Percentage Increase and Decrease Problems on the GRE

Remembering Percentage

In math, a percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred"). It is often denoted using the percent sign, " ". For example   (read as "forty-five percent") is equal to   or . Similarly  of the total number of students in a class = 

Percentage Increase or Decrease

Percentages are often used to express the increase or decrease of a measure relative to its original value. Some real life examples where you come across the changes expressed as percentages are:

Price of gasoline increased from   to   representing a   increase in price

Population of a town declined from    to  in a decade representing a   decline

And finally some of you may weigh twice as much as you were 10 years ago representing a 100% increase in weight!!

Here is a simple three step process to compute percentage changes:

1. Identify the change: First step is to find out what is the measure for which the percentage change needs to be calculated. You should identify the final value (i.e. the value after the change has occurred) and the original value (i.e. the value before the increase or decrease). If we are talking about an increase in price from  to , our original value is  and the final value is .
2. Find the change in value: This is the difference between final value and the original value. If we are talking about an increase in price from  to , the change in value is 
3. Express the change as Percentage: This can be easily done by dividing the change in value by the original value and multiplying by : In our example this is equivalent to:

Percentage change =   

 Percentage change problems are very common on the test. You may find percentage problems in the following situations:

1. Two step percentage change problems: In these types of problems you are first expected to calculate the original or final value based on the information provided. The context could be geometry or simple arithmetic. Once you have the original and final value, the question may ask you to calculate percentage changes
2. Find the original or final value based on percentage changes: In such problems you are expected to calculate the original value or the final value based on percentage change information.
3. Data interpretation: These problems expect you to obtain the final value and the original from graphs and expect you to calculate the percentage changes
   
   

Example:

The regular price for a television is $1900. At a sale, George bought the television at a discount of 10%. What was the amount of discount that George got for the television?

A) $19

B) $150

C) $180

D) $190

E) $200

Solution:

Step 1: In this problem we are told that George is getting a discount of 10% and that means there is a percentage decrease of 10%. We are expected to calculate the change in value based on the percentage decrease. Let’s summarize what we know:

 To calculate the discount amount, we need to calculate 10% of the regular price i.e. $1900.The discount amount = 

The correct answer is D.

Remember, if a quantity is increased or decreased more than once, you cannot simply add or subtract the percentages. You have to work out each increase or decrease step by step.

In order to solve percentage change problems quickly, it’s a good idea to remember some common percentage change values. The following tables show Percentage Increases and Percentage decreases for some commonly used numbers. 

Original value 100: Percentage change - Final values
Percentage Change	10	20	30	40	50	60	70	80	90	100	150	200	250	400
Increase - Final value	110	120	130	140	150	160	170	180	190	200	250	300	350	500
Decrease - Final value	90	80	70	60	50	40	30	20	10	0	-50	-100	-150	-300

Original value 50: Percentage change - Final values
Percentage Change	10	20	30	40	50	60	70	80	90	100	150	200	250	400
Increase - Final value	55	60	65	70	75	80	85	90	95	100	125	150	175	250
Decrease - Final value	45	40	35	30	25	20	15	10	5	0	-25	-50	-75	-150