In order to give his customers a 25-percent discount on the price and

Let's talk strategy here. It looks like many of the approaches in this forum focus blindly on the math, but remember: the GMAT is a critical-thinking test. For those of you studying for the GMAT, you will want to use strategies that actually minimize the amount of math that needs to be done, making it easier to manage your time. The "GMAT Jujitsu" I will show you here will be useful for numerous questions, not just this one. My solution here is going to walk through not just what the answer is, but how to strategically think about it.

Let's start with breaking down the original question. We know that the the cost of the item is \($16.80\). We also know that \(Profit = Revenue - Cost\). If the merchant wants to have a profit of 25% of the cost, that means that the revenue (the price he actually charged for the item) must be \(1.25*Cost\). After all, \(Profit = 1.25*Cost - Cost = .25*Cost\). Note that this part of the problem is not a percentage change issue, but it looks a little like one, because in the end you are looking for Revenue. In order for Profit to be 25% of Cost, then the Revenue must be 125% "of" cost. Our leverage from here on out, however, is the revenue (\($16.80*1.25\)), since this is the amount of money the merchant receives.

Here is where the first strategic approach comes in. I call it in my classes "Fractions Are Your Friends." Many math questions are made easier if you can think of decimals in terms of their corresponding fractional equivalents. Decimal multiplication and division -- while useful -- are often the long way around when it comes to math. It should be easy to see that \(1.25 = \frac{5}{4}\). Thus,

\(Price_{(Actual)}=$16.80*1.25=$16.80(\frac{5}{4}\))

You should be able to see how quickly we can divide \($16.80\) by \(4\), and then multiply by \(5\). If you use the fractions and break up math into easier-to-digest parts, the math is doable in your head. This is not accidental. The GMAT often designs problems so that the math is easy for those that know how to think about the problems. For purposes of visualization, here is what it looks like:

\(16.80*\frac{5}{4}=(\frac{(16+.80)}{4})*5=(4+.2)*5=20+1=21\)

The actual price is \($21\).

Now, this price is the what the merchant is actually charging his customers. This, however, is the already-discounted price. The target of this question is the price at which the original item was marked. A discount is a percentage change, so we can use the formula \(V_{(final)}=V_{(initial)}*(1\pm(\frac{\%}{100}))\). In the case of this question, our actual price is the final value, \(V_{(final)}\). Our initial value, \(V_{(initial)}\), is what the merchant originally wanted to charge. Using "Fractions Are Your Friends" again, we get:

\(V_{(final)}=V_{(initial)}*(1\pm(\frac{\%}{100}))\)
\($21=\text{Price}_{(initial)}*(1-(\frac{25}{100}))\)
\($21=\text{Price}_{(initial)}*(1-\frac{1}{4})\)
\($21=\text{Price}_{(initial)}*(\frac{3}{4})\)
\(\text{Price}_{(initial)}=21*(\frac{4}{3})=$28\)

Again, notice how easy it is if you keep the numbers in fractions. \($21*1.3333\) is messy. But cancelling out the factor of \(3\) from \(21\) (leaving \(7*4\) in the numerator) is a piece of proverbial cake.

The answer, therefore, is E.