Question

GRE Review: Percentages

Answer 1

\({\bf{Overview:}}\) remember, "percent" is derived from "per cent" which means "per 100"
so x% of y is (x/100) * y

> decimal to percents: remove the % symbol and divide by 100, or in other words, move the decimal place two to the left
ex: 25% becomes 25/100 or 0.25
> percent to decimal: multiply by 100 and add a % symbol
ex: 1/2 becomes 100/2, or 50, then add a % sign to get 50%

you'll want to know certain fractions as decimals from memory, like 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10. but if you forget you can always just divide the numerator by the denominator and then convert from decimal to percent

three most basic percent problems:

1. calculating x% of y, which, as we said earlier, is (x/100) * y
2. calculating "x is y% of what number"? we set x = y/100 * (the mystery number) and solve for the unknown
3. calculating "x is what percent of y" we set up x/y = unknown/100, where solving for unknown will give the unknown percentage

Answer 2

\({\bf{Percent~Increases~and~Decreases:}}\)

in general

percent change = [(final amount - initial amount)/initial amount] * 100
if the result is +, report a positive percent (decrease) and if the result is - report a negative percent change (decrease)

memorization tips:

- if a < b then the increase from a to b is greater than the decrease from b to a
- a decrease of a%, then a decrease by b% from that amount is smaller than a decrease of (a+b)% from the original amount
- an increase of a% then an increase by b% is greater than a (a+b)% increase from the original amount
- an increase by a% then another increase by a% is never equal to an increase of (a+a)%, same logic for decreases

to increase a number by a%, multiply by (1 + a%)
to decrease a number by a%, multiply by (1 - a%)

**** note **** a "percent increase" is not the same as "percent of"

let's say we increase from 100 to 300. 300 is "300% of" 100, using 300/100 = x/100, but it is a "200% increase" , using (300-100)/100 * 100 = 200%

Answer 3

Adapted from Barron's test prep book for the new GRE, 19th edition