## Population increase

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### Population increase

by piyush_nitt » Fri May 08, 2009 5:37 am
What is the % increase in population of City K from 1980 to 1990?
a. In 1970 population of K was 160,000
b. In 1980 population of K was 20% greater than 1970 and in 1990 population is 30% greater than in 1970

IMO: B

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by DanaJ » Fri May 08, 2009 10:27 am
1 is useless because we don't have any info on 1980 or 1990.

2. Let x = population in 1970.
Population in 1980 will be 120% * x = 1.2x.
Population in 1990 will be 130% * x = 1.3x.

Now, say that from 1980 to 1990 the population grew by n%. This means that: 1.3x = (100 + n)/100 * 1.2x. As you can see, x can be very easiliy eliminated from both sides to get:

1.3 = (100 + n)/100 * 1.2

Solving for n is a breeze.
So 2 is indeed sufficient.

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