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# If 75% of guest at a certain banquet ordered dessert, what

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If 75% of guest at a certain banquet ordered dessert, what [#permalink]

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23 Feb 2011, 03:43
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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.
[Reveal] Spoiler: OA

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Last edited by Baten80 on 23 Feb 2011, 19:47, edited 1 time in total.
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23 Feb 2011, 18:11
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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 7703 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 7702 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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Math Expert Joined: 02 Sep 2009 Posts: 36531 Followers: 7071 Kudos [?]: 92969 [3] , given: 10541 If 75% of guest at a certain banquet ordered dessert, what [#permalink] ### Show Tags 23 Feb 2011, 05:28 3 This post received KUDOS Expert's post 3 This post was BOOKMARKED 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 --> 0.6*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. _________________ SVP Joined: 16 Nov 2010 Posts: 1672 Location: United States (IN) Concentration: Strategy, Technology Followers: 33 Kudos [?]: 514 [3] , given: 36 Re: 116. DS. Percentage [#permalink] ### Show Tags 13 Mar 2011, 18:32 3 This post received KUDOS 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. _________________ Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership - big benefits and savings Senior Manager Joined: 31 Oct 2011 Posts: 484 Schools: Johnson '16 (M) GMAT 1: 690 Q45 V40 WE: Asset Management (Mutual Funds and Brokerage) Followers: 38 Kudos [?]: 217 [2] , given: 57 Re: word pblm [#permalink] ### Show Tags 10 Jan 2012, 04:34 2 This post received KUDOS 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+z Stmt 1) 0.6x chose coffee. But nothing is known about y or z. INSUFF Stmt 2) 0.9y chose dessert. But nothing is given about x or z. INSUFF Combining (1) and (2) 0.6x=0.9y Thus 0.6*0.75T = 0.9y Which gives us y=0.5T Or y=50%. SUFF ANS: C _________________ My Applicant Blog: http://hamm0.wordpress.com/ Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7119 Location: Pune, India Followers: 2130 Kudos [?]: 13629 [2] , given: 222 Re: IF 75% of guest at a certain banquet ordered dessert, what [#permalink] ### Show Tags 04 Jul 2012, 01:29 2 This post received KUDOS Expert's post 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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23 Feb 2011, 05:56
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Nice problem. Creating a table to keep track of the values would be helpful here.

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Re: If 75% of guest at a certain banquet ordered dessert, what [#permalink]

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20 Sep 2015, 07:19
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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.

Hey Bunuel please check the bolded part in statement 1. This should be 0.6*75=45 not the original one. 0.45*75=33.75. Thanks!
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Re: If 75% of guest at a certain banquet ordered dessert, what [#permalink]

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22 Sep 2015, 03:49
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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 360 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% of guest at a certain banquet ordered dessert,what [#permalink]

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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+B-AnB

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

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% of guest 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+B-AnB

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

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% of guest at a certain banquet ordered dessert,what [#permalink]

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02 Jul 2012, 01:26
How do we be sure that there are only desert & coffee and in offering? Why is answer not E.
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Re: IF 75% of guest 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% of guest 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(C|D)= P(C)*P(D|C)/P(D) and so P(C)= P(C|D)*P(D) / P(D|C). P(D)=.75 is given.

1. "60%of the guest who ordered dessert also ordered coffee." => P(C|D)=.6. Not sufficient.
2. "90%of the guest who ordered coffee also ordered dessert." => P(D|C)=.9. Not sufficient.
1 and 2: P(C)= P(C|D)*P(D) / P(D|C) = .6*.75/.9 = .5. Sufficient.

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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.

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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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.

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: if-75-of-guest-at-a-certain-banquet-ordered-dessert-what-109889.html#p1101532
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Re: If 75% of guest at a certain banquet ordered dessert, what [#permalink]

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15 Jul 2013, 22:37
Bumping for review and further discussion.
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23 Sep 2013, 01:54
VeritasPrepKarishma 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:
The attachment Ques1.jpg is no longer available

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

2. 90% of C ordered Dessert too.
Attachment:
The attachment Ques2.jpg is no longer available

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)

But Karishma, if we assume that sample is 100(since finally we need to calculate only percentage), so dessert 75% = 75 and 60% of 75% = 45
Please check this image this is how Venn diagram will come out-
Attachments

venn.png [ 14.16 KiB | Viewed 3849 times ]

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23 Sep 2013, 02:04
honchos wrote:
VeritasPrepKarishma 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)

But Karishma, if we assume that sample is 100(since finally we need to calculate only percentage), so dessert 75% = 75 and 60% of 75% = 45
Please check this image this is how Venn diagram will come out-

You cannot get the answer from (1) since you don't know how many of the guests ordered neither coffee nor dessert.
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Re: If 75% of guest at a certain banquet ordered dessert, what [#permalink]

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