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Dessert and coffee

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Junior | Next Rank: 30 Posts
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by safina » Fri Feb 21, 2014 7:47 am
I cant get the right answer to this problem. Any one please help:

The waiter at a restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability that the next couples the waiter seats will not order dessert?
A) 20%
B) 25%
C) 40%
D) 60%
E) 75%
OA - B

My solution is as follows:
P(D and C) = 60% or 3/5
P(only dessert) = 20% or 1/5
So, P(only coffee) = ????
So, to get P(only coffee), I subtracted P(D and C ) and P(only deserrt) i.e. 1-3/5 = 2/5-1/5 = 1/5 or 20% but the OA is 25%
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by Brent@GMATPrepNow » Fri Feb 21, 2014 8:21 am
safina wrote:
The waiter at a restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability that the next couples the waiter seats will not order dessert?
A) 20%
B) 25%
C) 40%
D) 60%
E) 75%
This question is typically best solved using the Double Matrix method, but that method is hard to show in a text format. Since I'm about to watch the Canada/US Olympic hockey game (:-)), I'll provide the text solution (with possible a double matrix approach later in the day, unless someone else provides one) :

Let's say there are 100 couples altogether.
Let's let x = the total number of couples who order dessert.

Important: (# of couples who order dessert and coffee) + (# of couples who order dessert but no coffee) = total number of people who order dessert

Given: 60 couples order dessert and coffee

Given: 20% of the couples who order dessert don't order coffee
In other words, 20% of x = number of couples who order dessert don't order coffee
So, 0.2x = number of couples who order dessert don't order coffee

So, we get: (60) + (0.2x) = x
Solve... 60 = 0.8x
60/0.8 = x
75 = x

If 75 couples order dessert, then 25 couples do not order dessert (since we said there were 100 couples altogether).
This means that [spoiler]25%[/spoiler] of couples do not order dessert.

Cheers,
Brent
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by Patrick_GMATFix » Fri Feb 21, 2014 9:16 am
Great question Safina. It can be solved in several ways; below are two of them.

Solve with Venn Diagram
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Groups Table
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Hope that helps,
-Patrick
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by GMATGuruNY » Fri Feb 21, 2014 6:23 pm
safina wrote:I cant get the right answer to this problem. Any one please help:

The waiter at a restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability that the next couples the waiter seats will not order dessert?
A) 20%
B) 25%
C) 40%
D) 60%
E) 75%
Let total people = 100.
We can plug in the answers, which represent the number of people who do not order dessert.

Answer choice C: 40 do not order dessert.
Thus, the total number who order dessert = 60.
Too small.
It is given that the number who order BOTH dessert and coffee = 60.
Since some people order ONLY dessert but not coffee, the TOTAL number who order dessert must be GREATER than 60.
To INCREASE the total number who order dessert, the number who do not order dessert must DECREASE from 40.
Eliminate C, D and E.

Answer choice B: 25 do not order dessert.
Thus, the total number who order dessert = 75.
Since 20% of these people do not order coffee, the number who order dessert but not coffee = (.2)*75 = 15.
Thus, number who order BOTH dessert and coffee = (total who order dessert) - (number who order dessert but not coffee) = 75-15 = 60.
Success!

The correct answer is B.
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by safina » Sat Feb 22, 2014 7:31 am
thanks everyone!!:)
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by Brent@GMATPrepNow » Sat Feb 22, 2014 7:59 am
safina wrote:
The waiter at a restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability that the next couples the waiter seats will not order dessert?
A) 20%
B) 25%
C) 40%
D) 60%
E) 75%
Here's another way to set up the Double Matrix.

Before showing this, I'll mention that the Double Matrix Method 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 couples, and the two characteristics are:
- dessert or no dessert
- coffee or no coffee

So, we can begin my setting up our diagram as follows:
Image

NOTICE that the question does not ask us to find the actual number of couples who didn't have dessert. It asks us to find a probability. This means we can assign whatever value we wish to the total number of couples.
So, let's say there are 100 couples and add this to our diagram:
Image

60% of the couples order dessert and coffee
60% of 100 = 60, so 60 couples order dessert AND coffee.
Add that to the diagram to get:
Image

20% of the couples who order dessert don't order coffee.
Hmmm, we don't know how many couples order dessert, so it's hard to find 20% of that value.
So, let's assign a variable.
Let's let x = number of couples who order dessert, and add it to our diagram:
Image
So, x of the 100 couples order dessert.

20% of the couples who order dessert don't order coffee.
If x couples order dessert, then 20% of x don't order coffee.
In other words, 0.2x = number of couples don't order coffee.
Add this to our diagram:
Image

At this point, we see that the top two boxes add to x.
So, we can write the equation: 60 + 0.2x = x
Rearrange to get 60 = 0.8x
Rewrite 0.8 as fraction to get: 60 = (4/5)x
Multiply both sides by 5/4 to get: 75 = x

If x = 75, then we know that 75 of the 100 couples order dessert:
Image

This means that 25 of the 100 couples DON'T order dessert:
Image

So, P(couple doesn't order dessert) = 25/100 = 25% = B

Cheers,
Brent

---------------------------------------------------------
To learn more about this technique, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with the Double Matrix Method, you can attempt these additional practice questions:

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