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18 00:00

Difficulty:   95% (hard)

Question Stats: 23% (02:57) correct 77% (03:01) wrong based on 132 sessions

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The GDP of a country is $13.8 billion, and the total production of one of its industries is$3.3 billion. If the GDP were to grow by 5% per year in the future, which of the following would be the MINIMUM required annual growth in this industry that would it represent more than half of the GDP in ten years?

A. 10%
B. 15%
C. 20%
D. 25%
E. 30%

Are You Up For the Challenge: 700 Level Questions

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GMAT Club Legend  V
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2
should be solved like this. i'm not sure how we gonna solve it without calculator.

$$0.5*[13.8*(1.05)^{10}]$$ < 3.3 $$(1+\frac{x}{100})^{10}$$

$$[2.1]^{\frac{1}{10}}*1.05 < (1+\frac{x}{100})$$

$$1.07*1.05< 1+\frac{x}{100}$$

Archit3110 wrote:
Bunuel wrote:
The GDP of a country is $13.8 billion, and the total production of one of its industries is$3.3 billion. If the GDP were to grow by 5% per year in the future, which of the following would be the MINIMUM required annual growth in this industry that would it represent more than half of the GDP in ten years?

A. 10%
B. 15%
C. 20%
D. 25%
E. 30%

Are You Up For the Challenge: 700 Level Questions

giving a try not sure though of the solution

total GDP is 13.8
and production = 3.3
annual growth of GDP = 13.8*1.05 ; 14.49 ~ 14.5
i.e for every increase in GDP the production rate has to increase by 14.5/3.3 = 4.39
i.e % change of ~33% but question has asked for MINIMUM required annual growth in this industry that would it represent more than half of the GDP in ten years
IMO E. 30% is what the industry will have to gain to match >= half of GDP rate
Senior Manager  P
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1
Current GDP = $13.8 billion = ~$14 billion

Current total production of one industry = $3.3 billion = ~$3.5 billion, about 25% of current GDP.

GDP and the total production grow at an annual factor of 1.05 and x, respectively.

In order to increase from ~25% to >50% of the GDP in 10 years, the total production needs to double in 10 years. Thus,

(x/1.05)^9 >=2
--> x/1.05 >=2^(1/9)
--> x/1.05 >=~1.1
--> x >= 1.15

I just approximate that:
1.1^2 = 1.1 * 1.1 = 1.2
1.1^4 = 1.1^2 * 1.1^2 = 1.2*1.2 = 1.4
1.1^8 = 1.1^4 * 1.1^4 = 1.4*1.4 = 1.96
So 1.1^9 must be greater than 2. Therefore, 2^(1/9) =~1.1

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AnirudhaS wrote:
Interested to know how we calculate$$2^\frac{1}{9}$$

Plz someone explain??

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Bunuel wrote:
The GDP of a country is $13.8 billion, and the total production of one of its industries is$3.3 billion. If the GDP were to grow by 5% per year in the future, which of the following would be the MINIMUM required annual growth in this industry that would it represent more than half of the GDP in ten years?

A. 10%
B. 15%
C. 20%
D. 25%
E. 30%

1/2*13.8* (1.05)^9 < 3.3 * (1+t/100)^9

2.3*(1.05)^9<1.1(1+t/100)^9)

Since 2.2 (2*1.1) < 2.3 < 3.3 (3*1.1). So the real growth rate of the industry must be greater than twice of GDP's (5%*2 = 10%) and smaller than thrice of GDP's (5%*3 = 15%).

The question asks for the MINIMUM required annual growth, so we should not take 10%. Looking at the choices, 15% is the smallest bound. IMO B. This approach can be easily screwed if A was 12%, so yeah it's not a general solution to solve this kind of questions.
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Re: The GDP of a country is $13.8 billion, and the total production of one [#permalink] ### Show Tags 1 Bunuel wrote: The GDP of a country is$13.8 billion, and the total production of one of its industries is $3.3 billion. If the GDP were to grow by 5% per year in the future, which of the following would be the MINIMUM required annual growth in this industry that would it represent more than half of the GDP in ten years? A. 10% B. 15% C. 20% D. 25% E. 30% Are You Up For the Challenge: 700 Level Questions GDP now =$13.8 billion
GDP 10 years from now = $13.8*1.05^10 =$22.48 billion
Industry 10 years from now = $11.24 billion minimum Industry now =$3.3 billion
Industry growth in 10 years = 11.24/3.3 = 3.4
(1+x)^10 = 3.4
x = ~13 % ~ 15%

IMO B
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com Re: The GDP of a country is $13.8 billion, and the total production of one [#permalink] 28 Mar 2020, 03:09 # The GDP of a country is$13.8 billion, and the total production of one  