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A dessert chef prepares the dessert for every day of a week starting
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22 Apr 2019, 01:47
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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 dessert chef prepares the dessert for every day of a week starting
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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
Re: A dessert chef prepares the dessert for every day of a week starting
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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
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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
Re: A dessert chef prepares the dessert for every day of a week starting
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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
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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.
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42% (02:14) correct 
