Percents

The Original Value

An important consideration when dealing with percents is the size of the total that you are taking a percent of. For example:

An item is discounted by 20%, and then a 20% surcharge is applied to the discounted price.
Quantity A	Quantity B
The price after the discount and surcharge	The original price

Two percent operations are performed. First, a price is discounted by 20 percent. The new price is now 80 percent of the original. Next, 20 percent is added to this new price. Two things are important to note here:

1. The percent increase (as a percentage) is the same as the percent decrease, and
2. the percent increase is based on the NEW, smaller price.

In dollar terms, the 20-percent increase will have to be smaller than the original 20-percent decrease, because you are adding 20 percent to a smaller number. Without any actual calculations, you can be confident that the price after the discount and the surcharge will be less than the original price.

You can also demonstrate this principle by picking a price for the item. As always, a good number to use when you work with percents is 100.

The 20-percent discount is 20 percent of 100 = 0.2 × 100 = $20.

The new price is $100 − $20 = $80.

The 20-percent surcharge is 20 percent of 80 = 0.2 × 80 = $16. Use the calculator for this if you need to.

The final price is $80 + $16 = $96.

The original price ($100) is larger than the final price after the discount and surcharge ($96). The answer is (B).

Strategy Tip:

When dealing with percents, always pay attention to the size of the original value. Thus, 20 percent of a small number is less than 20 percent of a larger number.