Are we assuming that there are only 2 things to order- Coffee and dessert and everyone made a choice from these 2 things only... Implying that the sum total of coffee and non-coffee takers = 100%?

I have the same doubt. Bunuel, how do we deduce that there isn't a category of people who haven't ordered anything?

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Lets say there are total 100 Guests. We are told 75 ordered Deseret, and we have to calculate % of people who ordered coffee
So what we need is no of people who ordered coffee which is no of people who ordered only coffee and and number of people who ordered both coffee and desert.

Stmt 1: Tells us no of people who ordered both = 45, So if 45 ordered both then only 30 ordered only desert. but we have no information on no of people who ordered only coffee and no of people who ordered none.

Stmt 2: 90 % of those who ordered coffee also ordered desert. Since we don't have the values of those who ordered coffee or those who ordered coffee and desert we cant calculate any thing from this information.

Now we already know from second statement if we have information about no of people ordering both we can calculate no of people who ordered coffee.

So combining Stmt 1 and Stmt 2, We have
90% of x= 45, so x =50, this is number of people who ordered coffee. So we can calculate the required % which is about 50 %
So Only Desert 30, Desert & Coffee 45, Only Coffee 5, 20 none , which gives total 100.

Probus
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Thanks for the explanation....I think to assume there is neither Dessert nor coffee case exist would help in solving the problem...Sometimes assuming total = 100 and then dividing them to different groups makes you to forget that neither case.... Whether my thought process correct?

Hi Bunuel
Can we assume that there wasn't any other edible item ?

In such questions, do we consider that every guest has ordered something which is not stated in the question explicitly? I marked the answer E just because of this reason.

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.

How to identify if we need to consider # people who ordered neither Coffee or dessert ?

Though, I have hit the right answer; however, I feel not been able to catalyze this response and find why it is wrong?!

can anybody help?

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.

Let's use the Double Matrix method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of guests, and the two characteristics are:
- ordered dessert or did not order dessert
- ordered coffee or did not order coffee

Target question: What percent of the guests ordered coffee?
Since the target question is asking for a percent, let's say that there are 100 guests in total.

Given: 75 percent of the guests ordered dessert
Since we're saying that there is a total of 100 guests, we know that 75 of them ordered dessert.
This also tells us that 25 guests did not order dessert.
So, we can set up our diagram as follows:

Notice that I have let x = the total number of guests who ordered coffee.

Statement 1: 60 percent of the guests who ordered dessert also ordered coffee.
75 guests ordered dessert. 60% of 75 = 45, so 45 guests ordered coffee AND dessert.
So, we get:

As you can see, we still don't have enough information to determine the value of x (the number of guests who ordered coffee)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 90 percent of the guests who ordered coffee also ordered dessert.
We get:

As you can see, we still don't have enough information to determine the value of x (the number of guests who ordered coffee)
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When we combine the statements, we see that we have 2 different pieces of information describing the top-left box.

This means that 0.9x = 45
Solve to get x = 50
In other words, 50 guests ordered coffee, which means 50% of the guests ordered coffee.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

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