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Anjeanette inserts light bulbs in a row of light sockets in the repeat

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Anjeanette inserts light bulbs in a row of light sockets in the repeat  [#permalink]

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New post 14 Apr 2017, 11:55
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A
B
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Difficulty:

  35% (medium)

Question Stats:

71% (01:46) correct 29% (02:38) wrong based on 57 sessions

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Anjeanette inserts light bulbs in a row of light sockets in the repeating pattern red bulb, white bulb, white bulb, red bulb, white bulb, and white bulb. If she inserts a total of n red bulbs in the row, including the first and last bulbs, how many white bulbs did she insert in the row?

A. 2n − 2
B. 2n − 1
C. 2n + 1
D. 3n − 2
E. 3n + 1

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Re: Anjeanette inserts light bulbs in a row of light sockets in the repeat  [#permalink]

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New post 14 Apr 2017, 12:32
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SajjadAhmad wrote:
Anjeanette inserts light bulbs in a row of light sockets in the repeating pattern red bulb, white bulb, white bulb, red bulb, white bulb, and white bulb. If she inserts a total of n red bulbs in the row, including the first and last bulbs, how many white bulbs did she insert in the row?

A. 2n − 2
B. 2n − 1
C. 2n + 1
D. 3n − 2
E. 3n + 1


The pattern is as follows
RWWR----------------2R 2W
RWWRWWR----------3R 4W
RWWRWWRWWR----4R 6W

this pattern is given by 2n-2 for a total of n red bulbs in the row, including the first and last bulbs

Hence option A is correct
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Re: Anjeanette inserts light bulbs in a row of light sockets in the repeat  [#permalink]

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New post 14 Apr 2017, 15:50
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Each red bulb is followed by two white bulbs, so for 'n' red bulbs 2n white bulbs will be inserted. As the last \(n^t^h\) bulb was red, we need to subtract the 2 white bulbs from the total count 2n, hence it is 2n-2
Answer: A
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Re: Anjeanette inserts light bulbs in a row of light sockets in the repeat  [#permalink]

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New post 14 Apr 2017, 17:28
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Given that this sequence holds for any n, we can play with N=1 which we know it is red (and 0 white)

Answer A 2(1)-2=0
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Re: Anjeanette inserts light bulbs in a row of light sockets in the repeat  [#permalink]

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New post 15 Apr 2017, 01:37
Pattern: RWWRWW

Consider an example:

Since pattern ends with red:

RWWRWWR or RWWRWWRWWR

First pattern --> R =3 and white = 4; Second pattern --> R= 4 and W = 6

Since R = n; substitute in options

A satisfies
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Re: Anjeanette inserts light bulbs in a row of light sockets in the repeat  [#permalink]

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New post 04 Oct 2018, 17:09
Thank you all so much. I'm one month into my 3 month study plan and I'm almost done with princeton review. Their explanations are horrible. The explanations on this site are much more rigorous and elegant. As soon as I get my score where I want it to be, I'm going to be sure to give back by helping others on this site.
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Re: Anjeanette inserts light bulbs in a row of light sockets in the repeat   [#permalink] 04 Oct 2018, 17:09
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