GRE Math: How to solve Word Problems with Examples

GRE Math: How to solve Word Problems with Examples ?

The ONLY formula we need to solve this kind of problems is:

Base x Rate = Percentage

where:
Percent (Rate): A fraction whose denominator is 100.
Percentage: The product of a rate (percent) and another number called the base.

Percentages have the unit of the base and the description of the rate.

Example Problem 1: 

ITT graduated 120 students from a math class after having "washed out" 40 of them. What percent of the class graduated?

Solution:
120 = number of students graduated
40 = number of students not graduated
percent of students graduated = ???
The total number of students in the class is 120 + 40 = 160
If 120 graduated out of 160, then the percent is 120/160 = 0.75 = 75%

Example Problem 2: 

A company produced 800 good shafts and 30 defective shafts. What percent of
their production was defective?

Solution:

800 = number of good shafts
30 = number of defective shafts
percent of defective shafts = ???
The percent is 30/830 = 0.0361 = 3.61% (830=800+30)

Example Problem 3: 

Mary received $90 for her weekly allowance. Then she received two 15% increases. How much is her weekly allowance after the second increase?

Solution:

NOTE: you cannot add percents.

90 = old allowance
15% = first increase
15% = second increase
allowance after the second increase = ???

After the first increase, her allowance was: 90 + 90(.15) = $103.5
After the second increase, her allowance is: 103.5 + 103.5(.15) = $119.03

Example Problem 4: 

John just received a 10% raised on his salary. If he now receives $170 per week,
what was his salary before the raise?

170 = current salary
10% = raise
salary before the raise = ??? = x5

Looking at the previous example we know that: x + x(.1) = 170 (Why?)
Solve for x: 1.1x = 170
x = $154.54

Does the answer make sense?

Well, if he is getting $170 now, and we know that he got a raise; then, he used to get less than $170 or $154.54. So, yes, the answer makes sense.