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New cars leave a car factory in a repeating pattern of red, blue, blac

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New cars leave a car factory in a repeating pattern of red, blue, blac  [#permalink]

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New post 13 Aug 2018, 05:01
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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.

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Re: New cars leave a car factory in a repeating pattern of red, blue, blac  [#permalink]

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New post 13 Aug 2018, 07:16
Waiting for the OA. Is the answer (C) Black?
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.

I have simply divided 460/4 to get 115 (115th car should be Gray) and then counted three more to 463, hence black. Is there a robust method as well?
Thanks, in advance!
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Re: New cars leave a car factory in a repeating pattern of red, blue, blac  [#permalink]

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New post 13 Aug 2018, 07:37
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.


463/4 = 115 Cycles + 3 Cars

So, After 115 Cycles the 3rd Cycle is Black, Answer must be (C)
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Re: New cars leave a car factory in a repeating pattern of red, blue, blac  [#permalink]

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New post 14 Aug 2018, 06:39

Solution


Given:
    • Cars leave a car factory in a repeating pattern : red, blue, black and grey
    • The first car to exit the factory was red

To find:
    • The color of the 463rd car that exits the factory

Approach and Working:
    • Since, the total number of cars is four and they follow a repeated pattern and the first car to exit is red.
      o The pattern will be red, blue, black, grey, red, blue and so on
      o So, again the 5th car, 9th car and so on will be red.
      o We can write the general form as, every number of the car, which is in the form, 4n + 1 will be red, where n is a non-negative integer.
      o Similarly, every number of the car, which is in the form,
         4n + 2 will be blue,
         4n + 3 will be black, and
         4n + 4 will be grey
    • 463 can be written as 4 * 115 + 3, which is of the form 4n + 3.

Therefore, the 463rd car to exit will be black in color

Hence, the correct answer is option C .

Answer: C

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Re: New cars leave a car factory in a repeating pattern of red, blue, blac  [#permalink]

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New post 18 Aug 2018, 19:31
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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Re: New cars leave a car factory in a repeating pattern of red, blue, blac &nbs [#permalink] 18 Aug 2018, 19:31
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