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# If 75 percent of the guests at a certain banquet ordered des

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If 75 percent of the guests at a certain banquet ordered des [#permalink]

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31 Jan 2012, 09:52
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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.

In the book it is solved using venn diagrams. Could someone explain how this problem can be solved using the two set matrix ?

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-75-of-guest-at-a-certain-banquet-ordered-dessert-what-109889.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 23 Sep 2013, 01:48, edited 1 time in total.
Edited the question and moved to DS forum.
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Re: If 75 percent of the guests at a certain banquet ordered des [#permalink]

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31 Jan 2012, 14:50
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Dear gpkk

I'm happy to help with this.

I didn't know how to make the matrices comprehensible & clear in the the simple text of the post, so I did them in MS Word, and attached a pdf.

Please let me know if any of it doesn't make sense, or if you have any further questions.

Mike
Attachments

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Re: If 75 percent of the guests at a certain banquet ordered des [#permalink]

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01 Feb 2012, 01:13
Thanks a lot Mike for the solution
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Re: If 75 percent of the guests at a certain banquet ordered des [#permalink]

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05 Feb 2012, 00:54
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Since this is DS, and no numerical answer is required, you can also use a theoretical approach:

Stem: We know that 75% of the guests ordered dessert, but this tells us nothing about what percent ordered coffee. It could be anywhere from 0% to 100%.

1) This tells us about the dessert eaters who ordered coffee, but what about those who didn’t order dessert (i.e. the remaining 25%)? Insufficient.
2) This tells us about the same group (coffee & dessert), only as a percentage of coffee drinkers rather than of dessert eaters. We still don’t know how many people had coffee without dessert. Insufficient.

At this point, we know enough to narrow the choices to C & E. While I’m a big fan of the double-set matrix, eliminating choices this way is good exercise, too. After all, we want to focus on what kind of information would be sufficient to solve the problem. Now let’s try combining statements:

1&2) We now know two things about the same group. This is often a good sign that we can solve. In this case, we can find the number of people in this group (60% of 75 = 45), and we know what percent of the coffee drinkers it represents. We can certainly solve this (45=.9C, C=50), but we don’t need to. We know that we have the ability to calculate the number, and that this number is 90% of the target number. That’s all we need to know. Sufficient.
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Re: If 75 percent of the guests at a certain banquet ordered des [#permalink]

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20 Sep 2013, 23:07
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DmitryFarber wrote:
Since this is DS, and no numerical answer is required, you can also use a theoretical approach:

Stem: We know that 75% of the guests ordered dessert, but this tells us nothing about what percent ordered coffee. It could be anywhere from 0% to 100%.

1) This tells us about the dessert eaters who ordered coffee, but what about those who didn’t order dessert (i.e. the remaining 25%)? Insufficient.
2) This tells us about the same group (coffee & dessert), only as a percentage of coffee drinkers rather than of dessert eaters. We still don’t know how many people had coffee without dessert. Insufficient.

At this point, we know enough to narrow the choices to C & E. While I’m a big fan of the double-set matrix, eliminating choices this way is good exercise, too. After all, we want to focus on what kind of information would be sufficient to solve the problem. Now let’s try combining statements:

1&2) We now know two things about the same group. This is often a good sign that we can solve. In this case, we can find the number of people in this group (60% of 75 = 45), and we know what percent of the coffee drinkers it represents. We can certainly solve this (45=.9C, C=50), but we don’t need to. We know that we have the ability to calculate the number, and that this number is 90% of the target number. That’s all we need to know. Sufficient.

This can be solved with venn diagram

lets 100 be total, 75% ordered coffee and 60% of 75 = ordered Both.... = 45

so I believe A can give the answer..
Attachments

venn.png [ 14.16 KiB | Viewed 6240 times ]

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Re: If 75 percent of the guests at a certain banquet ordered des [#permalink]

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21 Sep 2013, 00:47
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Double set matrix will help here. Think about 2 groups. Dessert (D) and No Dessert ( ND). Coffee (C) and No Coffee (NC). Then we set up the matrix:

Lets assume the total number of guests to be 100. The question stem states that 75% of the guests ordered dessert.

D ND

C = x

NC

Total: 75 25 = 100

So need to find x. Now (1) says that 60% who ordered dessert also ordered coffee. So, 60% of 75 ordered both

D [align=][/align] ND

C 60%*75 = x

NC

Total=75 + 25 = 100

Still cant find x, so move to satement (2). 90% of the guests who ordered coffee also ordered dessert. so that's 90% of x
D ND Total

C 90%*x = x

NC
Total 75 25 = 100

Still cant find x, however, if you combine the two, you can see that: 0.90x = 60%*75. Now you can find x

So (1) and (2) together are suff. The answer is C
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Re: If 75 percent of the guests at a certain banquet ordered des [#permalink]

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21 Sep 2013, 03:52
igotthis wrote:
Double set matrix will help here. Think about 2 groups. Dessert (D) and No Dessert ( ND). Coffee (C) and No Coffee (NC). Then we set up the matrix:

Lets assume the total number of guests to be 100. The question stem states that 75% of the guests ordered dessert.

D ND

C = x

NC

Total: 75 25 = 100

So need to find x. Now (1) says that 60% who ordered dessert also ordered coffee. So, 60% of 75 ordered both

D [align=][/align] ND

C 60%*75 = x

NC

Total=75 + 25 = 100

Still cant find x, so move to satement (2). 90% of the guests who ordered coffee also ordered dessert. so that's 90% of x
D ND Total

C 90%*x = x

NC
Total 75 25 = 100

Still cant find x, however, if you combine the two, you can see that: 0.90x = 60%*75. Now you can find x

So (1) and (2) together are suff. The answer is C

What is matrix method, and why my result is different with Venn Diagram Method.
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Re: If 75 percent of the guests at a certain banquet ordered des [#permalink]

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21 Sep 2013, 05:34
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honchos wrote:
igotthis wrote:
Double set matrix will help here. Think about 2 groups. Dessert (D) and No Dessert ( ND). Coffee (C) and No Coffee (NC). Then we set up the matrix:

Lets assume the total number of guests to be 100. The question stem states that 75% of the guests ordered dessert.

D ND

C = x

NC

Total: 75 25 = 100

So need to find x. Now (1) says that 60% who ordered dessert also ordered coffee. So, 60% of 75 ordered both

D ND

C 60%*75 = x

NC

Total=75 + 25 = 100

Still cant find x, so move to satement (2). 90% of the guests who ordered coffee also ordered dessert. so that's 90% of x
D ND Total

C 90%*x = x

NC
Total 75 25 = 100

Still cant find x, however, if you combine the two, you can see that: 0.90x = 60%*75. Now you can find x

So (1) and (2) together are suff. The answer is C

What is matrix method, and why my result is different with Venn Diagram Method.

_________________________________________________________________________

The matrix approach is a convenient and structured way of using venn diagrams when there are 2 elements involved. The 2 mutually exclusive events ( coffee, no coffee) appear in rows, and 2 mutually exclusive events (dessert, no dessert) appear in the columns. The ends of the columns and rows should sum up. (as seen in the example, where 75+25 = 100)

Your result with the venn diagram approach does not give the answer, since you assumed that 25% only drink coffee. But those 25% do not represent the people who 'did not have dessert' ( If they didn't have dessert it does not mean that they had only coffee, what if they didn't have anything?).

I've attached a word file with an explanation. Hope it helps!

abhi47 wrote:
If 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.

In the book it is solved using venn diagrams. Could someone explain how this problem can be solved using the two set matrix ?

Attachments

Matrix method.docx [17.91 KiB]

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Re: If 75 percent of the guests at a certain banquet ordered des [#permalink]

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21 Sep 2013, 06:06
igotthis wrote:
honchos wrote:
igotthis wrote:
Double set matrix will help here. Think about 2 groups. Dessert (D) and No Dessert ( ND). Coffee (C) and No Coffee (NC). Then we set up the matrix:

Lets assume the total number of guests to be 100. The question stem states that 75% of the guests ordered dessert.

D ND

C = x

NC

Total: 75 25 = 100

So need to find x. Now (1) says that 60% who ordered dessert also ordered coffee. So, 60% of 75 ordered both

D ND

C 60%*75 = x

NC

Total=75 + 25 = 100

Still cant find x, so move to satement (2). 90% of the guests who ordered coffee also ordered dessert. so that's 90% of x
D ND Total

C 90%*x = x

NC
Total 75 25 = 100

Still cant find x, however, if you combine the two, you can see that: 0.90x = 60%*75. Now you can find x

So (1) and (2) together are suff. The answer is C

What is matrix method, and why my result is different with Venn Diagram Method.

_________________________________________________________________________

The matrix approach is a convenient and structured way of using venn diagrams when there are 2 elements involved. The 2 mutually exclusive events ( coffee, no coffee) appear in rows, and 2 mutually exclusive events (dessert, no dessert) appear in the columns. The ends of the columns and rows should sum up. (as seen in the example, where 75+25 = 100)

Your result with the venn diagram approach does not give the answer, since you assumed that 25% only drink coffee. But those 25% do not represent the people who 'did not have dessert' ( If they didn't have dessert it does not mean that they had only coffee, what if they didn't have anything?).

I've attached a word file with an explanation. Hope it helps!

abhi47 wrote:
If 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.

In the book it is solved using venn diagrams. Could someone explain how this problem can be solved using the two set matrix ?

I dindt assumed that 25% drink coffe, I just took a sample space of 100 out of which 75% was given that they eat dessert and out of these 60%(75%) both, so 25 automatically comes out, as 60% of 75%(= 75 as we have chosen a sample space of 100) so only who eat dessert are 75-45 = 30

30 + 45 + C = 100
c=25, it didnt assumd it comes out to be...

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Re: If 75 percent of the guests at a certain banquet ordered des [#permalink]

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23 Sep 2013, 01:48
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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-75-of-guest-at-a-certain-banquet-ordered-dessert-what-109889.html
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Re: If 75 percent of the guests at a certain banquet ordered des   [#permalink] 23 Sep 2013, 01:48
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