Let’s go shopping.
After receiving an email from your favorite online shoe store with a voucher code for 35 percent off of any purchase, you decide it’s the perfect time to buy some new shoes. On the store’s website, you find that for today only the store is running a special sale where all shoes on their website are marked 25 percent off.
Doing some simple addition in your head (35 + 25), you figure that if you combine the voucher with the sale discount, you can buy any pair of shoes on the site for 60 percent off. What a deal!
Unfortunately, you’re in for a small surprise when go to checkout. You’ve miscalculated the combined discount.
Perhaps you’d never make this mistake in real life, but under the time crunch of the GMAT, it’s all too easy to make problems simpler than they actually are. Combined discounts, or otherwise known as stacked percentages, are a favorite trap on the GMAT.
The mistake in the example occurs when we added the percentages to arrive at a total discount of 60 percent. However, the discounts are being applied to two different entities – 25 percent off the original price and then 35 percent off this reduced price – so the percentages need to be multiplied and not added.
Let’s look again at this problem.
The one-day sale takes 25 percent off the original price of any pair of shoes, and then if you use the voucher, an additional 35 percent would be taken off the sale price. So the total discount would be
(1 – .25)(original price) x (1 – .35) =
.75(original price) x .65 =
The total discount is approximately 49 percent off. Still not too bad.
An easy way to work through these types of problems is to substitute 100 as the original price. So let’s say you want to apply your voucher and the sale discount to a pair of boots that originally cost $100.
The discount of 25 percent from the one-day sale makes the boots $75, ((100 – (.25 x 100) which is the same as ((1-.25) x 100)
Now we apply the voucher’s 35 percent discount to the $75 price tag, which equals $48.75
(1- .35)(75) = 48.75
This is $8.75 more than what you original thought you’d pay when you calculated a 60 percent discount: close, but not close enough for GMAT standards. Whenever you see stacked percentages, don’t be lulled into adding or subtracting the percentages. Multiply percentages when they’re being applied to different entities, and eliminate any answer choices that simply add or subtract the percentages.