The double matrix method can be used when you have a question that asks you to segment a population twice in two different ways. It can be a great alternative to Venn diagrams.
The following example walks you through the approach to a typical “double matrix” question.
A parking lot contains 80 vehicles. Each vehicle is either a car or a truck, and each vehicle is either red or green. 35 vehicles are red, and 60 vehicles are cars. If there are 9 green trucks, how many red cars are there?
The first step is recognizing that this question is a “double matrix” question. You have a population of vehicles that can be segmented twice in two ways each: (1) into cars and trucks and (2) into red and green. Note the following statement from the question:
Each vehicle is either a car or a truck, and each vehicle is either red or green.
Double matrix questions all take the following format:
Based on the segments in the question you can setup the following matrix:
Using the information in the question, fill in as much of the template as you can. For this question, you know the following:
- A parking lot contains 80 vehicles
- 35 vehicles are red
- 60 vehicles are cars
- There are 9 green trucks
Therefore you can create the following matrix:
Now you can begin filling in some additional information, such as total green vehicles and total trucks, using simple algebra.
35 red vehicles + # of green vehicles = 80
Subtract 35 from each side: # of green vehicles = 45
There are 45 green vehicles
Total trucks: 60 cars + # of trucks = 80
Subtract 60 from each side: # of trucks = 20
There are 20 trucks
You can now add the new findings into the matrix:
Again, with some more basic algebra you can complete more of the matrix.
# of red trucks + 9 green trucks = 20 trucks
Subtract 9 from each side: # of red trucks = 11
There are 11 red trucks
With one more step, you can calculate the number of red cars:
# of red cars + 11 red trucks = 35 red vehicles
Subtract 11 from each side: # of red trucks = 24
There are 24 red cars
Note that you can verify your answer by calculating the # of green cars, completing the matrix.
The final answer is B, 24.
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