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The GDP of a country is $13.8 billion, and the total production of one

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The GDP of a country is $13.8 billion, and the total production of one  [#permalink]

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New post 01 Nov 2019, 05:28
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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%

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The GDP of a country is $13.8 billion, and the total production of one  [#permalink]

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New post Updated on: 04 Nov 2019, 10:25
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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%

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hello need an expert help on this question please look into the question and advise :| GMATinsight VeritasKarishma

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

Originally posted by Archit3110 on 02 Nov 2019, 02:27.
Last edited by Archit3110 on 04 Nov 2019, 10:25, edited 1 time in total.
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Re: The GDP of a country is $13.8 billion, and the total production of one  [#permalink]

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New post 02 Nov 2019, 03:06
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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%

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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
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The GDP of a country is $13.8 billion, and the total production of one  [#permalink]

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New post 30 Dec 2019, 02:16
nick1816 wrote:
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%

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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

....
Hi nick, i have used exactly the same approach for the go ahead. However, i feel the power raised should be 9 and not 10 because the first year there was no increase !!
10th year will have compounded effect of 9 years with increased gdp. What do you think ?
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Re: The GDP of a country is $13.8 billion, and the total production of one  [#permalink]

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New post 30 Dec 2019, 02:53
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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

Final answer is (B)

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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Re: The GDP of a country is $13.8 billion, and the total production of one  [#permalink]

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New post 31 Dec 2019, 09:09
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Interested to know how we calculate\( 2^\frac{1}{9}\)
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Re: The GDP of a country is $13.8 billion, and the total production of one  [#permalink]

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New post 02 Jan 2020, 09:02
AnirudhaS wrote:
Interested to know how we calculate\( 2^\frac{1}{9}\)

Plz someone explain??

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The GDP of a country is $13.8 billion, and the total production of one  [#permalink]

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New post 22 Feb 2020, 09:08
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Used a bit of a trick to solve this.

The ratio of total GDP to industry production is roughly 1/4. This needs to double over ten years. So that means the effective change in the ratio per year is (1+x/100)/1.05.

Using rule of 72, the approximate change in the fraction per year for it to double in 10 years is roughly 72/10 or 7.2%. the actual percentage may be a little higher since the actual ratio is a little lower than 25%, so let's take it to be around 8%

This means (1+ x/100 )/1.05 = 1.08, this gives x ~=1.134. so the answer is greater than 10, but safely less than than 20. So the best option to go with is 15%.

Took roughly 2.5 minutes with this.
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Re: The GDP of a country is $13.8 billion, and the total production of one  [#permalink]

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New post 29 Feb 2020, 09:24
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]

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New post 28 Mar 2020, 03:09
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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%

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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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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

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