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MathNet 2019-part-04 — 184 problems (EN–VI) Question 87

Math Olympiad Vault · MathNet 2019-part-04 — 184 problems (EN–VI)

Question 87

Agatha, Isa and Nick each have a different kind of bike. One of them has an electric bike, one has a racing bike, and one has a mountain bike. The bikes have different colours: green, blue and black. The three owners make two statements each, of which one is true and the other is false:
* Agatha says: "I have an electric bike. Isa has a blue bike."
* Isa says: "I have a mountain bike. Nick has an electric bike."
* Nick says: "I have a blue bike. The racing bike is black."
Exactly one of the following statements is certainly true. Which one?
A) Agatha has a green bike. B) Agatha has a mountain bike. C) Isa has a green bike. D) Isa has a mountain bike. E) Nick has an electric bike.