How to solve problem with multiple percentage changes on th GRE?

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.

 Let’s see an example where this important concept is used.

Example:

The population of a town increased by 20% between 1989 and 1995. If the population increased again by 10% from 1995 till 2003, what is the percentage increase in the population between 1989 and 2003?

A) 

B) 

C) 

D) 

E) 

Solution:

Step 1: This is a two-step percentage change problem. Remember if a measure 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.

Even though 30% is a very tempting answer, it’s wrong!

Let’s say the original population in 1989 is  . Sure we don’t know  . However the question wants us to know the percentage increase and therefore it will eventually get canceled.

Since the population increased by 20% between 1989 and 1995, the population at the end of 1995 is

Since the population increased by 10% between 1995 and 2003, the population at the end of 2003 will be (remember you now need to use the population in 1995 as the original value i.e.  )

Step 2: % Change in population between 1989 and 2003 =

 .

The correct answer is D

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
Increase - Final value	110	120	130	140	150	160	170	180	190	200
Decrease - Final value	90	80	70	60	50	40	30	20	10	0

Original value 50: Percentage change - Final values

Percentage Change	10	20	30	40	50	60	70	80	90	100
Increase - Final value	55	60	65	70	75	80	85	90	95	100
Decrease - Final value	45	40	35	30	25	20	15	10	5	0