It's more a logic question than a math one. The confusion spawns from the fact that the three numbers present in the question are 10, 2, and 3 (so the thought process would be 2 = 10 min so 1 = 5 min, thus 3 = 15 min).
But 2 represents the final state, though requires only 1 action (cut). And the required answer (time spent) is related to the number of actions, not the final state.
This reminds me of the water lily problem: a water lily doubles in size every day. It takes 30 days to cover the whole pond. How many days does it take for the water lily to cover half the pond? (Answer: 29, not 15).
My teacher used to give me this example when I was a kid: You see one matchstick with one eye. How many will you see with two eyes? :-)
Here's another one that used to confuse high school students in my class: You look at a 10 degrees angle with a lens of 3X magnification. How much would the angle look like? :-)
I hadn't heard of the water lily problem either. The answer was completely obvious to me, but I don't think this was because I'm particularly intelligent or math savvy, but rather because I'm used to working in binary, which I think gives you a better intuitive sense of the concept of doubling.
But 2 represents the final state, though requires only 1 action (cut). And the required answer (time spent) is related to the number of actions, not the final state.
This reminds me of the water lily problem: a water lily doubles in size every day. It takes 30 days to cover the whole pond. How many days does it take for the water lily to cover half the pond? (Answer: 29, not 15).