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Confusing data sufficiency question, need a littel help

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Confusing data sufficiency question, need a littel help

by asim » Sat Jun 18, 2011 12:24 pm
Hi guys, would you please help me understand the question below:

If 75% 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.

This question was mentioned on the Official guide and it's said that there are 4 groups:
1- Ordered dessert
2- Ordered coffee
3- Ordered both.
4- Ordered neither.

How can we say that there are 4 groups of guests, dessert, coffee, both and neither, while on the question nothing was mentioned in terms of specifying that there are 4 groups?.
From the question, I can predict that there are three groups, dessert, coffee and both groups.
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by Brent@GMATPrepNow » Sat Jun 18, 2011 7:08 pm
The OG solution is correct in that there are 4 groups - that is 4 groups worth considering for this question. There may well be other ways in which we could categorize the guests (e.g., those who had salad and those who didn't, or those who danced later and those who didn't), but those extra categories are superfluous to the question at hand.

A good way to solve this question is to apply the Double Matrix method: https://www.beatthegmat.com/mba/2011/05/ ... question-1

Give it a shot.

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by edvhou812 » Sat Jun 18, 2011 7:14 pm
asim wrote:Hi guys, would you please help me understand the question below:

If 75% 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.

This question was mentioned on the Official guide and it's said that there are 4 groups:
1- Ordered dessert
2- Ordered coffee
3- Ordered both.
4- Ordered neither.

How can we say that there are 4 groups of guests, dessert, coffee, both and neither, while on the question nothing was mentioned in terms of specifying that there are 4 groups?.
From the question, I can predict that there are three groups, dessert, coffee and both groups.
It too is in my nature to ask, "Hey couldn't guests have had dinner since there was desert? This makes no sense!" However we can only go by what the GMAT tells us. Here they are only telling us about desert and coffee, so we must work thinking that people either had coffee, desert, coffee and desert, or neither.

As for the answer IMO it is B

1) if we plugged in 100 as our number of guests, we would have 75 people that had desert. If 60% of those order coffee, then 45 people, or 45%, had both coffee and desert. However it would be a mistake to assume 40% of the remaining guests had coffee. (Insufficient)

2) With this info we can figure out the percentage of every group at the banquet. No need to write out the algebra because there isn't any need to do so. (Sufficient)

What is the OA?
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by amit2k9 » Sun Jun 19, 2011 3:07 am
using the table

c !c
d 0.6*75 0.4*75 75

!d 25

total x 100-x 100

using a+b

0.9x = 0.6*75 thus x and 100-x can be found out.
x=30 and 100-x = 70 it is.

C .
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by asim » Sun Jun 19, 2011 8:02 am
OG:

D+C-B+N=100%

D+B=75%

C= needed

From (1) 60% of D=B, so B=75%*60%=45%
but no further information helping to solve C because N is still unknown, for this 1 is insufficient.

From (2) 90% of C=B, but B is unknown, so would be C, for that 2 is insufficient.

taking A & B together gives that B = 45% and from that C = 50%, so C is the right answer.

OG used Venn Diagram to solve this problem which is pretty close to the Double Matrix method, although I like DM method,

thanks everyone
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