# A Guide to the GRE/Percentages

## Percentages

Percentage is a fraction of 100. 11% = .11 =

Percent simply means “per hundred.” However, be careful not to mix up the two key ways in which percentages are used.

Do not mix up changing to a percentage with changing by a percentage.

If a group of 100 members decreases to 20% of its membership, its membership goes down to 20. If the group decreases by 20%, it goes down to 80. Increasing to 110% is the same as increasing by 10%. This also applies to fractions and decimals but is an especially common error with percentages.

### Practice

1. What is 30% of 80?

2. If a bank account worth \$10,000 increased in value by 25%, how much did it increase, and how much is it worth now?

3. If a bank account worth \$10,000 decreased in value to 25% of its worth, how much did it decrease, and how much is it worth now?

1. 24

30% of 80 = .30(80) = .3(80) == 24

2. The bank account's value increased by \$2,500. It increased to \$12,500.

25% of 10,000 = .25(10,000) =

This value must be added to the original total. The account increased by 25%, and increased to 125% of its previous value.

3. The bank account's value decreased by \$7,500. It decreased to \$2,500.

25% of 10,000 = .25(10,000) =

Since the bank account decreased to this percentage, this amount is the new value. It must be subtracted from the old value to determine how much the account decreased by.