If one of the cities contains exactly two hospitals and exactly one university, then which one of the following lists...

Lizzie on July 4, 2019

Correct Answer

Why is the correct answer A? I wasn't sure how to approach this question because i felt like 2,4,1,3,and 5 could have all been options. I'm not sure what deduction i missed here. Thank you!

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Ravi on July 4, 2019


Happy to help. This is definitely a tricky question. We're looking to
find a group of cities that could all have no hospitals in them.

From the rules, we know that city 2 and city 3 have universities and
city 6 has a jail and hospital. Given the information in this
question, we know that either city 2 or city 3 will have two
hospitals, but we don't know which one will have the two hospitals. We
also know that at least one of them has to have two hospitals. This
means that we can eliminate (C) because (C) is saying that both city 2
and city 3 wouldn't have a hospital.

We also know that (D) and (E) are out because we know that city 6 must
have a hospital since it has a jail. This gets us down to (A) and (B).
Looking at (B), we can eliminate it because the second jail has to go
in either city 1, city 4, or city 5, and this means that one of these
cities will also have a hospital in it because every city with a jail
has a hospital. Since we know we can't have a scenario where 1, 4, and
5 don't have a hospital, we can get rid of (B).

This leaves us with (A). We know (A) works because it could be true
that the two hospitals and one university are in city 2 and the jail
and hospital are in city 4. This means that city 1, city 3, and city 5
wouldn't have a hospital.

Does this make sense? Let us know if you have any more questions!