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What was the percent increase in population of City K from

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What was the percent increase in population of City K from

by BTGmoderatorLU » Tue Jul 17, 2018 3:13 pm
What was the percent increase in 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% greater than it was in 1970, and in 1990 the population of City K was 30% greater than it was in 1970.

The OA is B.

Please, can someone assist me with this DS question? Thanks in advance!
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Source: — Data Sufficiency |

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by [email protected] » Tue Jul 17, 2018 7:10 pm
Hi All,

We're asked for the percent increase in population of City K from 1980 to 1990. This question can be solved in a couple of different ways. If we knew the exact populations in 1980 and 1990, then that would be enough information to answer the question (since we could then use the Percent Change Formula to calculate the percent increase). In addition, if we had a way to 'relate' the two numbers (re: a ratio or other percentage-based relationship), then that would also be enough to answer the question.

1) In 1970 the population of City K was 160,000

Fact 1 tells us NOTHING about the populations in 1980 or 1990.
Fact 1 is INSUFFICIENT

2) In 1980 the population of City K was 20% greater than it was in 1970, and in 1990 the population of City K was 30% greater than it was in 1970.

With the information in Fact 2, we can create the following Algebraic values...
Population in 1970 = X
Population in 1980 = 1.2X
Population in 1990 = 1.3X

Thus, we CAN determine the percent increase: (New - Old)/(Old) = (1.3X - 1.2X)/(1.2X) = .1X/1.2X = 1/12 = 8 1/3%
Fact 2 is SUFFICIENT

Final Answer: B

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Rich
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by Brent@GMATPrepNow » Sun Dec 01, 2019 4:53 pm
BTGmoderatorLU wrote:What was the percent increase in 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% greater than it was in 1970, and in 1990 the population of City K was 30% greater than it was in 1970.

The OA is B.

Please, can someone assist me with this DS question? Thanks in advance!
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
Brent Hanneson - Creator of GMATPrepNow.com
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