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

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Re: If 75 percent of the guests at a certain banquet ordered dessert, what  [#permalink]

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New post Updated on: 28 Nov 2016, 08:43
ts30 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.


Are we assuming that there are only 2 things to order- Coffee and dessert and everyone made a choice from these 2 things only... Implying that the sum total of coffee and non-coffee takers = 100%?


I have the same doubt. Bunuel, how do we deduce that there isn't a category of people who haven't ordered anything?
Attachments

File comment: Bunuel, this attached file is my interpretation, although I'm still not clear on how the set of people who don't order coffee or dessert doesn't affect the solution
QR2-DS-116.PNG
QR2-DS-116.PNG [ 20.43 KiB | Viewed 3156 times ]


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Originally posted by herbgatherer on 27 Nov 2016, 17:01.
Last edited by herbgatherer on 28 Nov 2016, 08:43, edited 1 time in total.
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what  [#permalink]

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New post 28 Nov 2016, 00:34
1
herbgatherer wrote:
ts30 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.


Are we assuming that there are only 2 things to order- Coffee and dessert and everyone made a choice from these 2 things only... Implying that the sum total of coffee and non-coffee takers = 100%?


I have the same doubt. Bunuel, how do we deduce that there isn't a category of people who haven't ordered anything?


We are not assuming that but the number of people who ordered neither coffee or desert does not play any part in the solution.
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what  [#permalink]

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New post 14 Aug 2018, 16:08
Lets say there are total 100 Guests. We are told 75 ordered Deseret, and we have to calculate % of people who ordered coffee
So what we need is no of people who ordered coffee which is no of people who ordered only coffee and and number of people who ordered both coffee and desert.

Stmt 1: Tells us no of people who ordered both = 45, So if 45 ordered both then only 30 ordered only desert. but we have no information on no of people who ordered only coffee and no of people who ordered none.

Stmt 2: 90 % of those who ordered coffee also ordered desert. Since we don't have the values of those who ordered coffee or those who ordered coffee and desert we cant calculate any thing from this information.

Now we already know from second statement if we have information about no of people ordering both we can calculate no of people who ordered coffee.

So combining Stmt 1 and Stmt 2, We have
90% of x= 45, so x =50, this is number of people who ordered coffee. So we can calculate the required % which is about 50 %
So Only Desert 30, Desert & Coffee 45, Only Coffee 5, 20 none , which gives total 100.

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Re: If 75 percent of the guests at a certain banquet ordered dessert, what  [#permalink]

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New post 30 Apr 2019, 00:24
VeritasKarishma wrote:
Baten80 wrote:
IF 75% of guest at a certain banquet ordered dessert,what percent of guest ordered coffee?

1)60%of the guest who ordered dessert also ordered coffee.

2)90%of the guest who ordered coffee also ordered dessert.


In questions involving sets, venn diagrams can be used. They tend to make questions simple.

We need to find the % of total guests (G) who ordered coffee (C). So we want C in terms of G.
Given D = 75% of G

1. 60% of D ordered coffee too
Attachment:
Ques1.jpg

From the diagram, we see that we do not know what % people ordered only coffee.

2. 90% of C ordered Dessert too.
Attachment:
Ques2.jpg

From the diagram, we see that we do not know what % people ordered only coffee.

Using both the statements, we see that
60% * 75% * G = 90% * C
Since we get C in terms of G, this is sufficient. Answer (C)


Thanks for the explanation....I think to assume there is neither Dessert nor coffee case exist would help in solving the problem...Sometimes assuming total = 100 and then dividing them to different groups makes you to forget that neither case.... Whether my thought process correct?
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what  [#permalink]

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New post 25 Aug 2019, 01:46
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.


Hi Bunuel
Can we assume that there wasn't any other edible item ?
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what  [#permalink]

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New post 20 Feb 2020, 01:25
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.


Data Sufficiency
Question: 116
Category: Arithmetic Statistics
Page: 161
Difficulty: 700


The Official Guide For GMAT® Quantitative Review, 2ND Edition


In such questions, do we consider that every guest has ordered something which is not stated in the question explicitly? I marked the answer E just because of this reason.
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what  [#permalink]

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New post 18 Apr 2020, 23:15
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.
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what  [#permalink]

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New post 18 Apr 2020, 23:36
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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.
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what  [#permalink]

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New post 07 May 2020, 01:15
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.


How to identify if we need to consider # people who ordered neither Coffee or dessert ?
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what   [#permalink] 07 May 2020, 01:15

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