# If one of the cities is visited by both Gleeson and Haley, which one of the following must be true?

on June 15 at 06:59PM

Why D?

Hello, I am having trouble with this question. Why is the answer D?

Shunhe on June 16 at 02:48PM

Hi @aonyonyi,

Thanks for the question! So we have to assume that one of the three cities is visited by both G and H, and find out what must be true.

First things first: can both G and H visit Sydney? No. Why? Well, because G can’t visit Sydney (last rule), and so Sydney can’t be the city both of them visit.

OK. Now can G and H visit Tokyo? Sure. They could both visit Tokyo, and then there’s a number of ways to fill in the rest of the game.

Finally, can G and H both visit Manila? Sure. What does that mean, though? According to rule 3, if G visits Manila, then H visits Tokyo. So H has to visit Tokyo in this case as well.

So there’s two possibilities: G and H visit Tokyo, or G and H visit Manila. If G and H visit Tokyo, then obviously, H visits Tokyo. If G and H visit Manila, then by rule 3, H visits Tokyo. So if one of the cities is visited by both, then H has to visit Tokyo, which is what (D) tells us.

Hope this helps! Feel free to ask any other questions that you might have.