Mahmoudfawzy83 wrote:
The dealer of an electronic store discounted the price of a television and a microwave oven by the same percentage. On which of the two articles did the shopkeeper make a greater profit?
(1) The articles were marked up by the same percentage
(2) The amount of discount was same for both the articles
This problem requires you to assume that the situation works like this:
Dealer purchases an item for a certain price -> marks it up by a certain percentage -> discounts it by a certain percentage -> sells it for the resulting price
The GMAT
does assume that you know how profit, revenue, and costs basically work, but I suspect that in an official problem, they would be more explicit
in the question stem about the fact that there was a markup. Without that information, I got a bit confused when I got to the first statement.
With that said, let's understand the question. We're looking to compare the dollar amount of profit on each item. That dollar amount is
the difference between the sales price, and the cost to the dealer. For the television, if the markup and discount are expressed as decimals, the profit is:
(cost of television * (1 + tv markup) * (1 - discount)) - cost of television
Or, simplifying by combining like terms, it's:
(cost of television) * ((1 + tv markup) * (1 - discount) - 1)
For the microwave, it's:
(cost of microwave) * ((1 + microwave markup) * (1 - discount) - 1)
Which one of these is greater?
Statement 1: The markup percentage was the same. So, we're comparing these two values:
(cost of television) * ((1 + markup) * (1 - discount) - 1)
and
(cost of microwave) * ((1 + markup) * (1 - discount) - 1)
Really, this is the same as just comparing the original cost of the television, and the original cost of the microwave. However, we don't know which one had a higher original cost, so we can't answer the question. This statement is insufficient.
Statement 2: The dollar amount of the discounts were the same. We already know that the percent of the two discounts were the same. For the dollar amount of the discounts to also be equal, that percent discount would have to be applied to the same marked up price. So, this statement is really saying:
(cost of television) * (1 + tv markup) = (cost of microwave) * (1 + microwave markup)
However, it's still possible that the original costs were different. For instance, suppose that the television originally cost the dealer almost nothing, and was subject to a huge markup. The microwave originally cost the dealer a lot, and was subject to a small markup. Even though the discounts were equal, the dealer would make more profit on the television. It could just as easily go the other way around, as well! So, this statement is also insufficient.
Statements 1 and 2 The dollar amount of the discounts were the same, according to statement 2. Based on this (plus the info in the question), we already figured out that the marked up price of each item was equal. Plus, from statement 1, we know that the markup percentages were equal. If the marked up prices both came out the same after applying the exact same markup, the original costs must have been equal as well!
These two statements together tell us that the two items cost the same amount. We also know that the markups and discounts were equal between the two items. Therefore, the shopkeeper made the same profit on both. That makes the question seem a bit strange: can we really answer "which is greater" with "neither, they're both the same?" Regardless, there's definitely a definitive answer, so the two statements are sufficient together and the answer to the problem is
C.
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