If 75 percent of the guests at a certain banquet ordered dessert, what

In questions involving sets, venn diagrams can be used. They tend to make questions simple.

We need to find the % of total guests (G) who ordered coffee (C). So we want C in terms of G.
Given D = 75% of G

1. 60% of D ordered coffee too

From the diagram, we see that we do not know what % people ordered only coffee.

2. 90% of C ordered Dessert too.

From the diagram, we see that we do not know what % people ordered only coffee.

Using both the statements, we see that
60% * 75% * G = 90% * C
Since we get C in terms of G, this is sufficient. Answer (C)

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.

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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Let there be 100 guests

75 guests ordered Dessert


and 60% of 75 = 60/100 * 75 = 45 guests ordered coffee also, but there could be other people from remainig 25 who didn't order dessert (they might or might not have ordered dessert)


So (1) is not suff


Let x guests order coffee, 0.9x ordered dessert too, but we don't know x, so (2) is not sufficient

However, taking (1) and (2) together, 45 = 0.9x, so the answer is C.

Hey Bunuel,

What mistake am I making?

A- # of people who order desert
B- # of people who order coffee
AnB - # of people who order both dessert and coffe

Given: A=75
Statement 1: AnB=.6*70=45
Given that we know AuB=A+B-AnB

100=75+B-45 ----> B=75. Hence statement 1 should be sufficient.

What am I doing wrong here!!!?? So confused? Please help. Thank you!


When I solve this problem by using the 2x2 grid, its obvious that there is not enough information. But when I try to just use the formula it gives me suffient info.

Do you know how many ordered neither? We cannot say that AuB = 100.

What if there were certain guests who ordered neither coffee nor dessert ?
Would the answer be E in that case?

We have already taken into account that there could be some people who ordered neither. In fact, if you see the answer you get, 75% ordered dessert, 50% ordered coffee and 45% ordered both. This means that 75 + 50 - 45 = 80% people ordered at least one of dessert and coffee. The rest of the 20% people ordered neither dessert nor coffee. They could have ordered something else or nothing - it doesn't matter to us. The answer remains (C).
From both the statements, we see that 45% of all = 90% of C which means C is half of all. Hence C = 50%. Our questions asks the % of all who ordered coffee. We get that as 50%. We are not concerned about the remaining people.

Hi

Just to clear a major fundamental misunderstanding I have here - why didn't we use the formula method to solve this problem?So:

Total guests=Coffee + Dessert - Both --(a)

Let guests be 100. Hence dessert =75. From (1), Both = 45

Hence from equation (a) Coffee should = 30..

I know this is wrong, but I need someone to pinpoint why my approach is wrong here

Thanks guys

It should be {Total}={Coffee}+{Dessert}-{Both}+{Neither}. Since we don't know how many of the guests ordered neither coffee nor dessert we cannot calculate the number of guests who ordered coffee based on the info from (1).

Check Karishma's post above about the same issue: if-75-of-guest-at-a-certain-banquet-ordered-dessert-what-109889.html#p1101532

Bunuel, can we assume the number of guests as 100??...what if the number of guest is 200?
coz in the question, it is given as percent. please clarify...thanks...

We are asked to find what percent of the guests ordered coffee. You can assume any number for the number of guests and you should get the same answer. Try it with 200 to check.

Hope it helps.

Hi Bunuel,

I am stuck at the following equation, which I am not able to understand. Please clarify.

Assuming total # of guests = 100
Guests who ordered dessert (D) = 75
Guests who ordered coffee (C) = x

Stmt (1) D + C = 45
So, 75 + x - 45 = 100
=> x = 100 - 30 = 70

Is this deduction incorrect?

Thanks,
S.

Yes, because there might be people who ordered neither coffee nor dessert:

{Total} = {Dessert} + {Coffee} - {Both} + {Neither}
100 = 75 + {Coffee} - 45 + {Neither}

As you can see we cannot find {Coffee}.

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?

We are not assuming that but the number of people who ordered neither coffee or desert does not play any part in the solution.