The waiter at an expensive restaurant has noticed that 60%

Question

The waiter at an expensive restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability that the next couple the waiter seats will not order dessert?

A. 20%
B. 25%
C. 40%
D. 60%
E. 75%

A. 20% 
B. 25% 
C. 40% 
D. 60% 
E. 75%

Bunuel · Accepted Answer

Probably the best way to solve this question is using the double set matrix, as shown below: https://gmatclub.com/forum/download/file.php?id=19841 From above, we have that 60+0.2x=x --> x=75. Thus, the probability that the next couple will not order dessert (yellow box) is 100-75=25. Answer: B. Hope it's clear. Coffee and Dessert.png

gmatprav · Answer

Let total number of couples be 100.

60% order Dessert & Coffee = 60 couples.
20% who order Dessert do not order coffee => 80% who order dessert also order coffee this is given to be 60.
Hence total number of couples who order Dessert is 60*100/80 = 75. 
Number of couples who do NOT order Dessert = 100-75 = 25. 
The probability that next order will not have dessert is 25%.

mau5 · Answer

Let the number of people ordering only desert = d, only ordering coffee be c and ordering both be b. Given that , 20 % of (b+d) = d

or 4d = b.

Thus, as b = 60, d = 15. The total number of people not ordering desert = 100-(60+15) = 25.

B.

TGC · Answer

Solving for X in the figure shown below we will get Couples for deserts as 75%
And couples not ordering deserts =100-75=25%

Asifpirlo · Answer

Let, total dessert ordered = T and total couple = 100
 From question,
 60+20% of T = T
 or, T = 75 % ordered dessert.

So next couple will not order dessert = 100-75 = 25 %

LaxAvenger · Answer

I solved this pretty fast this way:

60% dessert and coffee
--> 40% nothing, dessert, or coffee

Let them be the same probability --> 40% / 3 = 13,333%

40% - 13% = 27% --> Answer has to be around this range --> B is closest

gracie · Answer

let total couples=100
let d=couples who order dessert
d-60=.2d
d=75 couples
100-75=25 couples who don't order dessert
25/100=25%

colorblind · Answer

60% order (C+D) i.e Both = 60% of Total
20% of D is without C; i.e. 80% of D also orders C 
80% of D = Both
80% of D = 60% of Total
 \frac{D}{Total} =\frac{60}{80} = \frac{3}{4} 
Hence,  \frac{C}{Total} = \frac{1}{4}  = 25%

yezz · Answer

what about (Neither) those who didnt order coffee nor desert

Bunuel · Answer

To get the probability that the next couple will not order dessert we need the percentage of those who do not order dessert which is 25. Those 25% include Coffee/No Dessert and No Coffee/No Dessert (Neither).

Nikita16 · Answer

Please help me to understand why is the equation is 60+0.2x = x. 
Why shouldn't it be solved as 
60 + 20 = x.

Posted from my mobile device

Bunuel · Answer

We are given that 20% of the couples who order dessert don't order coffee. We denoted those who order dessert by x, thus those who order dessert but don't order coffee is 20% of that, which is 0.2x.

ScottTargetTestPrep · Answer

You can use the following equation:

Total = Dessert only + Coffee only + Both + Neither

Instead of using percents, let’s use numbers. If we let the total number of customers be 100, then we see that 60 of them will order dessert and coffee:

100 = D + C + 60 + N

Since we have let D = the number of couples ordering Dessert only, we know that the total number of couples ordering Dessert is (D + 60), which is “Dessert only” plus “Both.”. Since 20% of the couples who order dessert don't order coffee, that means “Dessert only” is 20% of the total of “Dessert only” and “Both;” that is,

D = 0.2(D + 60)

5D = D + 60

4D = 60

D = 15

Substituting, we have:

100 = 15 + C + 60 + N

100 = 75 + C + N

25 = C + N

Since those who don’t order dessert are the total of “Coffee only” and “Neither,” we have 25% of the couples who don’t order dessert.

Answer: B

ninadantro · Answer

there are 3 cases here:
1) dessert = D (this includes couples who order only dessert + couples who order dessert and coffee) 
2) dessert and coffee = b
3) coffee = C (this includes couples who order only coffee + couples who order dessert and coffee)

We have been told that 60% of couples order both. 
=> b is a an intersection of D & C

Also, mentioned in the question is that 20% couples order dessert only but not coffee. If you rephrase it, it means 80% of couples who order dessert also order coffee.

Now let's consider total # couples as 100 (as percentage numbers can be used as is without any conversion)

=> b = 60 => 80% of D=60 => D=75
That tells us that 75 couples out of 100 i.e 75% couples order desserts, that means 25% dont order dessert which is the probability asked.

Answer is 25% (B)

Here please note that no where it is mentioned in the question stem that every couple orders at least a dessert or a coffee or both. So we need to consider the possibility that few couples order nothing. So don't split the numbers as only dessert =20,both= 60, only coffee =20. This is wrong

Here 25% includes only coffee + neither

Posted from my mobile device

Kinshook · Answer

Given: The waiter at an expensive restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee.

Asked: What is the probability that the next couple the waiter seats will not order dessert?

Dessert  ˜Dessert  Total  
  Coffee  .8x%=60%      
  ˜Coffee  .2x%      
  Total  x%

.8x% = 60%
x = 60/.8 = 75

Dessert  ˜Dessert  Total  
  Coffee  .8x%=60%      
  ˜Coffee  .2x% = 15%      
  Total  x%=75%   100%-75%=25%   100%

The probability that the next couple the waiter seats will not order dessert = 25%

IMO B

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The waiter at an expensive restaurant has noticed that 60%

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	Dessert	˜Dessert	Total
Coffee	.8x%=60%
˜Coffee	.2x% = 15%
Total	x%=75%	100%-75%=25%	100%

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The waiter at an expensive restaurant has noticed that 60%

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