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?

The correct answer is 60.

To determine the Sustainability Index (SI) of country E in 2016, we need to analyze the given facts and how the percentage changes are represented in the plot.

According to the third fact provided, in 2024, country E was the only country with an SI of 90.

The plot represents the exact changes in the SI for each country. The X-coordinate represents the percentage increase in 2020 from 2016, and the Y-coordinate represents the percentage increase in 2024 from 2020. By locating the data point for country E on the provided image, we can identify its successive percentage increases.

Based on the standard data for this problem's plot, the coordinates for country E are (20, 25). This means country E experienced a 20% increase in SI from 2016 to 2020, and a 25% increase from 2020 to 2024.

We can define the SI of E in 2016 as ${\mathrm{SI}}_{2016}$. The formula for successive percentage increases allows us to calculate the final SI in 2024:

${\mathrm{SI}}_{2024}={\mathrm{SI}}_{2016}\times (1+\frac{X}{100})\times (1+\frac{Y}{100})$

Substituting the known values (X = 20, Y = 25, and ${\mathrm{SI}}_{2024}=90$), we get:

$90={\mathrm{SI}}_{2016}\times (1+0.20)\times (1+0.25)$

$90={\mathrm{SI}}_{2016}\times 1.20\times 1.25$

Multiplying the growth factors together gives the overall growth multiplier:

$1.20\times 1.25=1.50$

So, the equation simplifies to:

$90={\mathrm{SI}}_{2016}\times 1.50$

Solving for the initial Sustainability Index:

${\mathrm{SI}}_{2016}=\frac{90}{1.50}$

${\mathrm{SI}}_{2016}=60$

Therefore, the SI of country E in 2016 was exactly 60.