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

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23 Feb 2011, 06:28

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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.

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.

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)

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

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

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04 Jul 2012, 02:29

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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. _________________

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

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20 Sep 2015, 08:19

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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.

Answer: C.

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! _________________

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

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22 Sep 2015, 04:49

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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 224 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. _________________

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

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01 Jul 2012, 17:56

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.

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.

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

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01 Jul 2012, 22:25

Expert's post

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.

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. _________________

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

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03 Jul 2012, 08:28

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.

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

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).

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- download/file2.php?id=21119

Attachments

venn.png [ 14.16 KiB | Viewed 3249 times ]

_________________

Like my post Send me a Kudos It is a Good manner. My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

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- download/file2.php?id=21119

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

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01 Nov 2014, 01:50

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