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

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by AAPL » Thu Nov 29, 2018 5:11 am

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Manhattan Prep

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.

OA C.
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by Brent@GMATPrepNow » Thu Nov 29, 2018 6:08 am
AAPL wrote:Manhattan Prep

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

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by fskilnik@GMATH » Thu Nov 29, 2018 7:08 am
AAPL wrote:Manhattan Prep

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.
$$?\,\,\,:\,\,\,{463^{{\text{rd}}}}\,\,\,{\text{in}}\,\,\,\boxed{\text{R}}{\text{,U,A,G,}}\boxed{\text{R}}{\text{,U,A,G,}}\boxed{\text{R}}, \ldots \,\,\,\,{\text{sequence}}$$
$${\text{R}}\,\,{\text{positions}}\,\,\,{\text{::}}\,\,\,\,{\text{1}}\,\,{\text{,}}\,\,\,{\text{1 + 4}}\,\,{\text{,}}\,\,{\text{1 + 2}} \cdot {\text{4}}\,\,{\text{,}}\,\,{\text{1 + 3}} \cdot {\text{4}}\,\,{\text{,}}\,\, \ldots $$
$$115 \cdot 4 + 1 = 461\,\,\, \to \,\,\,R\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,?\,\,\,:\,\,\,463 \to A\,\,\,\left( {{\text{Black}}} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {\text{C}} \right)$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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