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# The population of City X doubles every 25 years. If this rate continue

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
The population of City X doubles every 25 years. If this rate continue  [#permalink]

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06 Apr 2017, 01:42
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Difficulty:

25% (medium)

Question Stats:

78% (01:36) correct 22% (01:48) wrong based on 74 sessions

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The population of City X doubles every 25 years. If this rate continues for the foreseeable future, how many centuries will it take for the population to increase from 20,000 to 1,280,000?

A. 6
B. 4.5
C. 2.5
D. 2
E. 1.5

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Re: The population of City X doubles every 25 years. If this rate continue  [#permalink]

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06 Apr 2017, 03:20
1
Bunuel wrote:
The population of City X doubles every 25 years. If this rate continues for the foreseeable future, how many centuries will it take for the population to increase from 20,000 to 1,280,000?

A. 6
B. 4.5
C. 2.5
D. 2
E. 1.5

20000---after 25 years---40000---after 25 years---80000---after 25 years---160000---after 25 years---320000---after 25 years---640000---after 25 years---1280000

so from 20000 to 1280000 it takes 25*6 years i.e. 150 years = 1.5 centuries

Hence option E is correct
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Re: The population of City X doubles every 25 years. If this rate continue  [#permalink]

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06 Apr 2017, 07:01
1,280,000/20,000 = 64 times = 2^6 times

25*6 = 150 years = 1.5 centuries

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Re: The population of City X doubles every 25 years. If this rate continue  [#permalink]

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06 Apr 2017, 08:14

20000*2^n=1280000

2^n=64
n=6

it takes 25 years to double
6 times will take 25*6=150/100=1.5 centuries
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Re: The population of City X doubles every 25 years. If this rate continue  [#permalink]

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12 Apr 2017, 12:05
1
Bunuel wrote:
The population of City X doubles every 25 years. If this rate continues for the foreseeable future, how many centuries will it take for the population to increase from 20,000 to 1,280,000?

A. 6
B. 4.5
C. 2.5
D. 2
E. 1.5

We are given that the population of City X doubles every 25 years. We need to determine the number of centuries it will take the population to increase from 20,000 to 1,280,000.

We can start by making a list (or table) that keeps track of doubling the population every 25 years:

Current: 20,000
After 25 years: 40,000
After 50 years: 80,000
After 75 years: 160,000
After 100 years: 320,000
After 125 years: 640,000
After 150 years: 1,280,000

Thus it takes 150 years, or 1.5 centuries, to increase the population from 20,000 to 1,280,000.

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Re: The population of City X doubles every 25 years. If this rate continue  [#permalink]

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02 Dec 2018, 20:37
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Re: The population of City X doubles every 25 years. If this rate continue   [#permalink] 02 Dec 2018, 20:37
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# The population of City X doubles every 25 years. If this rate continue

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