Problem Solving

AIM TO CRACK GMAT wrote:The waiter at an expensive 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 couple the waiter seats will not order dessert?


20% 25% 40% 60% 75%

OA = 25%

When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

This question is typically best solved using the Double Matrix method, but that method is hard to show in a text format.
So, here's another option:

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.
This means that [spoiler]25%[/spoiler] of couples do not order dessert.

Cheers,
Brent

As I mentioned earlier, this question is easily solved using a technique called the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two criteria associated with it.
Here, the criteria are:
- having or not having dessert
- having or not having coffee

For more information about this technique and some additional practice questions, check out these 3 BTG articles:

- https://www.beatthegmat.com/mba/2011/05/ ... question-1
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent

Hi buzzdeepak,

Whenever you use the Double Matrix Method, the 2 columns must have "either-or" titles, and the 2 rows must have "either-or" titles. By "either-or," I mean that each population member must meet exactly one of the two criteria.

For example, a couple either orders dessert or doesn't order dessert. Exactly one of these things must occur for a given couple. Similarly, a given couple must either order coffee or not order coffee.

The problem with your first approach is that your titles aren't "either-or". For example, the column titles are "dessert" and "coffee." Is it the case that a given couple must either order coffee or order dessert? No, a couple can order neither. Or a couple can order both.

I hope that helps.

Cheers,
Brent

AIM TO CRACK GMAT wrote:The waiter at an expensive 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 couple the waiter seats will not order dessert?

A. 20%
B. 25%
C. 40%
D. 60%
E. 75%

You can use the following equation:

Total = Dessert only + Coffee only + Both + Neither

Instead of using percents, let's use numbers. If we let the total number of customers be 100, then we see that 60 of them will order dessert and coffee:

100 = D + C + 60 + N

Since we have let D = the number of couples ordering Dessert only, we know that the total number of couples ordering Dessert is (D + 60), which is "Dessert only" plus "Both.". Since 20% of the couples who order dessert don't order coffee, that means "Dessert only" is 20% of the total of "Dessert only" and "Both;" that is,

D = 0.2(D + 60)

5D = D + 60

4D = 60

D = 15

Substituting, we have:

100 = 15 + C + 60 + N

100 = 75 + C + N

25 = C + N

Since those who don't order dessert are the total of "Coffee only" and "Neither," we have 25% of the couples who don't order dessert.

Answer: B