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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]  23 Feb 2011, 04:43
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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.
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Last edited by Baten80 on 23 Feb 2011, 20:47, edited 1 time in total.
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Re: 116. Percentage [#permalink]  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 --> 0.45*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.

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Re: 116. Percentage [#permalink]  23 Feb 2011, 06:56
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Nice problem. Creating a table to keep track of the values would be helpful here.

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Re: 116. Percentage [#permalink]  23 Feb 2011, 19:11
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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 3315 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 3317 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: 116. DS. Percentage [#permalink]  13 Mar 2011, 19:32
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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: word pblm [#permalink]  10 Jan 2012, 05:34
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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+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
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Re: IF 75% of guest at a certain banquet ordered dessert,what [#permalink]  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.

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]  01 Jul 2012, 22:25
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]  02 Jul 2012, 02:26
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]  03 Jul 2012, 07:29
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]  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.

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Re: IF 75% of guest at a certain banquet ordered dessert, what [#permalink]  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.
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Re: 116. Percentage [#permalink]  12 Aug 2012, 04:20
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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Re: 116. Percentage [#permalink]  12 Aug 2012, 07:21
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: 116. Percentage   [#permalink] 12 Aug 2012, 07:21
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