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?
(A) 11
(B) 24
(C) 28
(D) 36
(E) 45
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.
For more GMAT tips, be sure to visit the Beat The GMAT community. Also, on July 7, Beat The GMAT will be hosting a free online GMAT/MBA conference called Achieve Your Dreams: The GMAT, B-School, and Everything After. Click here to view the conference agenda and be sure to RSVP for Accepted.com’s essay workshop!
Read the full article: GMAT Math Tip – The Double Matrix Method