# SAT Math: Arithmetic

## Percents

The price of an item was marked down 40% for a seasonal sale.  During the final clearance, it was marked down 20% from the sale price.  The final price was what percent of the original price before it was discounted?

A.      20%

B.      30%

C.      40%

D.      48%

E.       60%

## Knowsys Method

Read the question carefully.  There are three different prices for a single item: the original price, the sale price, and the final clearance price.  You will only get this question right if you keep these prices straight.

Identify the bottom line.  The question asks you to find what percent the final price is of the original price.

Assess your options.  There are many ways to look at this problem and many ways to get to the right answer.  You want to use the most efficient way.  In order to do that, you will have to make sure that you follow the steps of the problem.  Use your Knowsys strategy of picking 100 whenever you do not know the actual number in a percent problem.

Attack the problem.   You do not know the original price of the item.  Your Knowsys strategy tells you to pick the number 100.  Let's say that the original price is 100.  What happens to that 100?

40% of that 100 is taken away.  That means that 60% of that 100 is left.  You can find out how much is left by multiplying 100 times .6 (the 60% converted to decimal form).

100 x .6

Then what happens to that price?  20% of the second price is taken away.  That means that 80% of the price is left.  You can find out how much is left by multiplying by .8:

100 x .6 x .8

Plug that into your calculator.  That represents all three prices from beginning to end.

100 x .6 x .8 = 48

Loop back.  You accounted for every change made to the price of the item.  All that is left is to realize that if the price is 100, that means that it was originally 100% of itself.  That is why you can tack on a percent sign to the end of your answer: 48%.