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

Question

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

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

DinkarDK · Answer

2 × 2 × 1 × 2 × 2 × 2 = 2^5 option d

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Vpareek21 · Answer

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

JeffTargetTestPrep · Answer

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

AbbyJ · Answer

Although I arrived at the correct answers looking at the answer choices, initially I had gone through the problem like this:

if wednesday is fixed:
1. Thursday would have only 2 options
2.Monday would have 3 options
3. Tuesday would have only one option left (since Wed and Mon are already taken)
4. Rest of the days would have 2 option each, considering condition for desserts on consecutive days

Initial Answer: 3*1*2*2*2

Logically I cant find issue with this approach, can someone please help why this would be wrong?

pudu · Answer

why on Monday only 2 options? Sunday is a holiday. So consecutive days constraints is not there. Then why can't we take 3 for Monday?

lowkyprofessional · Answer

Same Question. Since Sunday is a holiday, don't I get 3 options to choose from on Monday? Please help me understand.

GK2722 · Answer

Can Anyone please help on this? won't we get 3 options on monday?

GiridharRamji · Answer

Hey,

Just breaking down the logic
1. Case 1 when Monday you select Brownie
Monday : Brownie (1)
Tuesday: two possibilities (cake or the other dessert) (2)
Wednesday: 1
Thursday : 2(Other than brownie)
Friday : 2( other than Thursday’s choice)
Saturday: 2(other than thursdays choice

So we have in case 1 where Monday we select brownies 
1*2*1*2*2*2 =2^4

Now let us consider the case when Monday has either of the two other desserts other than brownies

So Monday : 2 possibilities (other than Brownie)
Tuesday : 1 Possibility
As 1 of the choices are already selected on Monday, and the other is selected on Wednesday which leaves only one choice here 
Wednesday: 1
Thursday : 2(All choices other than wednesdays)
Friday : 2 (All choices other than Thursday)
Saturday : 2 (All choices other than Friday)

Hence for the second case, where on Monday we have any of the two desserts other than brownies, the number of menu options are

2*1*1*2*2*2 =2^4

Now we add both possibilities of both cases

We get 
2^4+2^4 =2^5

Hope it helps

Krunaal · Answer

Since Wednesday is fixed, we go reverse from Wednesday towards Monday (M <- Tu <- W), and forward from Wednesday to Saturday (W -> Th -> F -> Sa) _ _ B _ _ _ So, Tu has 2 choices (_ 2 B _ _ _), now based on what's selected on Tu, Monday will have remaining 2 choices ( 2 2 B _ _ _) That's the reason Monday doesn't get 3 options. Hope it helps.

pappal · Answer

3 choices cannot be assumed for any day as for the next day we will be left with no choice, as on no consecutive day we can have the same desert.

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

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