CAT 2024 Slot 3 · DILR · Set 4: GDP and Population Growth of Ten Countries

The full set and all 4 questions (Q14–Q17) from CAT 2024 Slot 3, with answers and solutions.

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.

Country

GDP

GDP per capita

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

0.1

0.36

0.7%

0.31%

Country 6

0.08

0.08

3.2%

0.61%

Country 7

0.08

0.3

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.

Question 14 · Tables

Which one among the countries 1 through 8, has the smallest population in 2024?
  1. A
    Country 8
  2. B
    Country 3
  3. C
    Country 7
  4. D
    Country 5
Pick an option, then check.
Answer & solution

Answer: Option A

Solving the set

Step 1 – Let Country 9's GDP be G and Country 10's GDP per capita be p. Then each country's GDP = (column 2) × G and GDP per capita = (column 3) × p.

Step 2 – Population = GDP ÷ GDP per capita = (column 2 ÷ column 3) × G/p. Since G/p is the same for every country, populations can be compared using column 2 ÷ column 3.

Country

GDP (× G)

GDP per capita (× p)

Population = GDP ÷ GDP per capita (× G/p)

GDP growth

Population growth

1

0.15

0.41

0.366

0.2%

−0.12%

2

0.14

0.25

0.560

0.9%

−0.41%

3

0.13

0.02

6.500

6.5%

0.70%

4

0.12

0.38

0.316

0.5%

0.49%

5

0.10

0.36

0.278

0.7%

0.31%

6

0.08

0.08

1.000

3.2%

0.61%

7

0.08

0.30

0.267

0.7%

−0.11%

8

0.07

0.41

0.171

1.2%

0.71%

Step 3 – Future values. After n years, GDP = GDP₂₀₂₄ × (1 + GDP growth)ⁿ and population = Population₂₀₂₄ × (1 + population growth)ⁿ. GDP per capita rises if the GDP growth rate is higher than the population growth rate.

This question

From the population column of the table, Country 8 has the smallest value (0.171).

Hence, the answer is option 1.

Question 15 · Tables

The ratio of Country 4’s GDP to Country 5’s GDP in 2026 will be closest to
  1. A
    1.195
  2. B
    0.963
  3. C
    1.314
  4. D
    1.032
Pick an option, then check.
Answer & solution

Answer: Option A

Solving the set

Step 1 – Let Country 9's GDP be G and Country 10's GDP per capita be p. Then each country's GDP = (column 2) × G and GDP per capita = (column 3) × p.

Step 2 – Population = GDP ÷ GDP per capita = (column 2 ÷ column 3) × G/p. Since G/p is the same for every country, populations can be compared using column 2 ÷ column 3.

Country

GDP (× G)

GDP per capita (× p)

Population = GDP ÷ GDP per capita (× G/p)

GDP growth

Population growth

1

0.15

0.41

0.366

0.2%

−0.12%

2

0.14

0.25

0.560

0.9%

−0.41%

3

0.13

0.02

6.500

6.5%

0.70%

4

0.12

0.38

0.316

0.5%

0.49%

5

0.10

0.36

0.278

0.7%

0.31%

6

0.08

0.08

1.000

3.2%

0.61%

7

0.08

0.30

0.267

0.7%

−0.11%

8

0.07

0.41

0.171

1.2%

0.71%

Step 3 – Future values. After n years, GDP = GDP₂₀₂₄ × (1 + GDP growth)ⁿ and population = Population₂₀₂₄ × (1 + population growth)ⁿ. GDP per capita rises if the GDP growth rate is higher than the population growth rate.

This question

2026 is 2 years after 2024.

Country 4's GDP in 2026 = 0.12G × (1.005)² = 0.12G × 1.010025 ≈ 0.12120G.

Country 5's GDP in 2026 = 0.10G × (1.007)² = 0.10G × 1.014049 ≈ 0.10140G.

Ratio = 0.12120/0.10140 ≈ 1.195.

Hence, the answer is option 1.

Question 16 · Tables

Which one among the countries 1, 4, 5, and 7 will have the largest population in 2027?
  1. A
    Country 1
  2. B
    Country 5
  3. C
    Country 7
  4. D
    Country 4
Pick an option, then check.
Answer & solution

Answer: Option A

Solving the set

Step 1 – Let Country 9's GDP be G and Country 10's GDP per capita be p. Then each country's GDP = (column 2) × G and GDP per capita = (column 3) × p.

Step 2 – Population = GDP ÷ GDP per capita = (column 2 ÷ column 3) × G/p. Since G/p is the same for every country, populations can be compared using column 2 ÷ column 3.

Country

GDP (× G)

GDP per capita (× p)

Population = GDP ÷ GDP per capita (× G/p)

GDP growth

Population growth

1

0.15

0.41

0.366

0.2%

−0.12%

2

0.14

0.25

0.560

0.9%

−0.41%

3

0.13

0.02

6.500

6.5%

0.70%

4

0.12

0.38

0.316

0.5%

0.49%

5

0.10

0.36

0.278

0.7%

0.31%

6

0.08

0.08

1.000

3.2%

0.61%

7

0.08

0.30

0.267

0.7%

−0.11%

8

0.07

0.41

0.171

1.2%

0.71%

Step 3 – Future values. After n years, GDP = GDP₂₀₂₄ × (1 + GDP growth)ⁿ and population = Population₂₀₂₄ × (1 + population growth)ⁿ. GDP per capita rises if the GDP growth rate is higher than the population growth rate.

This question

2027 is 3 years after 2024.

Country

Population 2024

Growth factor for 3 years

Population 2027

1

0.366

(0.9988)³ ≈ 0.9964

0.365

4

0.316

(1.0049)³ ≈ 1.0148

0.320

5

0.278

(1.0031)³ ≈ 1.0093

0.280

7

0.267

(0.9989)³ ≈ 0.9967

0.266

Country 1 has the largest population in 2027. Its lead in 2024 (0.366 against 0.316) is far bigger than the small growth differences over 3 years.

Hence, the answer is option 1.

Question 17 · Tables

For how many countries among Country 1 through Country 8 will the GDP per capita in 2027 be lower than that in 2024?
Answer & solution

Answer: 0

Solving the set

Step 1 – Let Country 9's GDP be G and Country 10's GDP per capita be p. Then each country's GDP = (column 2) × G and GDP per capita = (column 3) × p.

Step 2 – Population = GDP ÷ GDP per capita = (column 2 ÷ column 3) × G/p. Since G/p is the same for every country, populations can be compared using column 2 ÷ column 3.

Country

GDP (× G)

GDP per capita (× p)

Population = GDP ÷ GDP per capita (× G/p)

GDP growth

Population growth

1

0.15

0.41

0.366

0.2%

−0.12%

2

0.14

0.25

0.560

0.9%

−0.41%

3

0.13

0.02

6.500

6.5%

0.70%

4

0.12

0.38

0.316

0.5%

0.49%

5

0.10

0.36

0.278

0.7%

0.31%

6

0.08

0.08

1.000

3.2%

0.61%

7

0.08

0.30

0.267

0.7%

−0.11%

8

0.07

0.41

0.171

1.2%

0.71%

Step 3 – Future values. After n years, GDP = GDP₂₀₂₄ × (1 + GDP growth)ⁿ and population = Population₂₀₂₄ × (1 + population growth)ⁿ. GDP per capita rises if the GDP growth rate is higher than the population growth rate.

This question

GDP per capita in 2027 = GDP per capita in 2024 × [(1 + GDP growth)/(1 + population growth)]³. It is lower only if the population grows faster than GDP.

Country

GDP growth

Population growth

GDP grows faster?

1

0.2%

−0.12%

Yes

2

0.9%

−0.41%

Yes

3

6.5%

0.70%

Yes

4

0.5%

0.49%

Yes

5

0.7%

0.31%

Yes

6

3.2%

0.61%

Yes

7

0.7%

−0.11%

Yes

8

1.2%

0.71%

Yes

No country has its population growing faster than its GDP.

Hence, the answer is 0.

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