New cars leave a car factory in a repeating pattern of red, blue, black, and gray cars. If the first car to exit the

[M7MBA]

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.

[spoiler]OA=C[/spoiler]

Source: Manhattan GMAT

[Brent@GMATPrepNow]

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.

[spoiler]OA=C[/spoiler]

Source: Manhattan GMAT

Let's examine the pattern.

CAR # | color
1 | red
2 | blue
3 | black
4 | gray
5 | red
6 | blue
7 | black
8 | gray
9 | red
.
.
.
The pattern REPEATS EVERY 4 CARS. So, we say the pattern has CYCLE 4
Also, notice that every car # that's divisible by 4 is gray

So, let's find a car # that's close to 463 and that's divisible by 4, and we'll go from there.
460 is divisible by 4, so the 460th car will be gray
This means the 461st car will be red
The 462nd car will be blue
And the 463rd car will be black

Answer: C

Cheers,
Brent

[Scott@TargetTestPrep]

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.

[spoiler]OA=C[/spoiler]

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