If one of the cities contains exactly two hospitals and exactly one university, then which one of the following lists...
maonuoNovember 16, 2019
Please help
Shouldn't the answer choice definitely contain city 2 because J cannot be placed their, hence the hospital cannot go there either. I studied Mehran's explanation but I don't think I understand the question. Please explain.
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The question asks us if one of the cities contains exactly two hospitals and exactly one university, which of the following lists three cities that might contain no hospital.
Let's consider this scenario. If one of the cities contains exactly one hospital and exactly one university, we can infer that each of the cities that contain a jail contain one hospital, resulting in the following scenario:
1U - 2H 1J- 1H 1J -1H
We know that City 6 contains a jail so it must contain a hospital, thus we can eliminate (D) and (E).
We know that City 2 and 3 contain universities, and one of them also contains two hospitals in this hypothetical, thus we can eliminate (C) as it lists both City 2 and 3 as having no hospitals.
Now we know that City 6 contains a jail and one more city must contain a jail, but since no city can contain both a jail and a university, City 2 and 3 cannot contain a jail, thus the second jail must be in either City 1, 4, or 5. Every city that contains a jail must contain a hospital, thus no matter which combination of cities contain the two jails: 6 &1 6 & 4 or 6 &5
it is not possible that neither city 1, nor city 4, nor city 5 contain a hospital. At least one of the must definitely contain a jail and a hospital, thus we can eliminate (B), leaving us with (A) as the correct answer choice.
Just to demonstrate that (A) indeed could be true and none of the cities - 1, 3 or 5 contain a hospital, we can come up with the following scenario that complies with all the rules:
1: 2: 1U 2H 3: 1U 4: 1J 1H 5: 6: 1J 1H
Let me know if this makes sense and if you have any further questions.
IrinaNovember 17, 2019
@maunuo,
Just to add to this, the rules only tell us that any city that contains a jail must contain a hospital, we cannot infer that just because a city has no jail, it has no hospital. In fact, this question specifically presents a scenario where a city contains a university and two hospitals (and no jails).
