Percent Change for Graphs
Percent change also shows up in Data Interpretation problems such as the following:
__Employees' Annual Salary, 2012 to 2015__
What is the percent change in Jacob's annual salary from 2012 to 2015? Round the answer to the nearest tenth of a percent.
Is this problem asking you to calculate a percent increase or percent decrease?
Incorrect.
Right!
Since the original quantity is _smaller_, this problem involves a percent _increase_. Similarly, an original quantity that is larger means that you should calculate a percent decrease.
Also, by identifying the original quantity, you can make sure that you are __Plugging In__ the correct values into the percent change formula:
$$\displaystyle \mbox{Percent change} = \frac{\mbox{Difference}}{\mbox{Original}}\cdot 100\%$$
So, what is the percent increase in Jacob's annual salary from 2012 to 2015? Round the answer to the nearest tenth of a percent.
Incorrect.
Since you already identified that this problem involves a percent _increase_, you should immediately discard this answer choice.
Incorrect.
Make sure you plug in the _original_ value in the denominator.
Correct!
$$\displaystyle \mbox{Percent change} = \frac{50,000 - 45,000}{45,000}\cdot 100\%$$
$$\displaystyle \mbox{Percent change} =\frac{5,000}{45,000}\cdot 100\% \approx 0.111 \cdot 100\% = 11.1\% .$$
Now, try to answer another question regarding the same data:
__Employees' Annual Salary, 2012 to 2015__
Who had the greatest percent increase in their salary from 2012 to 2015?
Correct!
To determine who had the greatest percent increase in salary from 2012 to 2015, you may have calculated each percent increase separately and then compared.
However, you could have also saved time by __Ballparking__ the values from the graph and then estimating the calculations.
For example, Carlos' 2012 salary could be estimated as $89,000 and his 2015 salary as $98,500. Then, the difference of $9,500 would be approximately what portion of his original 2012 salary?
Incorrect.
$9,500 would be exactly 10% of $95,000, so $9,500 is a little _more_ than 10% of $89,000.
Incorrect.
Carlos had the greatest dollar amount increase, but when calculating the percent change, you need to compare the difference to the original amount.
Incorrect.
Check your calculations again carefully.
Default step content.
Exactly!
$9,500 would be exactly 10% of $95,000, so $9,500 is a little _more_ than 10% of $89,000.
To sum up:
[[summary]]
Problems that require __percent change__ calculations are commonly found on the GRE. Words like percent increase, percent decrease, percent more, percent less can help you identify percent change problems.
To calculate percent change, you should use the following formula:
$$\mbox{Percent change} = \frac{\mbox{Difference}}{\mbox{Original}}\cdot 100\%$$
Continuing this way with the rest of the employees, you could have quickly found that Grace had the greatest percent increase.
Percent decrease
Percent increase
-11.1%
10%
11.1%
Carlos
Grace
Jacob
10%
a little more than 10%
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