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A dessert chef prepares the dessert for every day of a week starting

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A dessert chef prepares the dessert for every day of a week starting  [#permalink]

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New post 22 Apr 2019, 01:47
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A
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Difficulty:

  55% (hard)

Question Stats:

42% (02:14) correct 58% (02:18) wrong based on 31 sessions

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A dessert chef prepares the dessert for every day of a week starting with Sunday. The dessert each day is either cake, pie, ice cream, or pudding. The same dessert may not be served two days in a row. There must be cake on Friday because of a birthday. How many different dessert menus for the week are possible?

(A) 729
(B) 972
(C) 1024
(D) 2187
(E) 2304

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A dessert chef prepares the dessert for every day of a week starting  [#permalink]

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New post 22 Apr 2019, 03:21
I've started counting possibilities from Friday

S - 3 posibilities
M - 3
T - 3
W - 3
Th - 3
F - 1 (cake)
Sat - 3

As on Friday we have got a cake on Thursday and Saturday we can have only 3 possibilities (pudding, ice-cream, pie)
As on Thursday we have 3 possibilities, on Wednesday we will have 3 as well, not the one which was on Thursday and so on.

Cant bet my approach is 100%, any expert reply wont be redundant

IMO
Ans: A
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Re: A dessert chef prepares the dessert for every day of a week starting  [#permalink]

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New post 22 Apr 2019, 03:30
Bunuel wrote:
A dessert chef prepares the dessert for every day of a week starting with Sunday. The dessert each day is either cake, pie, ice cream, or pudding. The same dessert may not be served two days in a row. There must be cake on Friday because of a birthday. How many different dessert menus for the week are possible?

(A) 729
(B) 972
(C) 1024
(D) 2187
(E) 2304


we will have 3 possibilities of dishes per day starting friday ;
total ; 3^6 ; 729
IMO A
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Re: A dessert chef prepares the dessert for every day of a week starting  [#permalink]

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New post 22 Apr 2019, 07:09
Archit3110 wrote:
Bunuel wrote:
A dessert chef prepares the dessert for every day of a week starting with Sunday. The dessert each day is either cake, pie, ice cream, or pudding. The same dessert may not be served two days in a row. There must be cake on Friday because of a birthday. How many different dessert menus for the week are possible?

(A) 729
(B) 972
(C) 1024
(D) 2187
(E) 2304


we will have 3 possibilities of dishes per day starting friday ;
total ; 3^6 ; 729
IMO A


Hi Archit3110 ,
Why not start with Sunday where we will have 4 possibilities and go on like
Monday - 3 , Tue-3, Wed-3, Thu- 2( 3-1 because cake on friday) , friday- 1(cake) , and saturday - 3

Could you explain why is this approach wrong?

TIA
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Re: A dessert chef prepares the dessert for every day of a week starting  [#permalink]

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New post 22 Apr 2019, 10:26
neha283 wrote:
Archit3110 wrote:
Bunuel wrote:
A dessert chef prepares the dessert for every day of a week starting with Sunday. The dessert each day is either cake, pie, ice cream, or pudding. The same dessert may not be served two days in a row. There must be cake on Friday because of a birthday. How many different dessert menus for the week are possible?

(A) 729
(B) 972
(C) 1024
(D) 2187
(E) 2304


we will have 3 possibilities of dishes per day starting friday ;
total ; 3^6 ; 729
IMO A


Hi Archit3110 ,
Why not start with Sunday where we will have 4 possibilities and go on like
Monday - 3 , Tue-3, Wed-3, Thu- 2( 3-1 because cake on friday) , friday- 1(cake) , and saturday - 3

Could you explain why is this approach wrong?

TIA


neha283
well if you start from sunday with 4 options then how will be sure that the option for Friday viz. cake will be correct?
which is why its better to start from friday ,
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Re: A dessert chef prepares the dessert for every day of a week starting  [#permalink]

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New post 22 Apr 2019, 21:58
Starting with friday as 1, moving on to the rest of the days with 3.
3^6

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Re: A dessert chef prepares the dessert for every day of a week starting  [#permalink]

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New post 24 Apr 2019, 17:02
ugh got tricked again. I started on a Sunday so I had
4 * 3 * 3 *3*3*1*3

Ugh it's soo annoying
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Re: A dessert chef prepares the dessert for every day of a week starting  [#permalink]

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New post 26 Apr 2019, 15:30
Bunuel wrote:
A dessert chef prepares the dessert for every day of a week starting with Sunday. The dessert each day is either cake, pie, ice cream, or pudding. The same dessert may not be served two days in a row. There must be cake on Friday because of a birthday. How many different dessert menus for the week are possible?

(A) 729
(B) 972
(C) 1024
(D) 2187
(E) 2304


We have only one option on Friday, which is a cake. Since the dessert on Saturday and Thursday cannot be a cake, there are 3 options for each of those days. The dessert on Wednesday must be different from Thursday; so there are 3 options for Wednesday as well. Similarly, the desert on Tuesday must be different from Wednesday; the desert on Monday must be different from Tuesday and the desert on Sunday must be different from Monday as well; therefore there are 3 options for each of those days as well. In total, there are 3^6 = 729 different menus.

Answer: A
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Re: A dessert chef prepares the dessert for every day of a week starting   [#permalink] 26 Apr 2019, 15:30
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