CAT 2025 Slot 2 · DILR · Question 21
CAT 2025 Slot 2 previous year question on Caselet Based DI, with the answer and a step-by-step solution.
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.
Which pair of cities definitely belong to the same state?
- A
Mumpypore, Zingaloo
- B
Splutterville, Quackford
- C
Blusterburg, Mumpypore
- D
Noodleton, Quackford
Answer & solution
Answer: Option D
The arrangement is unique:
Humbleset: NUR 40, Blusterburg 30, Zingaloo 90 (PI 50).
Whimshire: NUR 20, Splutterville 60, Mumpypore 80 (PI 45).
Fogglia: NUR 10, Noodleton 50, Quackford 70 (PI 35).
Option 1: Mumpypore (Whimshire) and Zingaloo (Humbleset) – different states.
Option 2: Splutterville (Whimshire) and Quackford (Fogglia) – different states.
Option 3: Blusterburg (Humbleset) and Mumpypore (Whimshire) – different states.
Option 4: Noodleton and Quackford are both in Fogglia.
Shortcut: from 50, 60, 70, 80 the only pairing with both sums divisible by 4 is (50, 70) and (60, 80), so Noodleton and Quackford must be together.
Hence, the answer is option 4.
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