NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 12:03 It is currently 26 Apr 2024, 12:03
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If 75 percent of the guests at a certain banquet ordered dessert, what

SORT BY:
Date
Kudos
   1   2 
Tags:
Difficulty: 605-655 Levelx   Overlapping Setsx   Percent and Interest Problemsx                                 
Find Similar Topics 
Show Tags
Hide Tags
User avatar
B
mzaid
Intern
Intern
Joined: 07 May 2017
Posts: 23
Own Kudos [?]: 14 [0]
Given Kudos: 34
Location: India
Concentration: Marketing, General Management
GPA: 4
WE:Analyst (Investment Banking)
Send PM
Reviews Badge
Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink] New post   19 Apr 2020, 00:15
Bunuel wrote:
SOLUTION

If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?

Assume there were 100 guests on the banquet. So we have that 75 of them ordered dessert.

(1) 60 percent of the guests who ordered dessert also ordered coffee --> 0.6*75=45 guests ordered both dessert AND coffee, but we still don't know how many guests ordered coffee. Not sufficient.

(2) 90 percent of the guests who ordered coffee also ordered dessert --> 0.9*(coffee) # of guests who ordered both dessert AND coffee. Not sufficient.

(1)+(2) From (1) # of guests who ordered both dessert AND coffee is 45 and from (2) 0.9*(coffee)=45 --> (coffee)=50. Sufficient.

Answer: C.


Could you please answer why we are not considering guests who would choose neither dessert nor coffee, since it is not explicitly mentioned that they order at least one of the two.
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5962
Own Kudos [?]: 13391 [1]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink] New post   19 Apr 2020, 00:36
1
Kudos
Expert Reply
mzaid wrote:
Bunuel wrote:
SOLUTION

If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?

Assume there were 100 guests on the banquet. So we have that 75 of them ordered dessert.

(1) 60 percent of the guests who ordered dessert also ordered coffee --> 0.6*75=45 guests ordered both dessert AND coffee, but we still don't know how many guests ordered coffee. Not sufficient.

(2) 90 percent of the guests who ordered coffee also ordered dessert --> 0.9*(coffee) # of guests who ordered both dessert AND coffee. Not sufficient.

(1)+(2) From (1) # of guests who ordered both dessert AND coffee is 45 and from (2) 0.9*(coffee)=45 --> (coffee)=50. Sufficient.

Answer: C.


Could you please answer why we are not considering guests who would choose neither dessert nor coffee, since it is not explicitly mentioned that they order at least one of the two.



Hi mzaid It's good to see you on GMAT CLUB :)

The question is

Quote:
If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?

(1) 60 percent of the guests who ordered dessert also ordered coffee.
(2) 90 percent of the guests who ordered coffee also ordered dessert.


We don't have to worry about the people who order none because that's not what the question wants use to figure out to answer the question

here the same number (people who order both coffee and desert) has been explained in two ways in two statements

The same number is representing 90% of those who order coffee so we find out that

90% of Total Coffee orders = 60% of 75

that gives us that 0.8 Coffee orders = 45

i.e. Coffee orders = 45/0.9 = 50

Though we can find out the people who order none by using the double matrix method but that would be unnecessary.

In fact, last calculation also is unnecessary when we have been sure that the solution of the equation (after combining statements) will give us a unique solution of the problem asked.
User avatar
L
Hovkial
Director
Director
Joined: 23 Apr 2019
Status:PhD trained. Education research, management.
Posts: 806
Own Kudos [?]: 1807 [0]
Given Kudos: 203
Send PM
Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink] New post   19 Sep 2020, 22:30
This problem can be solved quickly if we can visualize the information in the form of two overlapping circles, i.e., a Venn diagram. There is no need to assume any values or perform any calculations.

___________Only Dessert________ (both Dessert and Coffee)_____________Only Coffee_______________

The above representation shows a simplified form of overlapping circles. The "circle" on the extreme left shows guests who ordered dessert. This circle includes both guests who ordered only dessert and those who ordered both dessert and coffee. The "circle" on the extreme right shows guests who ordered coffee. This circle includes both guests who ordered only coffee and those who ordered both dessert and coffee. The overlapping portion of the preceding two circles represents guests who ordered both dessert and coffee.

We are asked to determine the number (percent) of the guests who ordered coffee. This number includes both guests who ordered only coffee and those who ordered both coffee and dessert. To determine this number, it is clear that we need to have concrete values for each of the above three categories (only dessert, both dessert and coffee, and only coffee).

(1) 60 percent of the guests who ordered dessert also ordered coffee.

INSUFFICIENT

This statement only provides information about the number (percent) of the guests who ordered both dessert and coffee. The information in the other categories is missing.

(2) 90 percent of the guests who ordered coffee also ordered dessert.

INSUFFICIENT

As in the preceding statement, this statement only provides information about the number (percent) of the guests who ordered both dessert and coffee. The information in the other categories is missing.

(1) and (2) together.

SUFFICIENT

Combining the two statements, we can see that the the category "both dessert and coffee" is clearly determined. Also determined are the values (percent) in the two remaining categories. We are given the "whole" value of each circle and the value of the overlapping category. Hence, the two statements together are sufficient to answer the question of what percent of the guests ordered coffee.
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5962
Own Kudos [?]: 13391 [0]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink] New post   07 Apr 2021, 21:18
Expert Reply
Bunuel wrote:
If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?

(1) 60 percent of the guests who ordered dessert also ordered coffee.
(2) 90 percent of the guests who ordered coffee also ordered dessert.


Answer: Option C

Video solution by GMATinsight



Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub :)
User avatar
B
prakashb2497
Manager
Manager
Joined: 20 Feb 2022
Posts: 148
Own Kudos [?]: 21 [0]
Given Kudos: 160
Send PM
Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink] New post   20 Sep 2022, 21:54
KarishmaB wrote:
alphabeta1234 wrote:
Hey Bunuel,

What mistake am I making?

A- # of people who order desert
B- # of people who order coffee
AnB - # of people who order both dessert and coffe

Given: A=75
Statement 1: AnB=.6*70=45
Given that we know AuB=A+B-AnB

100=75+B-45 ----> B=75. Hence statement 1 should be sufficient.

What am I doing wrong here!!!?? So confused? Please help. Thank you!


When I solve this problem by using the 2x2 grid, its obvious that there is not enough information. But when I try to just use the formula it gives me suffient info.


Do you know how many ordered neither? We cannot say that AuB = 100.




I made the same mistake. I was cognizant of the neither aspect but I didn't consider it. In some Set problems I've noticed we let go of the neither if it is not mentioned and in some we consider it even if it is not mentioned. Can you please help me fill in the gaps here?

KarishmaB Bunuel mikemcgarry
User avatar
G
BLTN
Senior Manager
Senior Manager
Joined: 25 Aug 2020
Posts: 252
Own Kudos [?]: 116 [0]
Given Kudos: 218
Send PM
Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink] New post   02 Nov 2022, 03:38
prakashb2497 wrote:
KarishmaB wrote:
alphabeta1234 wrote:
Hey Bunuel,

What mistake am I making?

A- # of people who order desert
B- # of people who order coffee
AnB - # of people who order both dessert and coffe

Given: A=75
Statement 1: AnB=.6*70=45
Given that we know AuB=A+B-AnB

100=75+B-45 ----> B=75. Hence statement 1 should be sufficient.

What am I doing wrong here!!!?? So confused? Please help. Thank you!


When I solve this problem by using the 2x2 grid, its obvious that there is not enough information. But when I try to just use the formula it gives me suffient info.


Do you know how many ordered neither? We cannot say that AuB = 100.




I made the same mistake. I was cognizant of the neither aspect but I didn't consider it. In some Set problems I've noticed we let go of the neither if it is not mentioned and in some we consider it even if it is not mentioned. Can you please help me fill in the gaps here?

KarishmaB Bunuel mikemcgarry



Dear prakashb2497
the equation is following
Total = A + B - Both (A and B) - Neither
So, "Neither" is mandatory attribute. Yet, you have take it into consideration only when necessary.
In our case we have to find "what percent of the guests ordered coffee?"

% of guests ordered coffee = Both (Coffee and Dessert) + Coffee but not Dessert.
Thus, there is no need to compute Neither.


The following posts can help
https://gmatclub.com/forum/overlapping- ... 05636.html
https://gmatclub.com/forum/advanced-ove ... 44260.html
https://gmatclub.com/forum/formulae-for ... 69014.html
User avatar
B
Sahil2208
Intern
Intern
Joined: 27 Sep 2022
Posts: 32
Own Kudos [?]: 3 [0]
Given Kudos: 12
Send PM
Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink] New post   09 Jan 2023, 04:23
Bunuel wrote:
If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?

(1) 60 percent of the guests who ordered dessert also ordered coffee.
(2) 90 percent of the guests who ordered coffee also ordered dessert.


Bunuel
I got the correct answer. But I have a doubt. Do I need to worry about the possibility of other dishes (dessert, coffee, and maybe something else)? Because the question stem doesn't explicitly mention the existence of only 2 dishes.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619222 [0]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink] New post   09 Jan 2023, 06:33
Expert Reply
Sahil2208 wrote:
Bunuel wrote:
If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?

(1) 60 percent of the guests who ordered dessert also ordered coffee.
(2) 90 percent of the guests who ordered coffee also ordered dessert.


Bunuel
I got the correct answer. But I have a doubt. Do I need to worry about the possibility of other dishes (dessert, coffee, and maybe something else)? Because the question stem doesn't explicitly mention the existence of only 2 dishes.


Some quests could have ordered something else but how is this relevant ? Say you knew that 25% of the guests ordered salad. So what?
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32688
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink] New post   10 Jan 2024, 06:13
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink]
10 Jan 2024, 06:13
   1   2 
Moderator:
Bunuel
Math Expert
92948 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions