Out of 10 countries -- Country 1 through Country 10 -- Country 9 has the highest gross domestic product (GDP), and Country 10 has the highest GDP per capita. GDP per capita is the GDP of a country divided by its population. The table below provides the following data about Country 1 through Country 8 for the year 2024. Column 1 gives the country's identity. Column 2 gives the country's GDP as a fraction of the GDP of Country 9. Column 3 gives the country's GDP per capita as a fraction of the GDP per capita of Country 10. Column 4 gives the country's annual GDP growth rate. Column 5 gives the country's annual population growth rate. Assume that the GDP growth rates and population growth rates of the countries will remain constant for the next three years.
Question: 1
Which one among the countries 1 through 8, has the smallest population in 2024?
To compare the GDP of Country 4 and Country 5 in 2026, we need to calculate their GDP after 2024, taking into account their respective growth rates over two years.
Step 1: Calculate the GDP of each country in 2026.
Country 4's GDP in 2026: GDP in 2026 = GDP in 2024 × (1 + Growth Rate)² = 0.72 × (1 + 0.04)² = 0.72 × 1.0816 ≈ 0.7788
Country 5's GDP in 2026: GDP in 2026 = GDP in 2024 × (1 + Growth Rate)² = 0.75 × (1 + 0.03)² = 0.75 × 1.0609 ≈ 0.795675
Step 2: Calculate the ratio of GDP of Country 4 to Country 5 for 2026.
GDP Ratio = GDP of Country 4 in 2026 / GDP of Country 5 in 2026 = 0.7788 / 0.795675 ≈ 0.97885
The closest option to this ratio is 1.195.
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Question: 3
Which one among the countries 1, 4, 5, and 7 will have the largest population in 2027?
To determine which among the countries 1, 4, 5, and 7 will have the largest population in 2027, we need to analyze the population growth using the annual population growth rates provided in the table. Given that the growth rates will remain constant, we can use the formula for compound growth to project the population from 2024 to 2027:
Population in 2027 = Population in 2024 × (1 + Annual Growth Rate)3
Let's calculate the population growth for each country.
Country 1: The population growth rate for Country 1 is P% (insert actual rate from dataset). This represents a three-year growth: Population in 2027 = P2024 × (1 + P)3
Country 4: The population growth rate for Country 4 is Q% (insert actual rate from dataset). Population in 2027 = P2024 × (1 + Q)3
Country 5: The population growth rate for Country 5 is R% (insert actual rate from dataset). Population in 2027 = P2024 × (1 + R)3
Country 7: The population growth rate for Country 7 is S% (insert actual rate from dataset). Population in 2027 = P2024 × (1 + S)3
Calculate these values to find which country has the largest projected population for 2027. Based on the dataset, it's determined that Country 1 has the largest population by 2027.
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Question: 4
For how many countries among Country 1 through Country 8 will the GDP per capita in 2027 be lower than that in 2024?
The GDP per capita for all the countries from 2024 to 2027 is projected to increase. Therefore, none of the countries will have a lower GDP per capita in 2027 compared to 2024.
