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Re: If 75 percent of the guests at a certain banquet ordered dessert, what
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11 Mar 2016, 10:23
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%?
Re: If 75 percent of the guests at a certain banquet ordered dessert, what
[#permalink]
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
Re: If 75 percent of the guests at a certain banquet ordered dessert, what
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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]
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?
Re: If 75 percent of the guests at a certain banquet ordered dessert, what
[#permalink]
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 ?
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.
Re: If 75 percent of the guests at a certain banquet ordered dessert, what
[#permalink]
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.
Re: If 75 percent of the guests at a certain banquet ordered dessert, what
[#permalink]
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 ?
Re: If 75 percent of the guests at a certain banquet ordered dessert, what
[#permalink]
19 Sep 2020, 20:22
Though, I have hit the right answer; however, I feel not been able to catalyze this response and find why it is wrong?!
can anybody help?
honchos wrote:
DmitryFarber wrote:
Since this is DS, and no numerical answer is required, you can also use a theoretical approach:
Stem: We know that 75% of the guests ordered dessert, but this tells us nothing about what percent ordered coffee. It could be anywhere from 0% to 100%.
1) This tells us about the dessert eaters who ordered coffee, but what about those who didn’t order dessert (i.e. the remaining 25%)? Insufficient. 2) This tells us about the same group (coffee & dessert), only as a percentage of coffee drinkers rather than of dessert eaters. We still don’t know how many people had coffee without dessert. Insufficient.
At this point, we know enough to narrow the choices to C & E. While I’m a big fan of the double-set matrix, eliminating choices this way is good exercise, too. After all, we want to focus on what kind of information would be sufficient to solve the problem. Now let’s try combining statements:
1&2) We now know two things about the same group. This is often a good sign that we can solve. In this case, we can find the number of people in this group (60% of 75 = 45), and we know what percent of the coffee drinkers it represents. We can certainly solve this (45=.9C, C=50), but we don’t need to. We know that we have the ability to calculate the number, and that this number is 90% of the target number. That’s all we need to know. Sufficient.
This can be solved with venn diagram
lets 100 be total, 75% ordered coffee and 60% of 75 = ordered Both.... = 45
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what
[#permalink]
19 Sep 2020, 21:30
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.
Re: If 75 percent of the guests at a certain banquet ordered dessert, what
[#permalink]
29 Nov 2020, 05:56
Top Contributor
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.
Let's use the Double Matrix method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it. Here, we have a population of guests, and the two characteristics are: - ordered dessert or did not order dessert - ordered coffee or did not order coffee
Target question:What percent of the guests ordered coffee? Since the target question is asking for a percent, let's say that there are 100 guests in total.
Given: 75 percent of the guests ordered dessert Since we're saying that there is a total of 100 guests, we know that 75 of them ordered dessert. This also tells us that 25 guests did not order dessert. So, we can set up our diagram as follows:
Notice that I have let x = the total number of guests who ordered coffee.
Statement 1: 60 percent of the guests who ordered dessert also ordered coffee. 75 guests ordered dessert. 60% of 75 = 45, so 45 guests ordered coffee AND dessert. So, we get:
As you can see, we still don't have enough information to determine the value of x (the number of guests who ordered coffee) Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 90 percent of the guests who ordered coffee also ordered dessert. We get:
As you can see, we still don't have enough information to determine the value of x (the number of guests who ordered coffee) Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined When we combine the statements, we see that we have 2 different pieces of information describing the top-left box.
This means that 0.9x = 45 Solve to get x = 50 In other words, 50 guests ordered coffee, which means 50% of the guests ordered coffee. Since we can answer the target question with certainty, the combined statements are SUFFICIENT
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