Data Interpretation

Scatter Plot

Hard

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.

In 2016, B, C, E, and A had ranks 1, 2, 3, and 4 respectively.
F had lower SI than any other country in 2016, 2020, and 2024.
In 2024, E was the only country with SI of 90.
The range of SI of the six countries was 60 in 2016 as well as in 2024.

Figure for CAT 2025 2025 Slot 2 DILR question 21 (Data Interpretation)

What was the SI of C in 2024?

Entered answer:

✅ Correct Answer: 84

Slide 1/7

We follow six countries, $A$ to $F$ , across the years $2016$ , $2020$ and $2024$ .

The plot supplies two percentages for each country:

$X$ = percentage change in SI from $2016$ to $2020$

$Y$ = percentage change in SI from $2020$ to $2024$

Reading these off the plot:

Country	$X\%$	$Y\%$
A	$+20$	$+20$
B	$-25$	$-40$
C	$+5$	$0$
D	$+20$	$0$
E	$+20$	$+25$
F	$0$	$-25$

Since

$\text{SI}_{2020} = \text{SI}_{2016}\,(1 + X/100)$

and

$\text{SI}_{2024} = \text{SI}_{2020}\,(1 + Y/100)$ ,

fixing any one year for a country fixes all three.

The anchors we will use:

2016 ranks give $B>C>E>A>D>F$ (since $B,C,E,A$ are ranks $1,2,3,4$ and $F$ is lowest, so $D$ is rank $5$ ).

$F$ is the lowest SI in every year.

$E$ is the only country at $90$ in $2024$ .

The range of SI is $60$ in $2016$ and again in $2024$ .

Country	$X\%$	$Y\%$	SI 2016	SI 2020	SI 2024
A	$+20$	$+20$
B	$-25$	$-40$
C	$+5$	$0$
D	$+20$	$0$
E	$+20$	$+25$	$60$	$72$	$90$
F	$0$	$-25$

$E$ in $2024$ is $90$ .

E's overall multiplier is

$(1+0.20)(1+0.25) = 1.20 \times 1.25 = 1.5$ .

$\text{SI}_{2016} = 90 / 1.5 = 60$

$\text{SI}_{2020} = 90 / 1.25 = 72$ .

The value $60$ also matches $E$ being rank $3$ in $2016$ .

Country	$X\%$	$Y\%$	SI 2016	SI 2020	SI 2024
A	$+20$	$+20$
B	$-25$	$-40$
C	$+5$	$0$
D	$+20$	$0$
E	$+20$	$+25$	$60$	$72$	$90$
F	$0$	$-25$	$40$	$40$	$30$

In $2024$ the six SIs span a range of $60$ . $E$ sits at $90$ , and no country exceeds it (the completed table confirms this), so $90$ is the maximum.

$F$ is always the lowest, so

$F_{2024} = 90 - 60 = 30$ .

Working back through F's percentages:

$F_{2020} = 30 / (1 - 0.25) = 30/0.75 = 40$

$F_{2016} = 40 / (1+0) = 40$ .

Country	$X\%$	$Y\%$	SI 2016	SI 2020	SI 2024
A	$+20$	$+20$
B	$-25$	$-40$	$100$	$75$	$45$
C	$+5$	$0$
D	$+20$	$0$
E	$+20$	$+25$	$60$	$72$	$90$
F	$0$	$-25$	$40$	$40$	$30$

In $2016$ the range is $60$ . $B$ is rank $1$ (the maximum) and $F$ is the minimum at $40$ , so

$B_{2016} = 40 + 60 = 100$ .

Applying B's percentages:

$B_{2020} = 100 \times (1 - 0.25) = 75$

$B_{2024} = 75 \times (1 - 0.40) = 45$ .

Country	$X\%$	$Y\%$	SI 2016	SI 2020	SI 2024
A	$+20$	$+20$
B	$-25$	$-40$	$100$	$75$	$45$
C	$+5$	$0$	$80$	$84$	$84$
D	$+20$	$0$
E	$+20$	$+25$	$60$	$72$	$90$
F	$0$	$-25$	$40$	$40$	$30$

$C$ is rank $2$ in $2016$ , between $B=100$ and $E=60$ , so $60 < C_{2016} < 100$ .

C's first step is $+5\%$ :

$C_{2020} = C_{2016}\times 1.05 = C_{2016}\times \tfrac{21}{20}$ .

For this to be a whole number, $C_{2016}$ must be a multiple of $20$ . The only multiple of $20$ strictly between $60$ and $100$ is $80$ .

$C_{2016} = 80,\quad C_{2020} = 84,\quad C_{2024} = 84$ (since $Y = 0$ ).

Country	$X\%$	$Y\%$	SI 2016	SI 2020	SI 2024
A	$+20$	$+20$	$50$	$60$	$72$
B	$-25$	$-40$	$100$	$75$	$45$
C	$+5$	$0$	$80$	$84$	$84$
D	$+20$	$0$
E	$+20$	$+25$	$60$	$72$	$90$
F	$0$	$-25$	$40$	$40$	$30$

$A$ is rank $4$ in $2016$ , below $E=60$ and above $F=40$ , so $40 < A_{2016} < 60$ .

A's overall multiplier is $1.20\times1.20 = 1.44 = \tfrac{36}{25}$ .

For $A_{2024}$ to be a whole number, $A_{2016}$ must be a multiple of $25$ . The only one in $(40, 60)$ is $50$ .

$A_{2016} = 50,\quad A_{2020} = 60,\quad A_{2024} = 72$ .

Country	$X\%$	$Y\%$	SI 2016	SI 2020	SI 2024
A	$+20$	$+20$	$50$	$60$	$72$
B	$-25$	$-40$	$100$	$75$	$45$
C	$+5$	$0$	$80$	$84$	$84$
D	$+20$	$0$	$45$	$54$	$54$
E	$+20$	$+25$	$60$	$72$	$90$
F	$0$	$-25$	$40$	$40$	$30$

$D$ is rank $5$ in $2016$ , between $A=50$ and $F=40$ , so $40 < D_{2016} < 50$ .

D's first step is $+20\% = \tfrac{6}{5}$ , so $D_{2016}$ must be a multiple of $5$ . The only one in $(40,50)$ is $45$ .

$D_{2016} = 45,\quad D_{2020} = 54,\quad D_{2024} = 54$ .

Checking the facts:

$2016$ : $100>80>60>50>45>40$ , ranks $B,C,E,A = 1,2,3,4$ , range $= 100-40 = 60$ .

$2024$ : maximum $90$ ( $E$ , the unique $90$ ), minimum $30$ ( $F$ ), range $= 90-30 = 60$ .

$F$ is the lowest in all three years.

Every entry is now fixed, so the table is fully determined.

C's row reads $80 \to 84 \to 84$ ; $C_{2016}=80$ is forced as the only multiple of $20$ between $60$ and $100$ . So C's SI in 2024 was $84$ .

Question 19

What was the SI of E in 2016?

Question 20

What was the SI of F in 2020?

Question 22

What was the SI of B in 2024?

What was the SI of C in 2024?

Solution

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