Question

There are 100 politicians in a room. Each politician is either honest or crooked, and there's at least ONE politician of each type. If you pick any two politicians at random, at least ONE in the pair is crooked. No matter how many times you pick any two politicians, at least ONE of them is crooked. How many honest politicians are there?

A) 1
B) 10
C) 50
D) 99

Answer 1

Given the scenario that any two politicians chosen at random must include at least one crooked politician, there can only be one honest politician among 100 politicians to avoid any possibility of choosing two honest ones. The correct option is A) 1.

Step-by-step explanation:

The problem presents a scenario with 100 politicians in a room where we know that there is at least one honest politician and one crooked politician and that any two politicians chosen at random will include at least one crooked politician.

This implies that there cannot be more than one honest politician because if there were at least two, there would be a possibility of picking both honest politicians, violating the given condition. Therefore, the only way to satisfy the condition is for there to be exactly one honest politician and 99 crooked politicians. The correct answer is A) 1