Problem Solving

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

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:


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


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

Cheers,
Brent

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

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