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# The waiter at an expensive restaurant has noticed that 60%

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Intern
Joined: 01 Apr 2013
Posts: 21
The waiter at an expensive restaurant has noticed that 60%  [#permalink]

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Updated on: 04 Apr 2013, 02:28
5
23
00:00

Difficulty:

85% (hard)

Question Stats:

52% (02:15) correct 48% (02:02) wrong based on 690 sessions

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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%

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Originally posted by Tagger on 03 Apr 2013, 17:06.
Last edited by Bunuel on 04 Apr 2013, 02:28, edited 1 time in total.
Renamed the topic and edited the question.
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Joined: 02 Sep 2009
Posts: 52182
The waiter at an expensive restaurant has noticed that 60%  [#permalink]

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04 Apr 2013, 02:46
16
8
Tagger wrote:
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%

Probably the best way to solve this question is using the double set matrix, as shown below:

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.

Hope it's clear.

Attachment:

Coffee and Dessert.png [ 3.79 KiB | Viewed 19373 times ]

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Re: The waiter at an expensive resturant has noticed  [#permalink]

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03 Apr 2013, 20:27
1
1
Tagger wrote:

The waiter at an expensive resturant has noticed that 60% of the couples order desert and coffee. However, 20% of the couples who order desert dont order coffee. what is the probability that the next couple the waiter seats will not order desert?

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

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.
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Re: The waiter at an expensive restaurant has noticed that 60%  [#permalink]

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17 Aug 2013, 21:25
Solving for X in the figure shown below we will get Couples for deserts as 75%
And couples not ordering deserts =100-75=25%
Attachments

2set.JPG [ 14 KiB | Viewed 15968 times ]

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Joined: 10 Jul 2013
Posts: 314
Re: The waiter at an expensive restaurant has noticed that 60%  [#permalink]

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18 Aug 2013, 15:31
1
Tagger wrote:
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%

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 %
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Asif vai.....

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Joined: 25 Oct 2013
Posts: 148
Re: The waiter at an expensive restaurant has noticed that 60%  [#permalink]

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24 Jan 2014, 05:09
2
1
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%.
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Re: The waiter at an expensive restaurant has noticed that 60%  [#permalink]

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12 Feb 2015, 23:24
Tagger wrote:
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%

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
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The waiter at an expensive restaurant has noticed that 60%  [#permalink]

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13 Apr 2016, 17:52
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%
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The waiter at an expensive restaurant has noticed that 60%  [#permalink]

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08 Oct 2016, 11:50
Tagger wrote:
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%

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%
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Re: The waiter at an expensive restaurant has noticed that 60%  [#permalink]

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24 Dec 2016, 12:28
Bunuel wrote:
Tagger wrote:
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%

Probably the best way to solve this question is using the double set matrix, as shown below:
Attachment:
Coffee and Dessert.png
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.

Hope it's clear.

what about (Neither) those who didnt order coffee nor desert
Math Expert
Joined: 02 Sep 2009
Posts: 52182
Re: The waiter at an expensive restaurant has noticed that 60%  [#permalink]

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25 Dec 2016, 00:53
yezz wrote:
Bunuel wrote:
Tagger wrote:
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%

Probably the best way to solve this question is using the double set matrix, as shown below:

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.

Hope it's clear.

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

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).
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Re: The waiter at an expensive restaurant has noticed that 60%  [#permalink]

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07 Mar 2017, 07:50
Why shouldn't it be solved as
60 + 20 = x.

Posted from my mobile device
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Joined: 02 Sep 2009
Posts: 52182
Re: The waiter at an expensive restaurant has noticed that 60%  [#permalink]

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07 Mar 2017, 08:20
Nikita16 wrote:
Why shouldn't it be solved as
60 + 20 = x.

Posted from my mobile device

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.
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Re: The waiter at an expensive restaurant has noticed that 60%  [#permalink]

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14 Mar 2018, 15:07
Tagger wrote:
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%

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.

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Re: The waiter at an expensive restaurant has noticed that 60% &nbs [#permalink] 14 Mar 2018, 15:07
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