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Did the population of Country P increase by more than 25% from 2000 to

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Did the population of Country P increase by more than 25% from 2000 to  [#permalink]

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New post Updated on: 28 Sep 2019, 15:14
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EMPOWERgmat DS Series:
Block 1, Question 2

Did the population of Country P increase by more than 25% from 2000 to 2005?

1) From 2000 to 2002, the population of Country P increased by 10% and from 2002 to 2005, the population of Country P increased by 14%
2) The Population of Country P in 2000 was 350,000 people


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Originally posted by EMPOWERgmatRichC on 24 Sep 2019, 16:30.
Last edited by EMPOWERgmatRichC on 28 Sep 2019, 15:14, edited 1 time in total.
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Re: Did the population of Country P increase by more than 25% from 2000 to  [#permalink]

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New post 24 Sep 2019, 18:01
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EMPOWERgmatRichC wrote:
EMPOWERgmat DS Series:
Block 1, Question 2

Did the population of Country P increase by more than 25% from 2000 to 2005?

1) From 2000 to 2002, the population of Country P increased by 10% and from 2002 to 2005, the population of Country P increased by 14%
2) The Population of Country P in 2000 was 350,000 people


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2) The Population of Country P in 2000 was 350,000 people

No info about percentage at all.

Insufficient

1) From 2000 to 2002, the population of Country P increased by 10% and from 2002 to 2005, the population of Country P increased by 14%

There is nice formula for successive percentage increase

\((a + b + \frac{ab}{100})\%\)=\((10 + 14 + \frac{140}{100})\%\)=25.4 %

Sufficient

Answer: A
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Re: Did the population of Country P increase by more than 25% from 2000 to  [#permalink]

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New post 28 Sep 2019, 15:04
OFFICIAL EXPLANATION

Hi All,

We're asked if the population of Country P increased by MORE than 25% from 2000 to 2005? This is a YES/NO question and can be solved in a couple of different ways, including logically (without doing any math) or TESTing VALUES.

1) From 2000 to 2002, the population of Country P increased by 10% and from 2002 to 2005, the population of Country P increased by 14%.

The information in Fact 1 gives us the necessary percentages to calculate what the overall percentage increase was from 2000 to 2005, so we would end up with a 'fixed' answer. Whether that value was more than 25% or not, it would be a definitive answer, so we would have the answer to the question - and thus, a Sufficient answer.

You can calculate the exact percentage increase in a couple of ways though:

Algebraically, it would be (X)(1.1)(1.14) = (1.1X)(1.14) = 1.254 = a 25.4% increase

With TESTing VALUES, let's set the initial population as 1,000.
The initial 10% increase would be 1,000 + (.1)(1,000) = 1,000 + 100 = 1,100
The next 14% increase would be 1,100 + (.14)(1,100) = 1,100 + 154 = 1,254
Total Percentage Increase = 1254/1000 = 1.254 = a 25.4% increase

Fact 1 is SUFFICIENT

2) The Population of Country P in 2000 was 350,000 people

Fact 2 tells us the 'starting number' of people in the year 2000, but tells us nothing about whether the population increased or decreased.
Fact 2 is INSUFFICIENT

Final Answer: A

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Re: Did the population of Country P increase by more than 25% from 2000 to   [#permalink] 28 Sep 2019, 15:04
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