Last visit was: 19 Jul 2024, 22:56 It is currently 19 Jul 2024, 22:56
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
User avatar
Intern
Intern
Joined: 01 Apr 2013
Posts: 15
Own Kudos [?]: 298 [94]
Given Kudos: 9
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642410 [43]
Given Kudos: 86332
Send PM
User avatar
Manager
Manager
Joined: 25 Oct 2013
Posts: 114
Own Kudos [?]: 166 [9]
Given Kudos: 55
Send PM
General Discussion
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 485
Own Kudos [?]: 3136 [5]
Given Kudos: 141
Send PM
Re: The waiter at an expensive resturant has noticed [#permalink]
3
Kudos
1
Bookmarks
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.
User avatar
Director
Director
Joined: 03 Aug 2012
Posts: 587
Own Kudos [?]: 3220 [0]
Given Kudos: 322
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE:Information Technology (Investment Banking)
Send PM
Re: The waiter at an expensive restaurant has noticed that 60% [#permalink]
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
2set.JPG [ 14 KiB | Viewed 38813 times ]

avatar
Manager
Manager
Joined: 10 Jul 2013
Posts: 228
Own Kudos [?]: 1049 [1]
Given Kudos: 102
Send PM
Re: The waiter at an expensive restaurant has noticed that 60% [#permalink]
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 %
avatar
Manager
Manager
Joined: 18 Aug 2014
Posts: 94
Own Kudos [?]: 149 [1]
Given Kudos: 36
Location: Hong Kong
Schools: Mannheim
Send PM
Re: The waiter at an expensive restaurant has noticed that 60% [#permalink]
1
Bookmarks
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
VP
VP
Joined: 07 Dec 2014
Posts: 1067
Own Kudos [?]: 1608 [0]
Given Kudos: 27
Send PM
The waiter at an expensive restaurant has noticed that 60% [#permalink]
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%
Manager
Manager
Joined: 30 Dec 2015
Posts: 58
Own Kudos [?]: 120 [1]
Given Kudos: 173
GPA: 3.92
WE:Engineering (Aerospace and Defense)
Send PM
The waiter at an expensive restaurant has noticed that 60% [#permalink]
1
Kudos
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%
Retired Moderator
Joined: 05 Jul 2006
Posts: 847
Own Kudos [?]: 1575 [0]
Given Kudos: 49
Send PM
Re: The waiter at an expensive restaurant has noticed that 60% [#permalink]
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.

Answer: B.

Hope it's clear.


what about (Neither) those who didnt order coffee nor desert
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642410 [0]
Given Kudos: 86332
Send PM
Re: The waiter at an expensive restaurant has noticed that 60% [#permalink]
Expert Reply
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.

Answer: B.

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).
avatar
Intern
Intern
Joined: 10 Jan 2017
Posts: 1
Own Kudos [?]: [0]
Given Kudos: 3
Send PM
Re: The waiter at an expensive restaurant has noticed that 60% [#permalink]
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
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642410 [0]
Given Kudos: 86332
Send PM
Re: The waiter at an expensive restaurant has noticed that 60% [#permalink]
Expert Reply
Nikita16 wrote:
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


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.
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19175
Own Kudos [?]: 22679 [1]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: The waiter at an expensive restaurant has noticed that 60% [#permalink]
1
Kudos
Expert Reply
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.

Answer: B
Intern
Intern
Joined: 25 Sep 2018
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 5
Send PM
Re: The waiter at an expensive restaurant has noticed that 60% [#permalink]
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
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5316
Own Kudos [?]: 4232 [0]
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
The waiter at an expensive restaurant has noticed that 60% [#permalink]
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˜DessertTotal
Coffee.8x%=60%
˜Coffee.2x%
Totalx%


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


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


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

IMO B
GMAT Club Bot
The waiter at an expensive restaurant has noticed that 60% [#permalink]
Moderator:
Math Expert
94421 posts