CAT 2025 Slot 2 · DILR · Question 20

CAT 2025 Slot 2 previous year question on Caselet Based DI, with the answer and a step-by-step solution.

Caselet Based DIDATA INTERPRETATION -High LevelType in the answer (TITA)Medium

Set 5: Pollution Index of Three States — this question belongs to a set. Read the full set with all 5 questions →

The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs). These nine PMs are all distinct multiples of 10, ranging from 10 to 90. The six cities in increasing order of their PMs are: Blusterburg, Noodleton, Splutterville, Quackford, Mumpypore, Zingaloo.

The Pollution Index (PI) of a state is a weighted average of the PMs of its NUR and cities, with a weight of 50% for the NUR, and 25% each for its two cities.

There is only one pair of an NUR and a city (considering all cities and all NURs) where the PM of the NUR is greater than that of the city. That NUR and the city both belong to Humbleset.

The PIs of all three states are distinct integers, with Humbleset and Fogglia having the highest and the lowest PI respectively.

What is the PI of Humbleset?

Answer & solution

Answer: 50

Humbleset has NUR 40 and Blusterburg 30, plus one city x from 50 to 90. PI = (80 + 30 + x) ÷ 4 = (110 + x) ÷ 4, so x must make 110 + x a multiple of 4, i.e. x = 50, 70 or 90.

x = 50 gives 40, but the other states would be at least 40, so Humbleset would not be the highest.

x = 70 gives 45, but the other states would be 40 and 45, a tie.

x = 90 gives 50, with the others at 45 and 35. This works.

Shortcut: Humbleset must be the highest, so try the largest admissible city, Zingaloo, first: (110 + 90) ÷ 4 = 50.

Hence, the answer is 50.

CAT 2025 Slot 2 · DILR · Question 20

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