It would be wrong to think that the 20% changes cancel each other out and yield
a value equal to the original value. This is so because the value that goes up 20%
from January 1 to January 2 is different from the value that goes down from
January 2 to January 3. Since the percents are pieces of different wholes, they do
not simply cancel out. So you should instead use the percent change formulas given
in the previous section:
price on January 1 = $400
price on January 2 = $400(100% + 20%) = $400(120%) = $400(1.2) = $480
price on January 3 = 480(100% – 20%) = 480(80%) = 480(0.8) = $384Percent Greater Versus Percent Of
If you don’t read the following question carefully, you might fall for a trap:
150 is what percent greater than 50?
Many test-takers simply use the percent formula for this question:
150
50 =p
100 →^ p = 300
But this is wrong. Why? Because the question is asking, 150 is what percent greater
than 50, not what percent of 50. To calculate percent greater, use the following
formula:
percent greater = % of – 100%
In the previous example, 150 is 300% of 50, so it is (300% – 100%) = 200% greater
than 50.Plugging in Numbers with Percentages
In the section on fractions and decimals, you read that plugging in numbers was
a useful strategy in Discrete Quantitative questions that only give fractions and
no specified amounts. The same applies to percent questions. If you see a Discrete
Quantitative question with only percents and no actual amounts, plug in 100 for
the total.20% of the employees in a company are managers. 10% of these managers
have been with the company for at least 10 years. The number of managers
who have not been with the company for at least 10 years is what percent of
all the employees?SOLUTION: Let the total number of employees = 100. Thus the number of
managers is 20%(100) = 20. The percentage of managers who have not been
with the company for 10 years is 100% – 10% = 90%. Thus the number of
managers who have not been with the company for 10 years is 90%(20) = 18.
Now the question is, 18 is what percent of 100? The answer is 18 (notice how
simple the calculations are when you choose 100!).CHAPTER 10 ■ PART-TO-WHOLE RELATIONSHIPS 23103-GRE-Test-2018_173-312.indd 231 12/05/17 11:52 am