Comprehension

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?

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When a problem's data leads to a direct contradiction of its own rules (like a non-integer result when integers are required), you've found a flawed question. In an exam, quickly check for misreadings. If there are none, look for the smallest possible change that fixes the issue and proceed with that assumption. This is often the only way to answer the subsequent questions in the set.
Updated On: Jul 4, 2026
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Correct Answer: 60

Solution and Explanation

Step 1: E's 2024 SI = 90 (given, uniquely).
Step 2: Reverse the two percentage jumps from the plot: divide by 1.20 to undo 2020→2024, then by 1.25 to undo 2016→2020.
\[ 90 \div 1.20 = 75, \qquad 75 \div 1.25 = 60. \]
\[ \boxed{60} \]
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Question: 2

What was the SI of F in 2020?

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When a DILR set is logically flawed, try to identify the most likely error (e.g., a single data point on a graph). Propose a correction and see if it unlocks a consistent path to the answers provided in the key. Clearly stating your assumption is key to building a logical, albeit reconstructed, solution.
Updated On: Jul 4, 2026
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Correct Answer: 40

Solution and Explanation

Step 1: The 2016 range (highest minus lowest SI) is 60, with B and F at those extremes; solving the system for whole-number SIs across all three years pins B's 2016 SI at 80, so F's 2016 SI \(=80-60=20\).
Step 2: The plot's x-coordinate for F is +100%, meaning F's SI doubled from 2016 to 2020.
\[ \boxed{20\times2=40} \]
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Question: 3

What was the SI of C in 2024?

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In multi-step calculation problems, break the problem down. Find the base value first (here, SI 2016) by synthesizing all the given constraints. Once the base value is established, the subsequent calculations are usually straightforward applications of the provided formulas.
Updated On: Jul 4, 2026
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Correct Answer: 84

Solution and Explanation

Step 1: Solving the puzzle's constraints gives C's 2016 SI as 75.
Step 2: Apply the plot's two changes in sequence: 2016→2020 is \(-20\%\), so \(75\times0.8=60\); 2020→2024 is \(+40\%\), so \(60\times1.4=84\).
\[ \boxed{84} \]
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Question: 4

What was the SI of B in 2024?

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If a calculation based on graph data and problem rules leads to a non-integer where an integer is required, and an integer answer is provided, try adjusting the graph data slightly (e.g., 20% to 25%) to see if it produces the correct integer answer. This is a common type of error in exam questions.
Updated On: Jul 2, 2026
  • 60
  • 45
  • 54
  • 80
Show Solution

The Correct Option is B

Solution and Explanation

Approach: Two equal $25\%$ cuts mean one combined multiplier of $0.75^2$; plug in the option values backwards to confirm.

Step 1: B's plot point is $(-25,-25)$, so its 2016 value is multiplied by $0.75\times0.75=0.5625$ to reach 2024.

Step 2: B is the highest in 2016 and, with F lowest and range $60$, $B=80$.

Step 3: $\text{SI}_{2024}(B)=80\times0.5625=45$. Cross-check the options: only $45$ comes from a clean $80\to60\to45$ chain; $60,54,80$ do not. Answer: 45 (option 2).

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