule out any answer choice that is just a sum of the percents in the stem.