|
|
Sometimes, percent problems on the GRE include unspecified numerical amounts; often, these unspecified amounts are described by variables. For example:
A shirt that initially cost d dollars was on sale for 20% off. If s represents the sale price of the shirt, d is what percentage of s?
This is an easy problem that might look confusing. To solve percent problems such as this one, simply pick 100 for the unspecified amount (just as you did when solving successive percents).
If the shirt initially cost $100, then d = 100. If the shirt was on sale for 20% off, then the new price of the shirt is $80. Thus, s = 80.
The question asks: d is what percentage of s, or 100 is what percentage of 80? Using a percent table, fill in 80 as the whole amount and 100 as the part. You are looking for the percent, so set up a proportion, cross-multiply, and solve:
|
|
Therefore, d is 125% of s.
The important point here is that, like successive percent problems and other percent problems that include unspecified amounts, this example is most easily solved by plugging in a real value. For percent problems, the easiest value to plug in is generally 100. The fastest way to success with GRE percent problems with unspecified amounts is to pick 100 as a value. (Note that, as you saw in the fractions chapter, if any amounts are specified, you cannot pick numbers—you must solve the problem algebraically.)
If your stock portfolio decreased by 25% and then increased by 20%, what percent of the original value would your new stock portfolio have?