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Coffee and Dessert

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Coffee and Dessert

by Oneva » Mon Jan 03, 2011 5:17 pm
If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?

1.) 60% of the guests who ordered dessert also ordered coffee.
2.) 90% of the guests who ordered coffee also ordered dessert.

Hi I'm new here and I was wondering if anyone would be able to help me out with this question? The solution was with Venn diagram (very abstract) but I was wondering if it could be done with a table (more concrete for me). Thanks
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by anshumishra » Mon Jan 03, 2011 7:37 pm
Oneva wrote:If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?

1.) 60% of the guests who ordered dessert also ordered coffee.
2.) 90% of the guests who ordered coffee also ordered dessert.

Hi I'm new here and I was wondering if anyone would be able to help me out with this question? The solution was with Venn diagram (very abstract) but I was wondering if it could be done with a table (more concrete for me). Thanks
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by GMATGuruNY » Mon Jan 03, 2011 7:50 pm
Oneva wrote:If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?

1.) 60% of the guests who ordered dessert also ordered coffee.
2.) 90% of the guests who ordered coffee also ordered dessert.

Hi I'm new here and I was wondering if anyone would be able to help me out with this question? The solution was with Venn diagram (very abstract) but I was wondering if it could be done with a table (more concrete for me). Thanks
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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by Oneva » Mon Jan 03, 2011 8:39 pm
Hi GMATGuru. It seems from most of your posts that you are an advocate of the variable = equation principle, which is a very quick way to process data sufficiency. Is it possible to convert all/ most problems which usually uses tables or venn diagrams into this system?
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by [email protected] » Tue Jan 04, 2011 11:35 pm
Isn's A itself sufficient?

Assuming total guests 100
Given: D=75
Asked: C
Taking A into consideration:
60%D = 60%(75) = 45 guests who ordered both
Guests who Ordered Only D= (75-45) = 30
Hence guests who ordered Only coffee = 100-(45+30) = 25

Hence guests who ordered C= 45+25 = 70

Ofcourse this assumes that there were no guests who didn't order anything.
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by Geva@EconomistGMAT » Wed Jan 05, 2011 12:34 am
Image

See table, as requested. I plugged in 100 people for the total / total box.

I agree that the table form is better here, if only to explain why stat. (1) isn't sufficient by itself: although we can find the Coffee / Desert box from stat. (1), we are missing the Coffee / no desert box to reach the desired Coffee / total box.

In other words: stat. (1) tells you how many people bought coffee AND desert, but doesn't tell you how many people bought coffee without desert - which will also be counted among "coffee drinkers".

Stat. (2) alone just tells you that the coffee / desert box is 90% of the required coffee / total box, but doesn't tell you how many people are in the coffee / desert box. Thus, we need both statements to say that the 45 people in coffee / desert are 90% of the required coffee total, from which we can find coffee / total. Answer is indeed C.
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