If each year the population of the country

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NandishSS: Master | Next Rank: 500 Posts; Posts: 366; Joined: Fri Jun 05, 2015 3:35 am; Thanked: 3 times; Followed by:2 members

If each year the population of the country

by NandishSS » Thu Feb 22, 2018 6:35 pm

If each year the population of the country grows by 20%, how many years will elapse before the population of the country doubles?

A. 3
B. 4
C. 5
D. 6
E. 7

OA: B

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Source: Beat The GMAT — Problem Solving | Thu Feb 22, 2018 6:35 pm

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ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 am; Thanked: 86 times; Followed by:15 members; GMAT Score:770

by ErikaPrepScholar » Fri Feb 23, 2018 8:36 am

If the population of the country grows by 20% each year, the population the next year will be 120% of the year before, or
$$1.2\cdot previous\ population$$
For each year, we'll multiply by 1.2 again. So after one year, the population will be
$$1.2\cdot original\ population$$
After two years, the population will be
$$1.2\cdot1.2\cdot original\ population=1.44\cdot original\ population$$
After three years, the population will be
$$1.44\cdot1.2\cdot original\ population=1.728\cdot original\ population$$
After four years, the population will be
$$1.728\cdot1.2\cdot original\ population=2.0736\cdot original\ population$$
We want to find how many years it will take to double the population, or
$$2\cdot original\ population$$
The population has slightly more than doubled after 4 years, so the answer is B.

Note: we could also express the equation for the country's population as $$1.2^x\cdot original\ population$$ where x is the number of years that have elapsed. Then we can set this equal to our expression for doubling the population: $$1.2^x\cdot original\ population=2\cdot original\ population$$ $$1.2^x=2$$ and then solve for x.

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by Scott@TargetTestPrep » Mon Jun 17, 2019 4:33 pm

NandishSS wrote:If each year the population of the country grows by 20%, how many years will elapse before the population of the country doubles?

A. 3
B. 4
C. 5
D. 6
E. 7

OA: B

We can use the formula N = P(1 + r/100)^t to solve the problem. Here P is the initial population and N is the population after t years with a growth rate of r percent. Furthermore, we can let P = 100; thus, N = 200 if the population doubles. So we can create the equation:

200 = 100(1 + 20/100)^t

2 = 1.2^t

We could use logarithms to solve this problem; however, we can also solve it by considering each answer choice.Notice that we need to find the smallest integer value of t such that 1.2^t is 2 (or more).

A) 3

1.2^3 = 1.728 (This doesn't work.)

B) 4

1.2^4 = 2.0736 (This works.)

Answer: B

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