Pollution 2 Cities | Teeny Numbers | CAT 2025 DILR Slot 2 | Hard

Q1CAT 2025 · Slot 2 · CAT Medium · TITA✓ Answer verified

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 Whimshire? ____

Q2CAT 2025 · Slot 2 · CAT Medium · TITA✓ Answer verified

Pollution 2 Cities | Teeny Numbers | CAT 2025 DILR Slot 2 | Hard

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? ______

Q3CAT 2025 · Slot 2 · CAT Medium · TITA✓ Answer verified

Pollution 2 Cities | Teeny Numbers | CAT 2025 DILR Slot 2 | Hard

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? _____

Q4CAT 2025 · Slot 2 · CAT Hard✓ Answer verified

Pollution 2 Cities | Teeny Numbers | CAT 2025 DILR Slot 2 | Hard

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?

Q5CAT 2025 · Slot 2 · CAT Hard · TITA✓ Answer verified

Pollution 2 Cities | Teeny Numbers | CAT 2025 DILR Slot 2 | Hard

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.

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

Pollution 2 Cities | Teeny Numbers | CAT 2025 DILR Slot 2 | Hard

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