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If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink]
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23 Feb 2011, 03:43
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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: 550 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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Last edited by Bunuel on 14 Aug 2017, 07:35, edited 2 times in total.
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If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink]
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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 [#permalink]
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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 9539 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 9538 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 [#permalink]
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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 [#permalink]
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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 [#permalink]
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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 [#permalink]
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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 [#permalink]
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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 [#permalink]
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03 Jul 2012, 07:28
Let D be the event that somebody order the dessert, let C be the event that somebody ordered coffee. From Bayes' Theorem, P(CD)= P(C)*P(DC)/P(D) and so P(C)= P(CD)*P(D) / P(DC). P(D)=.75 is given.
1. "60%of the guest who ordered dessert also ordered coffee." => P(CD)=.6. Not sufficient. 2. "90%of the guest who ordered coffee also ordered dessert." => P(DC)=.9. Not sufficient. 1 and 2: P(C)= P(CD)*P(D) / P(DC) = .6*.75/.9 = .5. Sufficient.
C.



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Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink]
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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 [#permalink]
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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 [#permalink]
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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 [#permalink]
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28 Feb 2014, 02:55
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: 550 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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Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink]
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01 Mar 2014, 05:11
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 [#permalink]
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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 [#permalink]
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18 May 2014, 08:57
Let D = total who ordered dessert. Let C = total who ordered coffee. Let B = total who ordered both dessert and coffee. Plug in guests = 100.
Then D = .75*100 = 75.
Statement 1: Tells us that B = .6*75 = 45. Not sufficient to determine C.
Statement 2: Tells us the .9C = B. Not sufficient to determine C.
Statements 1 and 2 together: .9C = 45. C = 50. Sufficient.
The correct answer is C.



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Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink]
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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 [#permalink]
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink]
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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 1805 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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