Dessert and coffee

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safina: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Fri Jan 10, 2014 2:47 am; Followed by:1 members

Dessert and coffee

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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Source: Beat The GMAT — Problem Solving | Fri Feb 21, 2014 7:47 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

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

Brent Hanneson - Creator of GMATPrepNow.com

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Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 am; Thanked: 335 times; Followed by:98 members

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

Groups Table

Hope that helps,
-Patrick

Check out my site: GMATFix.com

To prep my students I use this tool >> (screenshots, video)

Ask me about tutoring.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

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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safina: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Fri Jan 10, 2014 2:47 am; Followed by:1 members

by safina » Sat Feb 22, 2014 7:31 am

thanks everyone!!:)

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

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:

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:

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:

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:

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:

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: