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01 Nov 2019, 06:28
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B
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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
A. 10%
B. 15%
C. 20%
D. 25%
E. 30%
Are You Up For the Challenge: 700 Level Questions
30 Dec 2019, 03:53
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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
Posted from my mobile device
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
Posted from my mobile device
22 Feb 2020, 10:08
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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.
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.
