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19 Apr 2020, 00:15
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Bunuel
Could you please answer why we are not considering guests who would choose neither dessert nor coffee, since it is not explicitly mentioned that they order at least one of the two.
19 Apr 2020, 00:36
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mzaid
Hi mzaid It's good to see you on GMAT CLUB
The question is
Quote:
We don't have to worry about the people who order none because that's not what the question wants use to figure out to answer the question
here the same number (people who order both coffee and desert) has been explained in two ways in two statements
The same number is representing 90% of those who order coffee so we find out that
90% of Total Coffee orders = 60% of 75
that gives us that 0.8 Coffee orders = 45
i.e. Coffee orders = 45/0.9 = 50
Though we can find out the people who order none by using the double matrix method but that would be unnecessary.
In fact, last calculation also is unnecessary when we have been sure that the solution of the equation (after combining statements) will give us a unique solution of the problem asked.
19 Sep 2020, 22:30
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This problem can be solved quickly if we can visualize the information in the form of two overlapping circles, i.e., a Venn diagram. There is no need to assume any values or perform any calculations.
___________Only Dessert________ (both Dessert and Coffee)_____________Only Coffee_______________
The above representation shows a simplified form of overlapping circles. The "circle" on the extreme left shows guests who ordered dessert. This circle includes both guests who ordered only dessert and those who ordered both dessert and coffee. The "circle" on the extreme right shows guests who ordered coffee. This circle includes both guests who ordered only coffee and those who ordered both dessert and coffee. The overlapping portion of the preceding two circles represents guests who ordered both dessert and coffee.
We are asked to determine the number (percent) of the guests who ordered coffee. This number includes both guests who ordered only coffee and those who ordered both coffee and dessert. To determine this number, it is clear that we need to have concrete values for each of the above three categories (only dessert, both dessert and coffee, and only coffee).
(1) 60 percent of the guests who ordered dessert also ordered coffee.
INSUFFICIENT
This statement only provides information about the number (percent) of the guests who ordered both dessert and coffee. The information in the other categories is missing.
(2) 90 percent of the guests who ordered coffee also ordered dessert.
INSUFFICIENT
As in the preceding statement, this statement only provides information about the number (percent) of the guests who ordered both dessert and coffee. The information in the other categories is missing.
(1) and (2) together.
SUFFICIENT
Combining the two statements, we can see that the the category "both dessert and coffee" is clearly determined. Also determined are the values (percent) in the two remaining categories. We are given the "whole" value of each circle and the value of the overlapping category. Hence, the two statements together are sufficient to answer the question of what percent of the guests ordered coffee.
___________Only Dessert________ (both Dessert and Coffee)_____________Only Coffee_______________
The above representation shows a simplified form of overlapping circles. The "circle" on the extreme left shows guests who ordered dessert. This circle includes both guests who ordered only dessert and those who ordered both dessert and coffee. The "circle" on the extreme right shows guests who ordered coffee. This circle includes both guests who ordered only coffee and those who ordered both dessert and coffee. The overlapping portion of the preceding two circles represents guests who ordered both dessert and coffee.
We are asked to determine the number (percent) of the guests who ordered coffee. This number includes both guests who ordered only coffee and those who ordered both coffee and dessert. To determine this number, it is clear that we need to have concrete values for each of the above three categories (only dessert, both dessert and coffee, and only coffee).
(1) 60 percent of the guests who ordered dessert also ordered coffee.
INSUFFICIENT
This statement only provides information about the number (percent) of the guests who ordered both dessert and coffee. The information in the other categories is missing.
(2) 90 percent of the guests who ordered coffee also ordered dessert.
INSUFFICIENT
As in the preceding statement, this statement only provides information about the number (percent) of the guests who ordered both dessert and coffee. The information in the other categories is missing.
(1) and (2) together.
SUFFICIENT
Combining the two statements, we can see that the the category "both dessert and coffee" is clearly determined. Also determined are the values (percent) in the two remaining categories. We are given the "whole" value of each circle and the value of the overlapping category. Hence, the two statements together are sufficient to answer the question of what percent of the guests ordered coffee.
