The track of a racetrack is $20 \mathrm{~km}$ long and circular, as shown in the figure.

The marked points on the track are $\mathrm{A}$, which is the starting point; B, which is $5 \mathrm{~km}$ from A in the direction of the course; C, which is $3 \mathrm{~km}$ from $\mathrm{B}$ in the direction of the course; $\mathrm{D}$, which is $4 \mathrm{~km}$ from $\mathrm{C}$ in the direction of the course; and E, which is $5 \mathrm{~km}$ from $\mathrm{D}$ in the direction of the course. A car that starts from $\mathrm{A}$ and stops after traveling $367 \mathrm{~km}$ will be closest to which of the five points?
(a) $\mathrm{A}$
(b) B
(c) $\mathrm{C}$
(d) $\mathrm{D}$
(e) E

![](https://cdn.mathpix.com/cropped/2024_05_01_30c9a294a58a6e4b8190g-014.jpg?height=434&width=443&top_left_y=271&top_left_x=1383)
The correct option is (c).

Let's mark the four points starting from A. Since the track measures $20 \mathrm{~km}$, the length of each of the four quadrants is $5 \mathrm{~km}$, and we can then mark the points. Since $367=18 \times 20+7$, the car completed 18 full laps and traveled an additional $7 \mathrm{~km}$ from A. Therefore, it passes $2 \mathrm{~km}$ past B and stops $1 \mathrm{~km}$ from C. Thus, C is the closest point.

![](https://cdn.mathpix.com/cropped/2024_05_01_30c9a294a58a6e4b8190g-062.jpg?height=394&width=397&top_left_y=768&top_left_x=1429)