CAT 2025 Question Paper | DILR Slot 2

CAT Questions

CAT 2025 DILR was similar to CAT 2022 in pattern. All the four sets had 5 questions this year too. There were 6 TITA Questions. Atleast two sets were doable in each slot and one of the four sets was extremely tough. Choice of Sets became a crucial factor. Overall this section was at a medium to high level of difficulty.

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 17 : What was the SI of C in 2024?

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Video Explanation

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Explanatory Answer

We are given the following information regarding the percentatge growth between 2016 - 2020 and 2020 - 2024.

Country	16-20 growth	20-24 growth
A	25%	50%
B	-25%	-25%
C	-20%	40%
D	100%	20%
E	25%	20%
F	100%	-25%

If the SIs of A,B,C,D,E,F were A,B,C,D,E,F in 2016, we'd have their SI table looking like:

2016	2020	2024
A	\(\frac{5}{4}A\)	\(\frac{15}{8}A\)
B	\(\frac{3}{4}B\)	\(\frac{9}{16}B\)
C	\(\frac{4}{5}C\)	\(\frac{28}{25}C\)
D	\(2D\)	\(\frac{12}{5}D\)
E	\(\frac{5}{4}E\)	\(\frac{3}{2}E\)
F	\(2F\)	\(\frac{3}{2}F\)

In 2024, E was the only country with SI of 90, this means:
\(\frac{3}{2}E\) = 90
E = 60

Taking F = 4f, E = 4e, D = 5d, C = 25c, B = 16b and A = 8a, our table looks like:

2016	2020	2024
A = \(8a\)	\(10a\)	\(15a\)
B = \(16b\)	\(12b\)	\(9b\)
C = \(25c\)	\(20c\)	\(28c\)
D = \(5d\)	\(10d\)	\(12d\)
E = 60	75	90
F = \(4f\)	\(8f\)	\(6f\)

From the ranks in 2016, we know that B > C > E > A
B > C > E > A
B > C > 60 > A
C is a multiple of 25, above 60 between 1 and 100. C has to be 75.
B > 75 > 60 > A
B is a multiple of 16 above 75. B can be 80 or 96.
Also, since B ranks 1 and F ranks last, with the range being 60, B = F + 60.
If B = 96, F = 4f = 36, then SI of F in 2024 would be 6f = 54
This is impossible, We know that F has the least SI in 2024 and the range is still 60.
So, if SI of F in 2024 is 54, then the highest SI in 2024 would be 114. Which is not permisssible.
So, B = 80 and F = 20.

2016	2020	2024
\(A = 8a\)	\(10a\)	\(15a\)
\(B = 80\)	60	45
\(C = 75\)	80	84
\(D = 5d\)	\(10d\)	\(12d\)
\(E = 60\)	75	90
\(F = 20\)	40	30

E > A > F
60 > 8a > 20
Analyzing all the possible values of A ...

Year & Expression	Values
2016   \(8a\)	24	32	40	48	56
2020   \(10a\)	30	40	50	60	70
2024   \(15a\)	45	60	75	90	105
	SI of A < SI of F in 2020 and 2024.	SI of F is less than any other in all years. A & F can't have the same SI in 2020		In 2024, only E has a SI of 90.	SI of A can't be 105.

A = 40.
D is a multiple of 5. Assuming A & D can't hold a shared rank 4.
A > D > F
40 > D > 20
D can be 25, 30, 35
The final grid will thus be:

2016	2020	2024
\(A = 40\)	\(50\)	\(75\)
\(B = 80\)	60	45
\(C = 75\)	80	84
\(D = 25\) \(30\) \(35\)	\(50\) \(60\) \(70\)	\(60\) \(72\) \(84\)
\(E = 60\)	75	90
\(F = 20\)	40	30

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The question is " What was the SI of C in 2024? "

Hence, the answer is '84'

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