# A Guide to the GRE/The Up and Down Rule

## The "Up & Down" Rule

Increasing by a fraction or percentage requires decreasing by a smaller fraction or percentage to get back to the same quantity.

If a dress that sells for \$100 increases in price by 25%, its price goes up to \$125. To return the dress to its original price, its price would have to be reduced by 20%, not 25%. This is because the base number has increased. Increasing 60 by 20% yields a value of 72. 72, however, will have to be reduced by a lower percentage - about 16% - to get back to 60. With fractions, going down takes less than going up, since fractions are based on parts of the whole.

### Practice

1. A grocery store sells one third of its shortening. What percentage of its remaining shortening will it have to restock to restore the shortening supply to its present value?

2. An accountant's fees increase by 15%, but the account promises a discount to loyal customers which will make prices equal to the rate before the increase. What fraction of the new rate will the accountant have to charge customers receiving the discount?

3. Office supply sales increase by 40% in April but fall back to their original value in May. What fraction of April's office supply sales are May's office supply sales?

1. 50%

After selling of the shortening,remain. We are looking for the amount needed to return the shortening to the previous level. Let r equal the fraction that will be restocked.

+ r= 1 Take our initial equation.

r= Subtract from both sides.

r = .5 = 50% Divide both sides by r equals 50%.

2.

Let f equal the fraction that the account will charge of the new rate.

115(f) = 100

f == Divide both sides by 115. The fraction is

3.