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CAT 2025Slot 2DILRQues & Sol

Data InterpretationHard

Data Set

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 1

What was the SI of E in 2016?

Solution

Setup: We use the percentage changes read from the scatter plot for each country along with Fact 3 (E's SI in 2024 = 90) to back-calculate E's SI in 2016. The plot gives E an X-coordinate of +25% and a Y-coordinate of +20%.

Steps:

  1. From the plot, E's SI increased by 25% from 2016 to 2020, so SI(E, 2020) = (5/4)·e, where e = SI(E, 2016).
  2. E's SI then increased by 20% from 2020 to 2024, so SI(E, 2024) = (6/5)·(5/4)·e = (3/2)·e.
  3. We are told SI(E, 2024) = 90, so (3/2)·e = 90, giving e = 60.

Final Answer: The SI of E in 2016 was 60.

Question 2

What was the SI of F in 2020?

Solution

Setup: After establishing e = 60 (SI of E in 2016), we use the 2016 ranking (B is Rank 1, F is Rank 6), the range constraint (range = 60 in both 2016 and 2024), and the integrality condition on all SI values to pin down the value of b (SI of B in 2016) and f (SI of F in 2016). From the plot, F's X-coordinate is +100% and Y-coordinate is −25%.

Steps:

  1. From the plot: SI(F, 2020) = 2f and SI(F, 2024) = (3/4)·2f = (3/2)f. For SI(B, 2024) to be an integer, since SI(B, 2024) = (9/16)b, b must be a multiple of 16 that is greater than 60 and at most 99. Candidates: 64, 80, 96.
  2. Fact 4 gives range in 2016 = b − f = 60 (B is highest, F is lowest). Test each candidate:
    • b = 64 → f = 4 → SI(F, 2024) = 6, SI(E, 2024) = 90 → range in 2024 ≥ 84 ≠ 60. ❌
    • b = 96 → f = 36 → SI(F, 2024) = 54, SI(B, 2024) = 54 → F not strictly lowest in 2024. ❌
    • b = 80 → f = 20 → SI(F, 2024) = 30, SI(B, 2024) = 45 → range in 2024 = 90 − 30 = 60. ✅
  3. With f = 20, SI(F, 2020) = 2 × 20 = 40.

Final Answer: The SI of F in 2020 was 40.

Question 3

What was the SI of C in 2024?

Solution

Setup: With b = 80, f = 20, and e = 60 established, we use the 2016 ranking (C is Rank 2, so 60 < c < 80) and the integrality condition on SI(C, 2024) to find c. From the plot, C's X-coordinate is −20% and Y-coordinate is +40%.

Steps:

  1. From the plot: SI(C, 2020) = (4/5)c and SI(C, 2024) = (7/5)·(4/5)c = (28/25)c. For SI(C, 2024) to be an integer, c must be a multiple of 25.
  2. Since C is ranked 2nd in 2016, c must satisfy 60 < c < 80. The only multiple of 25 in this range is 75.
  3. Therefore c = 75, and SI(C, 2024) = (28/25) × 75 = 28 × 3 = 84.

Final Answer: The SI of C in 2024 was 84.

Question 4

What was the SI of B in 2024?

Solution

Setup: We use the already-established value b = 80 (SI of B in 2016) and the percentage changes from the plot for B. From the plot, B's X-coordinate is −25% and Y-coordinate is −25%.

Steps:

  1. From the plot: SI(B, 2020) = (3/4) × 80 = 60.
  2. SI(B, 2024) = (3/4) × 60 = 45.
  3. Verify: F's SI in 2024 = 30 < 45, confirming F is still the lowest, consistent with Fact 2. The 2024 range = 90 − 30 = 60, consistent with Fact 4. ✅

Final Answer: The SI of B in 2024 was 45 (Option D).