Sustainability Index Scatter Graph | CAT 2025 Slot 2 DILR | Graph Modern | Easy
The Sustainability Index (SI) of a country at a point in time is an integer between 1 and 100. This question is related to SI of six countries – A, B, C, D, E, and F – at three different points in time – 2016, 2020, and 2024. The plot represents the exact changes in their SI, with X-coordinate representing % increase in 2020 from 2016, i.e., (SI in 2020 minus SI in 2016) / (SI in 2016), and Y-coordinate representing % increase in 2024 from 2020. At any point in time, the country with highest SI is ranked 1, while the country with the lowest SI is ranked 6. The following additional facts are known.
1. In 2016, B, C, E, and A had ranks 1, 2, 3, and 4 respectively.
2. F had lower SI than any other country in 2016, 2020, and 2024.
3. In 2024, E was the only country with SI of 90.
4. The range of SI of the six countries was 60 in 2016 as well as in 2024.
What was the SI of E in 2016? Easy ______
Answer & Explanation
Correct Answer: 60
Let E₍₂₀₁₆₎ = x
From graph: E increases 25% then 20%
SI 2024 = 1.25x × 1.20 = 1.5x
Given SI 2024 = 90
1.5x = 90 → x = 60
| Country | % change 2016→2020 | % change 2020→2024 |
| A | +25% | +50% |
| B | −20% | −25% |
| C | −25% | +40% |
| D | +100% | +20% |
| E | +25% | +20% |
| F | +100% | −25% |
What was the SI of F in 2020? Easy ______
Answer & Explanation
Correct Answer: 40
Let F₍₂₀₁₆₎ = y
From graph: F increases 100% in 2020, then drops 25%
F₍₂₀₂₀₎ = 2y
F₍₂₀₂₄₎ = 0.75 × 2y = 1.5y
Since F is lowest in 2024, and range in 2024 = 60
Highest in 2024 = 90 → lowest = 30
So 1.5y = 30 → y = 20
Thus F₍₂₀₂₀₎ = 2y = 40
| Country | % change 2016→2020 | % change 2020→2024 |
| A | +25% | +50% |
| B | −20% | −25% |
| C | −25% | +40% |
| D | +100% | +20% |
| E | +25% | +20% |
| F | +100% | −25% |
What was the SI of C in 2024? Easy ______
Answer & Explanation
Correct Answer: 84
Let C₍₂₀₁₆₎ = z
From graph: −25% then +40%
C₍₂₀₂₀₎ = 0.75z
C₍₂₀₂₄₎ = 1.4 × 0.75z = 1.05z
Using 2016 ranks: B > C > E > A and E₍₂₀₁₆₎ = 60
Trying integer values consistent with range = 60 and F lowest = 20
C₍₂₀₁₆₎ = 80 works
Then C₍₂₀₂₄₎ = 1.05 × 80 = 84
Sustainability Index Scatter Graph Explained | CAT 2025 Slot 2 DILR | Graph Modern | Easy
| Country | % change 2016→2020 | % change 2020→2024 |
| A | +25% | +50% |
| B | −20% | −25% |
| C | −25% | +40% |
| D | +100% | +20% |
| E | +25% | +20% |
| F | +100% | −25% |
What was the SI of B in 2024? Easy ______
Answer & Explanation
Correct Answer: Option 3 (45)
Let B₍₂₀₁₆₎ = b
From graph: −25% then −25% (From the graph, B shows a 25% decrease from 2016 to 2020 and a further 25% decrease from 2020 to 2024)
B₍₂₀₂₀₎ = 0.75b
B₍₂₀₂₄₎ = 0.75 × 0.75b = 0.5625b
From 2016 ranks and range = 60
Highest = B = 80, lowest (F) = 20
So B₍₂₀₁₆₎ = 80
B₍₂₀₂₄₎ = 0.5625 × 80 = 45
| Country | % change 2016→2020 | % change 2020→2024 |
| A | +25% | +50% |
| B | −20% | −25% |
| C | −25% | +40% |
| D | +100% | +20% |
| E | +25% | +20% |
| F | +100% | −25% |
Final Calculations of the complete Sustainability Index Scatter Graph | CAT 2025 Slot 2 DILR | Graph Modern | Easy
| Country | SI2016 | X | SI2020 | Y | SI2024 | Rank 2016 | Rank 2024 |
| B | 80 | -0.25 | 60 | -0.25 | 45 | 1 | 4 |
| C | 75 | 0.20 | 90 | -0.07 | 84 | 2 | 2 |
| E | 60 | 0.25 | 75 | 0.20 | 90 | 3 | 1 |
| A | 50 | 0.20 | 60 | 0.40 | 84 | 4 | 2 |
| D | 40 | 1.00 | 80 | 0.05 | 84 | 5 | 2 |
| F | 20 | 1.00 | 40 | -0.25 | 30 | 6 | 6 |
