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

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

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Updated on: 28 Sep 2019, 15:14
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81% (01:14) correct 19% (01:14) wrong based on 58 sessions

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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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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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Earn KUDOS! Share your explanations for kudos from other members, and the EMPOWERgmat team. Even if you're not sure, share your explanation to help boost your learning. Post your reasoning why the answer you chose is correct within 48 hours of this post.

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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

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

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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

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Rich
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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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