Group Games Questions - - Question 14

If Hannah visits an equal number of cities in each of the countries, what is the greatest total number of days she ca...

carettir January 17, 2020

Common?

Please tell me that questions like this one are not common. This one actually hurt my brain.

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SamA January 17, 2020

Hello @carettir,

This is definitely an unusual question, probably because this test is from 1991. Its use of "must be true" is different than on modern tests, so you won't see that anymore. It took me a minute to get it as well, but then it wasn't so difficult. It is certainly possible that you get a weird question type on your test. However, this is not common. Maybe that answers your question, but I'm going to go over it just in case.

Hannah has 14 days to visit 6 cities. We know that she has to visit at least one city in X, Y, or Z. She has to spend at least two days in each city she visits. So, what can we say for certain? We know there are at least two days spent in each country.

X: 2
Y: 2
Z: 2

13. If Hannah spends 8 days in country X.
X: 8
Y: 2
Z: 2
This gives us only two extra days to place. If she visits only two cities in country X, we do not have enough days to reach our 6 city requirement. A cannot be true.

14. Hannah visits an equal number of cities in each country. That is two each, with a minimum of 4 days.
X: 4
Y: 4
Z: 4
We now have two days left to distribute. If we want to maximize time in country X, then 6 is the best we can do. D is correct.

15.
X: 4 (2 cities max)
Y: 3 (1 city max)
Z: 7 (must include 3 cities)
She has to visit 3 cities in Z to reach the 6 city requirement, so D cannot be true.

16. Other than Nomo, the five other cities (2 days each), need a minimum total of 10 days. 4 days in Nomo is the maximum.
X: 4 (Nomo)
Y: 2
Z: 2
We have 6 days left to distribute, and they don't have many restrictions. They could all go to any of the cities, which is why B is correct.

17. If she visits exactly 4 cities in X and Y, then she must visit two in Z. This is at least 4 days. She has ten days to divide between X and Y. Therefore, the maximum days in Y must be 8. C is correct.
X: 2
Y: 8
Z: 4