CAT 2024 Slot 3 — DILR Question 21

TablesEasy

Passage / Data

Answer the following questions based on the information given below.

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.

$Table of GDP fraction, GDP-per-capita fraction, GDP growth rate and population growth rate for Country 1 to 8$

Country	GDP (fraction of C9)	GDP per capita (fraction of C10)	GDP growth rate	Population growth rate
Country 1	0.15	0.41	0.2%	-0.12%
Country 2	0.14	0.25	0.9%	-0.41%
Country 3	0.13	0.02	6.5%	0.70%
Country 4	0.12	0.38	0.5%	0.49%
Country 5	0.10	0.36	0.7%	0.31%
Country 6	0.08	0.08	3.2%	0.61%
Country 7	0.08	0.30	0.7%	-0.11%
Country 8	0.07	0.41	1.2%	0.71%

Assume that the GDP growth rates and population growth rates of the countries will remain constant for the next three years.

Which one among the countries 1, 4, 5, and 7 will have the largest population in 2027?

Answer & solution

A
Country 7
Country 1
C
Country 4
D
Country 5

Solution

Medium

Start from the 2024 population index (GDP ÷ GDPpc) and grow it three years at each country's population growth rate; compare the four candidates.

2024 population index $=$ GDP ÷ GDPpc; project to 2027 (3 years) with $(1+\text{pop growth})^3$ . Candidates: C1, C4, C5, C7.

2027 population index for each candidate. C1 already starts highest and its tiny decline cannot be overtaken.

\begin{aligned} &C1{:}\tfrac{0.15}{0.41}(0.9988)^3\approx0.365\\ &\Rightarrow\ C4{:}\tfrac{0.12}{0.38}(1.0049)^3\approx0.321,\ C5{:}\tfrac{0.10}{0.36}(1.0031)^3\approx0.280\\ &\Rightarrow\ C7{:}\tfrac{0.08}{0.30}(0.9989)^3\approx0.266\\ &\Rightarrow\ \max = C1 \end{aligned}

Country 1