CAT 2025 Slot 2 · DILR · Question 19

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 Fogglia?

Answer & solution

Answer: 35

The PMs are fixed: NURs 10 and 20, Blusterburg 30, Humbleset's NUR 40, and Noodleton 50 to Zingaloo 90.

Humbleset must be Blusterburg + Zingaloo + NUR 40, giving PI = (80 + 30 + 90) ÷ 4 = 50; any other second city produces a tie or makes Humbleset not the highest.

The remaining cities pair as Noodleton–Quackford (50 + 70 = 120) and Splutterville–Mumpypore (60 + 80 = 140), since each pair's sum must be a multiple of 4.

Fogglia has the lowest PI, so it takes NUR 10 with the smaller pair: (20 + 120) ÷ 4 = 35.

Shortcut: with Humbleset at 50, the only distinct split of the other two states is 35 and 45; Fogglia takes 35.

Hence, the answer is 35.

CAT 2025 Slot 2 · DILR · Question 19

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