From the outskirts to the center of a city, there are three bus lines – lines 1, 2 and 3 – that make this journey, each of which takes no more than 2 hours to go back to the outskirts. Line 1 departs every 15 minutes, and Line 2 departs every 25 minutes. The three bus lines leave the periphery at the same time every 10 hours. All possible time intervals in which line 3 passes on the outskirts towards the city center are, in minutes, every: ...d) 8,24,40, 200 e) 8, 24,40, 120 (Answer:e)
I did not understand the answer. Why couldn't the letter "e" be?
I try: 10h = 600 min
$3.5^2.y = 600 \implies y = 8\\ 8,16,24,32,64...120...200...600$
$10h = 600 min\\ 3.5^2.y=600 \implies y=88,16,24,32,64...120...200...600$
Therefore, the interval for line $3$ to pass through the periphery would be multiples of $8 $min but it cannot take more than $2h = 120 min$ to pass through the outskirts therefore letter $"e"$