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If in a certain population, people are born at an average rate of 9 pe [#permalink]
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Bunuel wrote:
If in a certain population, people are born at an average rate of 9 people every 2 seconds and people die at an average rate of 3 people every 2 seconds, by approximately how many people does the population increase in 1 day?

A. 17,280
B. 25,920
C. 129,600
D. 259,200
E. 388,800

If 9 people are born and 3 people die every 2 seconds, then the rate of increase is (9-3)= 6 people every 2 seconds, \(\frac{6p}{2secs}=\frac{3p}{1sec}\)

Population increase in one day

\(\frac{3p}{1sec}*\frac{60secs}{1min}*\frac{60mins}{1hr}*\frac{24hrs}{1day}=\frac{259,200p}{1day}\)

In one day: 259,200 people

For the arithmetic in the numerator, estimating and using the doubling/halving trick is easier

\((3*60*60*24)\approx(75*3,600)\)
\(=(150*1,800)=(300*900)=270,000\)


Answers are far apart. Only one answer is close to 270,000:

259,200
Answer D

*This explanation of how to do conversion problems by canceling units is excellent.
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Re: If in a certain population, people are born at an average rate of 9 pe [#permalink]
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Bunuel wrote:
If in a certain population, people are born at an average rate of 9 people every 2 seconds and people die at an average rate of 3 people every 2 seconds, by approximately how many people does the population increase in 1 day?

A. 17,280
B. 25,920
C. 129,600
D. 259,200
E. 388,800



the above information gives 6 people are born every 2 seonds or 3 people every 1 second, that means we get the below calculation

3*60*60*24=259200 option D
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If in a certain population, people are born at an average rate of 9 pe [#permalink]
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Bunuel wrote:
If in a certain population, people are born at an average rate of 9 people every 2 seconds and people die at an average rate of 3 people every 2 seconds, by approximately how many people does the population increase in 1 day?

A. 17,280
B. 25,920
C. 129,600
D. 259,200
E. 388,800


Every 2 seconds we have a net increase of 6 people, or 3 people/second. 3p/s * 60s/1m * 60m/1hr * 24hr/d is approximately 10,000p/hr * 24 = 240,000 p/hr. D

Originally posted by TestPrepUnlimited on 07 Oct 2019, 10:16.
Last edited by TestPrepUnlimited on 24 Oct 2019, 21:40, edited 1 time in total.
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Re: If in a certain population, people are born at an average rate of 9 pe [#permalink]
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Bunuel wrote:
If in a certain population, people are born at an average rate of 9 people every 2 seconds and people die at an average rate of 3 people every 2 seconds, by approximately how many people does the population increase in 1 day?

A. 17,280
B. 25,920
C. 129,600
D. 259,200
E. 388,800


The growth rate, i.e., the difference between the number of people born and those who have died, per second, is:

9/2 - 3/2 = 4.5 - 1.5 = 3

So the growth rate is 3 x 3600 x 24 = 259,200 per day.

Answer: D
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If in a certain population, people are born at an average rate of 9 pe [#permalink]
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Bunuel wrote:
If in a certain population, people are born at an average rate of 9 people every 2 seconds and people die at an average rate of 3 people every 2 seconds, by approximately how many people does the population increase in 1 day?

A. 17,280
B. 25,920
C. 129,600
D. 259,200
E. 388,800


Population increases by = 9-3= 6 people every 2 seconds = 3 people / second = (3*60*60*24 = 259,200) people/ day

IMO D

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Re: If in a certain population, people are born at an average rate of 9 pe [#permalink]
Expert Reply
People are born at an average rate of 9 people every 2 seconds: 1 sec = \(\frac{9}{2}\) = 4.5

People die at an average rate of 3 people every 2 seconds: 1 sec = \(\frac{3}{2}\) = 1.5

=> Increase in '1' sec = 4.5 - 1.5 = 3

=> In a day: 24 * 3600 secs.

Total increase: 24 * 3600 * 3 = 259,200

Answer D
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If in a certain population, people are born at an average rate of 9 pe [#permalink]
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If in a certain population, people are born at an average rate of 9 people every 2 seconds and people die at an average rate of 3 people every 2 seconds, by approximately how many people does the population increase in 1 day?

A. 17,280
B. 25,920
C. 129,600
D. 259,200
E. 388,800


The people are born at an average rate of 9 people every 2 seconds and people die at an average rate of 3 people every 2 seconds.

From the above statement, we can conclude that the population increases by 9-3 = 6 people every 2 secs i.e 3 people every sec.

So in one day, we have 24 * 60 * 60 Secs and the population will increase by 24*60*60 * 3 people.

Trick here is, you don't need to do the entire calculation. If you do so, you might end up spending more time in this question .

Ans = 24*60*60 * 3

While analyzing the units digits of the product , we can definitely say that the answer should end with '200' . This is enough to figure out that Option D is the correct answer. The rest of the options can be eliminated.


Thanks,
Clifin J Francis,
GMAT QUANT SME
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