Airline B’s average rating for convenience was approximately

In a survey, $100$ travel agents each ranked Airlines $A$, $B$, and $C$ in order of preference. Each of the $100$ travel agents also rated the three airlines in five categories on a scale of $1$ through $10$, with $10$ being the best rating.

Airline $B$’s average rating for convenience was approximately what percent greater than Airline $A$’s average rating for convenience?

  1. $30%$
  2. $36%$
  3. $40%$
  4. $57%$
  5. $64%$

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 15 of Section 4 of Practice Test 1. Those questions testing our knowledge of Graphical Methods for Describing Data 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 our paper.

We have both a pie graph and a table containing numerical data, so this question likely tests what we know about Graphical Methods for Describing Data. Also, the question likely tests our knowledge of Percents, since all of the answer choices have percentages. Let’s keep what we’ve learned about these skills at the tip of our minds as we approach this question.

What Do We Know?

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

 

  1. We want to know what percent greater Airline $A$’s convenience rating was compared to Airline $A$’s convenience rating
  2. The convenience ratings are provided in a table

 

Develop a Plan

We want to calculate a “percent greater” in this question. Thinking of an equation for percent greater, we do know from our knowledge of Fractions, Decimals, and Percents how to calculate a percent difference:

$$\Percent \Change = {\New \Value – \Original \Value}/{\Original \Value}·100%$$

Here, the “Original Value” is the value that we start with, the one our comparison is made relative to. Since we want to know the percent difference in Airline $B$’s convenience rating relative to Airline $A$’s convenience rating, the Original Value is Airline $A$’s convenience rating and the New Value is Airline $B$’s convenience rating. From the table, we can find these two values and plug them into our percent difference equation.

Solve the Question

From the table, we can find the convenience ratings for Airline $A$ and Airline $B$:

$$A_{\Convenience} = 5.1$$
$$B_{\Convenience} = 8.0$$

Using our percent difference equation, we find:

$\Percent \Change$ $=$ ${\New \Value – \Original \Value}/{\Original \Value}·100%$
$ $ $ $
$\Percent \Change$ $=$ ${B_{\Convenience} – A_{\Convenience}}/{A_{\Convenience}}·100%$
$ $ $ $
$\Percent \Change$ $=$ ${8.0-5.1}/5.1·100%$
$ $ $ $
$\Percent \Change$ $=$ $2.9/5.1·100%$
$ $ $ $
$\Percent \Change$ $=$ $57%$

The correct answer is D, $57%$.

What Did We Learn

Percent difference questions can be tricky. The key is to slow down and take our time identifying which number is the Original Value and which number is the New Value. It can be very easy to mistakenly put the New Value in the denominator in the percent difference equation, so let’s avoid that mistake. Also, let’s commit the formula to memory.

$$\Percent \Change = {\New \Value – \Original \Value}/{\Original \Value}·100%$$

 

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