Multiple choice general knowledge math & puzzles

100 Politicians are attending a political convention. You know that the politicians are either corrupt or honest, nothing in between. There is at least one honest politician. If you randomly choose 2 politicians at least one of them will be corrupt. How many politicians are corrupt and how many are honest?

  1. 95 corrupt 5 honest

  2. 100 corrupt

  3. 99 corrupt and 1 honet

  4. 100 honest
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If there are 2 or more honest politicians, choosing those 2 would give 0 corrupt, violating the condition. With exactly 1 honest, any pair including that person plus any corrupt politician satisfies 'at least one corrupt.' Thus, 99 corrupt and 1 honest is the only solution.

AI explanation

If any two randomly chosen politicians must include at least one corrupt one, it means you can never pick two honest politicians together — so there can be at most one honest politician in the whole group. Combined with the condition that at least one honest politician exists, there must be exactly one honest politician and the remaining 99 are corrupt.

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