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If 75 percent of the guests at a certain banquet ordered dessert, what
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The Official Guide For GMAT® Quantitative Review, 2ND EditionIf 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 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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Originally posted by Bunuel on 23 Feb 2011, 03:43.
Last edited by Bunuel on 02 Sep 2018, 01:55, edited 3 times in total.
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what
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23 Feb 2011, 05:28
SOLUTIONIf 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.
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what
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23 Feb 2011, 18:11
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 [ 9.89 KiB  Viewed 11916 times ]
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 [ 9.41 KiB  Viewed 11916 times ]
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)
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what
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13 Mar 2011, 18:32
Let there be 100 guests 75 guests ordered Dessert and 60% of 75 = 60/100 * 75 = 45 guests ordered coffee also, but there could be other people from remainig 25 who didn't order dessert (they might or might not have ordered dessert) So (1) is not suff Let x guests order coffee, 0.9x ordered dessert too, but we don't know x, so (2) is not sufficient However, taking (1) and (2) together, 45 = 0.9x, so the answer is C.
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what
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10 Jan 2012, 04:34
Let x be the number of people who chose dessert. Let y be the number of people who chose coffee Let z be the number of people who chose neither dessert nor coffee Given: x=0.75T T = x+y+zStmt 1) 0.6x chose coffee. But nothing is known about y or z. INSUFFStmt 2) 0.9y chose dessert. But nothing is given about x or z. INSUFFCombining (1) and (2) 0.6x=0.9y Thus 0.6*0.75T = 0.9y Which gives us y=0.5T Or y=50%. SUFFANS: C
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what
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01 Jul 2012, 16:56
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+BAnB
100=75+B45 > 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.



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Re: If 75 percent of the guests at a certain banquet ordered dessert, what
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01 Jul 2012, 21:25
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+BAnB
100=75+B45 > 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.
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what
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03 Jul 2012, 06:29
What if there were certain guests who ordered neither coffee nor dessert ? Would the answer be E in that case?



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Re: If 75 percent of the guests at a certain banquet ordered dessert, what
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04 Jul 2012, 01:29
shekharverma wrote: What if there were certain guests who ordered neither coffee nor dessert ? Would the answer be E in that case? We have already taken into account that there could be some people who ordered neither. In fact, if you see the answer you get, 75% ordered dessert, 50% ordered coffee and 45% ordered both. This means that 75 + 50  45 = 80% people ordered at least one of dessert and coffee. The rest of the 20% people ordered neither dessert nor coffee. They could have ordered something else or nothing  it doesn't matter to us. The answer remains (C). From both the statements, we see that 45% of all = 90% of C which means C is half of all. Hence C = 50%. Our questions asks the % of all who ordered coffee. We get that as 50%. We are not concerned about the remaining people.
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what
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12 Aug 2012, 03:20
Bunuel 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. IF 75% of guest at a certain banquet ordered dessert, what percent of guest ordered coffee? Assume there were 100 guests on the banquet. So we have that 75 of them ordered dessert. (1) 60% of the guest who ordered dessert also ordered coffee > 0.45*75=45 guests ordered both dessert AND coffee, but we still don't know how many guests ordered coffee. Not sufficient. (2) 90% of the guest 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 Just to clear a major fundamental misunderstanding I have here  why didn't we use the formula method to solve this problem?So: Total guests=Coffee + Dessert  Both (a) Let guests be 100. Hence dessert =75. From (1), Both = 45 Hence from equation (a) Coffee should = 30.. I know this is wrong, but I need someone to pinpoint why my approach is wrong here Thanks guys



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Re: If 75 percent of the guests at a certain banquet ordered dessert, what
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12 Aug 2012, 06:21
deliverance wrote: Bunuel 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. IF 75% of guest at a certain banquet ordered dessert, what percent of guest ordered coffee? Assume there were 100 guests on the banquet. So we have that 75 of them ordered dessert. (1) 60% of the guest who ordered dessert also ordered coffee > 0.45*75=45 guests ordered both dessert AND coffee, but we still don't know how many guests ordered coffee. Not sufficient. (2) 90% of the guest 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 Just to clear a major fundamental misunderstanding I have here  why didn't we use the formula method to solve this problem?So: Total guests=Coffee + Dessert  Both (a) Let guests be 100. Hence dessert =75. From (1), Both = 45 Hence from equation (a) Coffee should = 30.. I know this is wrong, but I need someone to pinpoint why my approach is wrong here Thanks guys It should be {Total}={Coffee}+{Dessert}{Both}+{Neither}. Since we don't know how many of the guests ordered neither coffee nor dessert we cannot calculate the number of guests who ordered coffee based on the info from (1). Check Karishma's post above about the same issue: if75ofguestatacertainbanquetordereddessertwhat109889.html#p1101532
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what
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01 Mar 2014, 05:50
Bunuel, can we assume the number of guests as 100??...what if the number of guest is 200? coz in the question, it is given as percent. please clarify...thanks...



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Re: If 75 percent of the guests at a certain banquet ordered dessert, what
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13 Nov 2014, 16:57
Hi Bunuel,
I am stuck at the following equation, which I am not able to understand. Please clarify.
Assuming total # of guests = 100 Guests who ordered dessert (D) = 75 Guests who ordered coffee (C) = x
Stmt (1) D + C = 45 So, 75 + x  45 = 100 => x = 100  30 = 70
Is this deduction incorrect?
Thanks, S.



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Re: 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
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22 Sep 2015, 03:49
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. 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. Transforming the original condition and the question, we have the below 2by2 table that is common in GMAT math test. Attachment:
GC DS Baten80 If 75% of guest ar a certain banquet(20150921).jpg [ 39.43 KiB  Viewed 4171 times ]
from above, since the question is x+y(as it asks the %), we have 2 variables (x,y) and therefore need 2 equations to match the number of variables and equations. Since there is 1 each in 1) and 2), C has high probability of being the answer. Using both 1) & 2) together, 75G*0.6=45G leads to x=45, 0.9(45+y)G=45G leads to y=5. Therefore x+y=45+5=50 and the conditions are sufficient. Therefore the answer is C. Normally for cases where we need 2 more equations, such as original conditions with 2 variable, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using ) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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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 noncoffee takers = 100%?



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Re: If 75 percent of the guests at a certain banquet ordered dessert, what
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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 noncoffee 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?
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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
QR2DS116.PNG [ 20.43 KiB  Viewed 2137 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
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28 Nov 2016, 00:34
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 noncoffee 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
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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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