CAT 2025 Slot 2 · DILR · Set 4: Sustainability Index of Six Countries

The full set and all 4 questions (Q14–Q17) from CAT 2025 Slot 2, with answers and solutions.

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.

Question 14 · Mixed DI (Radar, Triangular, Stock etc)

What was the SI of E in 2016?

Answer & solution

Answer: 60

From the plot, E rose 25% from 2016 to 2020 and 20% from 2020 to 2024.

So SI(2024) = SI(2016) × 1.25 × 1.20 = 1.5 × SI(2016).

With SI(2024) = 90 (fact 3), SI(2016) = 90 ÷ 1.5 = 60. (Check: 2020 value = 75, an integer.)

Shortcut: multiply the growth factors first: 1.25 × 1.2 = 1.5, then 90 ÷ 1.5 = 60.

Hence, the answer is 60.

Question 15 · Mixed DI (Radar, Triangular, Stock etc)

What was the SI of F in 2020?

Answer & solution

Answer: 40

In 2016 the ranks are B, C, E (60), A, then D and F, with F last (fact 2). So B is the highest and F the lowest, and the 2016 range gives B − F = 60.

B falls 25% twice: B(2024) = B × 0.75 × 0.75 = 9B/16. For this to be an integer, B must be a multiple of 16. B must also be above C, which is above E = 60, and at most 100, so B = 80 or 96.

If B = 96, then F = 36. F doubles (+100%) and then falls 25%, so F(2024) = 36 × 2 × 0.75 = 54. The 2024 range of 60 would then need a top SI of 114, which is impossible.

So B = 80 and F = 20. F(2020) = 20 × 2 = 40.

Check: F(2024) = 30, and the 2024 top is E's 90, giving a range of 60.

Shortcut: B's two 25% drops force B to be a multiple of 16; the cap of 100 in 2024 rules out 96, so B = 80, F = 20, and F doubles to 40.

Hence, the answer is 40.

Question 16 · Mixed DI (Radar, Triangular, Stock etc)

What was the SI of C in 2024?

Answer & solution

Answer: 84

C is ranked 2 in 2016, so 60 < C < 80 (between E = 60 and B = 80).

C falls 20% and then rises 40%: C(2020) = 0.8C and C(2024) = 0.8 × 1.4 × C = 1.12C = 28C/25.

For 2024 to be an integer, C must be a multiple of 25. The only multiple of 25 between 60 and 80 is 75.

C: 75 → 60 → 84. So C(2024) = 84.

Shortcut: 1.12 = 28/25 forces C to be a multiple of 25, and only 75 lies between E and B.

Hence, the answer is 84.

Question 17 · Mixed DI (Radar, Triangular, Stock etc)

What was the SI of B in 2024?

  1. A

    60

  2. B

    54

  3. C

    80

  4. D

    45

Pick an option, then check.
Answer & solution

Answer: Option D

From the previous working, B(2016) = 80 (B must be a multiple of 16, and 96 fails the 2024 range condition).

B falls 25% in each period: 80 → 60 → 45.

So B(2024) = 45.

Shortcut: 9B/16 must be an integer and only B = 80 survives the 2024 range test, so B(2024) = 9 × 80 ÷ 16 = 45.

Hence, the answer is option 4.

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