Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 21 Jul 2019, 12:28

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56307
New cars leave a car factory in a repeating pattern of red, blue, blac  [#permalink]

### Show Tags

13 Aug 2018, 05:01
00:00

Difficulty:

15% (low)

Question Stats:

79% (00:53) correct 21% (00:58) wrong based on 113 sessions

### HideShow timer Statistics

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.

_________________
Manager
Joined: 10 May 2018
Posts: 123
Concentration: Finance, Sustainability
Re: New cars leave a car factory in a repeating pattern of red, blue, blac  [#permalink]

### Show Tags

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?
_________________
Stuck in the 600-700 score bracket? I welcome you to read my four-step course of action to a modest score.
I also invite you to critique and help me find flaws in my modus operandi. Thanks!
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4512
Location: India
GPA: 3.5
Re: New cars leave a car factory in a repeating pattern of red, blue, blac  [#permalink]

### Show Tags

13 Aug 2018, 07:37
1
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)
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2943
Re: New cars leave a car factory in a repeating pattern of red, blue, blac  [#permalink]

### Show Tags

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 .

_________________
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2822
Re: New cars leave a car factory in a repeating pattern of red, blue, blac  [#permalink]

### Show Tags

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.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

CEO
Joined: 12 Sep 2015
Posts: 3857
Re: New cars leave a car factory in a repeating pattern of red, blue, blac  [#permalink]

### Show Tags

29 Nov 2018, 07:16
Top Contributor
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.

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

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Re: New cars leave a car factory in a repeating pattern of red, blue, blac   [#permalink] 29 Nov 2018, 07:16
Display posts from previous: Sort by