The list price of a certain tool is $x$ dollars. In Store $A$ the original

The list price of a certain tool is $x$ dollars. In Store $A$ the original selling price of the tool was $\$50$ less than the list price, and the current selling price is $10$ percent less than the original selling price. In Store $B$ the original selling price of the tool was $10$ percent less than the list price, and the current selling price is $\$50$ less than the original selling price.

Quantity A $\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;$ Quantity B
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;$
The current selling price of the tool in Store $A$ $\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;$ The current selling price of the tool in Store $B$
  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal.
  4. The relationship cannot be determined from the information given.

So, you were trying to be a good test taker and practice for the GRE with PowerPrep online. Buuuut then you had some questions about the quant section—specifically question 1 of the second Quantitative section of Practice Test 1. Those questions testing our knowledge of Percents can be kind of tricky, but never fear, PrepScholar has got your back!

Survey the Question

Let’s search the problem for clues as to what it will be testing, as this will help shift our minds to think about what type of math knowledge we’ll use to solve this question. Pay attention to any words that sound math-specific and anything special about what the numbers look like, and mark them on your paper.

We see the word “percent” mentioned a couple of times. Percents of a number can be converted into decimal forms. We should expect to use our knowledge of Fractions and Decimals and Percents as we approach this question.
Let’s keep what we’ve learned about these math skills at the tip of our minds as we do this question.

What Do We Know?

Let’s carefully read through the question and make a list of the things that we know.

  1. The list price of a tool is $x$ dollars
  2. We want to compare the tool’s price after discounts between Stores A and B
  3. At Store A, the original selling price is $\$50$ less than the list price, and then the current selling price is $10$ percent less than the original selling price
  4. At Store B, the original selling price is $10$ percent less than the list price, and then the current selling price is $\$50$ less than the original selling price

Develop a Plan

We want to compare the current selling price of a tool between stores $A$ and $B$ . The question gives us the list price of the tool, which is $x$ dollars. Then from the question, it appears that we get to the current selling price by going from the list price, to the original selling price, and then to the current selling price.

$$\List \Price → \Original \Selling \Price → \Current \Selling \Price$$

Both stores apply the same two discounts to the tool, just in a different order. Store $A$ takes away $\$50$ from the price,
then deducts $10$ percent from the price. On the other hand, Store $B$ first deducts $10$ percent from the price, then takes away $\$50$ from the price. Let’s figure out which store gives the bigger overall discount.

Solve the Question

In Quantitative Comparison questions, we want to focus on what is different between the two quantities. The tool starts at $x$ dollars at both stores, and each store eventually takes away $\$50$ from the price of the tool. Doesn’t seem like we’ll get a difference between the stores there.

Both stores also took away $10$ percent of the cost of the tool. We know that the dollar amount of a $10$ percent reduction in price definitely depends on the price of an item when the percent deduction takes place. For example, if an item costs $\$200$, then we’ll take away $\$20$. But if an item costs $\$150$, then we’ll only take away $\$15$. So here we can see that the more expensive the tool is when the percent discount occurs, the greater the dollar discount equivalence of the $10$ percent discount.

Although the $\$50$ discount will always remove $\$50$ from the price, the $10$ percent discount will remove more from the tool’s price if it is applied when the tool is most expensive, i.e. before we discount the tool by $\$50$.

Since Store $B$ applies the $10$ percent discount before the $\$50$ discount, Store $B$’s $10$ percent discount will remove more from the tool’s price than Store $A$’s $10$ percent discount. And since Store $B$ has a bigger overall discount, the tool will cost less at Store $B$ than it does at Store $A$.

Since the tool will cost less at Store $B$, it’s price at Store $A$ is greater. So the answer is A, Quantity A is greater.

What Did We Learn

Sure, we could have chosen a random value for the tool’s price, plugged in numbers, did a bunch of calculations, and eventually figured out the answer. But you’re not taking the GRE to pursue a professional degree just to do things a mundane, uninspired, and inefficient way. Also, you could have read an inferior approach to solving this question somewhere else. Brute force will only get you so far, both in life and on the GRE, so let’s always keep our minds flexible and open to logical ways to approach problems.

 

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