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Year

CAT 2025

Section

Data

Topic

Quant Based LR

Difficulty

Hard

Question

Slot-2

Passage:

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.

Question 1

What is the PI of Whimshire?

Question 2

What is the PI of Fogglia?

Question 3

What is the PI of Humbleset?

Question 4

Which pair of cities definitely belong to the same state?

Blusterburg, Mumpypore

Splutterville, Quackford

Mumpypore, Zingaloo

Noodleton, Quackford

Question 5

For how many of the cities and NURs is it possible to identify their PM and the state they belong to?

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