Bad luck if you answered Buenos Aires, or even Santiago.
If you hadn't heard this question before, I reckon you'd be most likely to go for Buenos Aires – if only because it's on the south–west bank of the River Plate, while Montevideo is on the north–east bank. You might even go for Santiago, because Chile (like Argentina) extends much further south than Uruguay – and it does have the world's most southerly city, in Punta Arenas (which is in the extreme south of the continent).
In fact, as the map below shows, Montevideo just wins it. Without a map to hand however, you'd need a pretty accurate photographic memory to know it. The difference is so small as to make this almost a trick question. But I've heard it asked more than once in quizzes, and that's why it's included here.
Most quizzers would know that Montevideo and Buenos Aires are on opposite sides of the River Plate, even if (as already suggested) many would have gone for the latter as the more southerly. But how many would be able to place Santiago on a map?
Like Argentina, Chile is a big country – measuring well over 2,000 miles from north to south. In fact, Santiago is about two–fifths of the way down; but even that isn't much help in answering this question.
According to Wikipedia, Santiago is at latitude 33° 27' 0" south. Montevideo is at 34° 53' 1" south, and Buenos Aires is at 34° 36' 12" south. In other words, the difference in latitude between the most northerly and the most southerly of these three cities is 1° 26' 1". According to my calculations, one and a half degrees of latitude equate to about 116 miles, so this is the distance by which Montevideo is south of Santiago. In other words: to be able to place Santiago accurately, relative to Montevideo and Buenos Aires, you'd need to be able to place it to within an accuracy of about 5% of the length of Chile.
The difference in latitude between Montevideo and Buenos Aires, by the way, is just under 17 minutes, which (again according to my own calculations) equates to about 20 miles.
© Haydn Thompson 2023