Bunuel wrote:

New cars leave a car factory in a repeating pattern of red, blue, black, and gray cars. If the first car to exit the factory was red, what color is the 463rd car to exit the factory?

(A) Red

(B) Blue

(C) Black

(D) Gray

(E) It cannot be determined from the information given.

We see we have a repeating pattern of 4, so for a nonnegative integer k, we have:

(4k + 1)st car is red, (4k + 2)nd car is blue, (4k + 3)rd car is black and (4k + 4)th car is gray

Since 460 is a multiple of 4, then the 461st car was red, 462nd was blue, and 463rd was black.

Alternate Solution:

The 1st, 2nd, 3rd, and 4th car colors are red, blue, black, and gray, respectively. We note that the 4th, 8th, 12th, 16th, … cars are all gray. We see, then, that all cars that are multiples of 4 will be gray. Thus, the 460th car will be gray, the 461st will be red, the 462nd will be blue, and the 463rd will be black.

Answer: C

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