A straight one-way city street has 8 consecutive traffic lights. Every light remains green for 1.5 minutes, yellow for 3 seconds, and red for 1.5 minutes. The lights are synchronized so that each light turns red 10 seconds after the preceding one turns red. What is the longest interval of time, in seconds, during which all 8 lights are green?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Since each light turns red 10 seconds after the preceding one, and the lights are all on cycles of equal time, then each light will turn green 10 seconds after the preceding one. So let's say that the first light turns green at time 0 seconds. The question to ask is, "When will the last light turn green?"

Since it is the eighth light, it will turn green at time 70 seconds (seven intervals of 10 seconds later). At this point, the first light is still green, since it remains green for 1.5 minutes or 90 seconds, and will remain green for another 20 seconds.

(This first light will then turn yellow at time 90 seconds, and then red at time 93 seconds, and then each of the other lights will turn red until the eighth light turns red at time 163 seconds, when the first light is still red.)

So the only time when all eight lights are green is the interval above, and so the longest interval of time when all the lights are green is 20 seconds.

(Note that the length of time that the light was yellow has no relevance to the situation.)

ANSWER: (C)