What was the percent increase in the population of City K from 1980 to 1990 ?

[BTGModeratorVI]

What was the percent increase in the population of City K from 1980 to 1990 ?

(1) In 1970 the population of City K was 160,000
(2) In 1980 the population of City K was 20 percent greater than it was in 1970, and in 1990 the population of City K was 30 percent greater than it was in 1970.

Answer: B
Source: GMAT prep

[Brent@GMATPrepNow]

What was the percent increase in the population of City K from 1980 to 1990 ?

(1) In 1970 the population of City K was 160,000
(2) In 1980 the population of City K was 20 percent greater than it was in 1970, and in 1990 the population of City K was 30 percent greater than it was in 1970.

Answer: B
Source: GMAT prep

Target question: What was the percent increase in the population of City K from 1980 to 1990 ?

Statement 1: In 1970 the population of City K was 160,000
Since we're given no information about the population in 1980 or 1990, it's impossible to answer the target question.
Statement 1 is NOT SUFFICIENT

Statement 2: In 1980 the population of City K was 20 percent greater than it was in 1970, and in 1990 the population of City K was 30 percent greater than it was in 1970.
Let x = the population in 1970
So, 1.2x = the population in 1980
And 1.3x = the population in 1990

Percent increase = (100)(1990 population - 1980 population)/(1980 population)
= (100)(1.3x - 1.2x)/(1.2x)
= (100)(0.1x)/(1.2x)
= 10/1.2
So, the percent increase = 10/1.2 percent (we need not actually evaluate the actual fraction)

Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent