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CAT 2025Slot 1DILRQues & 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.

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Question 1

What was the SI of E in 2016?

Solution

Setup: We read the % change values for each country directly from the plot, then express their SI in 2020 and 2024 as multiples of their 2016 values. Fact 3 (E's SI in 2024 = 90) gives us a direct equation to solve for E's 2016 value.

Steps:

  1. From the plot, E increased by 25% from 2016→2020, and by 20% from 2020→2024. So: SI(E, 2020) = (5/4)e and SI(E, 2024) = (6/5) × (5/4)e = (3/2)e, where e = SI(E, 2016).
  2. Using Fact 3: SI(E, 2024) = 90, so (3/2)e = 90, which gives e = 60.
  3. Therefore, E's SI in 2016 is 60, and in 2020 it is (5/4) × 60 = 75. This is consistent with Fact 1 (E had rank 3 in 2016, meaning it was 3rd highest), which we can verify once other values are determined.

Final Answer: 60

Question 2

What was the SI of F in 2020?

Solution

Setup: After establishing e = 60 (from Q1), we use Fact 4 (range = 60 in 2016) and Fact 2 (F is lowest in all years) to narrow down B's 2016 value. Since B is ranked 1 and F is ranked 6 in 2016, range = b − f = 60. We then use integer constraints and Fact 4 (range = 60 in 2024) to find the unique valid value of b and f.

Steps:

  1. From the plot: F increased by 100% from 2016→2020 and decreased by 25% from 2020→2024. So SI(F, 2020) = 2f and SI(F, 2024) = (3/4) × 2f = (3/2)f. For SI(F, 2020) to be an integer, f must yield integer values — this is satisfied for any integer f. For SI(B, 2024) = (9/16)b to be an integer, b must be a multiple of 16.
  2. Since b − f = 60 and b > 60 (as f ≥ 1), the multiples of 16 in range (60, 100] are: 64, 80, 96. Testing each: b = 64 → f = 4, SI(F, 2024) = 6, but then range in 2024 ≥ 90 − 6 = 84 ≠ 60. Eliminated. b = 96 → f = 36, SI(F, 2024) = 54 and SI(B, 2024) = 54 — F cannot equal B (Fact 2 requires F strictly lower). Eliminated. b = 80 → f = 20, SI(F, 2024) = 30, SI(B, 2024) = 45. Range in 2024 = 90 − 30 = 60 ✓, and F < B ✓.
  3. With f = 20, SI(F, 2020) = 2 × 20 = 40.

Final Answer: 40

Question 3

What was the SI of C in 2024?

Solution

Setup: With b = 80, f = 20, and e = 60 established, we know 2016 rankings: B(80) > C > E(60) > A > D > F(20). We use the integer constraint on SI(C, 2024) = (28/25)c to find the valid value of c between 60 and 80.

Steps:

  1. From the plot: C decreased by 20% from 2016→2020 and increased by 40% from 2020→2024. So SI(C, 2024) = (28/25)c, where c = SI(C, 2016). For this to be an integer, c must be a multiple of 25.
  2. Since C had rank 2 in 2016 (Fact 1), we need: 80 > c > 60 (B = 80 is rank 1, E = 60 is rank 3). The only multiple of 25 strictly between 60 and 80 is 75. So c = 75.
  3. SI(C, 2024) = (28/25) × 75 = (28 × 3) = 84.

Final Answer: 84

Question 4

What was the SI of B in 2024?

Solution

Setup: This question is directly answered once we establish b = 80 (B's SI in 2016). From the plot, B decreased by 25% in 2020 and again by 25% in 2024, so SI(B, 2024) = (9/16)b.

Steps:

  1. From the plot: B decreased by 25% from 2016→2020, giving SI(B, 2020) = (3/4) × 80 = 60. Then B decreased by 25% again from 2020→2024, giving SI(B, 2024) = (3/4) × 60 = 45.
  2. Alternatively, SI(B, 2024) = (9/16) × b = (9/16) × 80 = 45.
  3. Verification: In 2024, F = 30 (lowest), B = 45, E = 90 (highest). Range = 90 − 30 = 60 ✓. F is strictly less than B ✓. E is the only country with SI = 90 ✓. All conditions are satisfied.

Final Answer: 45 (Option D)