Can you please explain why A is incorrect? How would we explicate A to prove that it is not necessarily true? The questions made it difficult by making it seem as if Nomo was the only city and I believe that's where I got confused and mislead. What is the best approach when this happens?
November 21, 2021
Thirded - can you please explain why A is incorrect? I thought it would be viable for her to spend 8 days in 1 city since she must spend at least 2 days. Can you please explain?
Jay-EtterJanuary 21, 2022
Ok so let's start by breaking down our approach to the question. We know Hannah spends 14 days in 6 cities, with at least 2 days in each city. The question is telling us that Hannah wants to spend as much time in city Nomo (which is in country X) and as few as days as possible in the other cities. So for the other 5 cities besides Nomo, we'll put the minimum number of days, so 2. We have c1 2 days c2 2 days c3 2 days c4 2 days c5 2 days and that leaves us with 4 days to allocate to Nomo, because it is all the days we have left Nomo 4 days.
Note that this means Hannah can never spend more than 4 days in a single city. Now let's put the cities into our countries.
X: Nomo(4) Y: any city (2) Z: any city(2)
Now we have three cities left with 2 days each, and we can allocate them however we want between counties X Y and Z. Running through our answer options
A) This could be true! we could put any of our remaining cities in country X. So it doesn't have to be true that there are no other cities in X. B) This is right! We could allocate all three remaining cities to country Y. (Note that although the question is a must be true, the option specifies " Hannah CAN visit four cities in country Y", making it essentially a could be true. Or, it MUST be true that Hannah COULD visit four cities in country Y). C) Nope, because then she wouldn't have enough days to visit 5 other cities. D) Nope, because we could put our free cities in country Z. E) Nope, because if we put all of our free cities in Y and Z then Hannah would visit five cities in these countries.
Feel free to follow up if you have further questions!
AndrewArabieSeptember 28, 2022
It seems to me that if Hannah goes to another city in country X, she'd have to spend two days there, cutting down her time in Nomo and therefore not reaching her maximum number of days which we see is four unless she decides she doesn't want to visit either Y or Z which I'm not sure is an option.
Can someone help explain where I'm going wrong?
Emil-KunkinNovember 28, 2022
Hi, she would have to spend two days in any city she visits. We already know she spends four days in nomo in X, and thus she spends two days in the remaining five cities, at least one of which is in Y and at least one is in Z. Beyond that, any allocation of our remaining three two-day trips to X y or z is acceptable.
Emil-KunkinNovember 28, 2022
There is no reason that visiting a second city in X means she has to spend less time in X. She could spend four days in nomo, and two in some other city in X.
