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A local restaurant prepares one of three desserts every day they are

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A local restaurant prepares one of three desserts every day they are  [#permalink]

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New post 17 Apr 2018, 05:08
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A
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  25% (medium)

Question Stats:

66% (02:07) correct 34% (02:29) wrong based on 64 sessions

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A local restaurant prepares one of three desserts every day they are open, Monday through Saturday: cake, pastries, or brownies. If the dessert on Wednesday must be brownies and the same dessert is not served on consecutive days, how many different menus for the week are possible?

A. 3*2^5
B. 3^6
C. 3^2*2^4
D. 2^5
E. 2^3*3^3

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Re: A local restaurant prepares one of three desserts every day they are  [#permalink]

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New post 17 Apr 2018, 05:11
2 × 2 × 1 × 2 × 2 × 2 = 2^5 option d

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Re: A local restaurant prepares one of three desserts every day they are  [#permalink]

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New post 18 Apr 2018, 05:34
hello,
mon tue wed thu fri sat

2c1 2c1 B 2c1 2c1 2c1 = 2 x 2 x 1 x 2 x 2 x 2= 2^5

treat WEDNESDAY as the center point for solving the problem and move in either direction.
since no desert can be served on consecutive days , hence tue and wed have 2c1 possibilities , and so on.

hence the answer is D
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Re: A local restaurant prepares one of three desserts every day they are  [#permalink]

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New post 19 Apr 2018, 16:56
Bunuel wrote:
A local restaurant prepares one of three desserts every day they are open, Monday through Saturday: cake, pastries, or brownies. If the dessert on Wednesday must be brownies and the same dessert is not served on consecutive days, how many different menus for the week are possible?

A. 3*2^5
B. 3^6
C. 3^2*2^4
D. 2^5
E. 2^3*3^3


Since Wednesday must be brownies, then on Tuesday and Thursday, we have two choices (cake and pastries) for each of these two days. Then on Monday and Friday, we have two choices for each of these two days also because the choice has to be different from the day before or after. Finally, we have two choices for Saturday also because the choice for Saturday has to be different from Friday. Thus, the number of choices we have (counting from Monday) is:

2 x 2 x 1 x 2 x 2 x 2 = 2^5

Answer: D
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Re: A local restaurant prepares one of three desserts every day they are &nbs [#permalink] 19 Apr 2018, 16:56
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