GMAT tricks can save you time, giving you added energy to focus on the really tough GMAT Questions. Watch this video to learn about the Double Matrix Method.
GMAT Tricks Using Double Matrix Method [Transcript]
In this video, we will examine a technique often referred to as the “double matrix method”. This technique can be used to solve questions involving population where each member of the population has two features associated with it. Now in this question, we have a population of vehicles and each vehicle has exactly two features. The two features are the vehicles’ color, red or green and the vehicles type, car or truck. Now we can also tackle these types of questions using Venn diagrams, but I believe that the double matrix method is particularly effective for solving upper level questions.
Here’s how the method works. We’re going to take each of the 80 vehicles and place them into 1 of the 4 boxes shown here. Now one of our two features is vehicle type. So in the two boxes in the top row, we’ll place cars and in the two boxes in the bottom row, we’ll place trucks. The other feature is color, so in the two boxes in the left hand column, we’ll places red vehicles and in the two boxes in the right hand column, we’ll place green vehicles.
Our ultimate goal will be to place each of our 80 vehicles in 1 of the 4 boxes depending on the vehicles’ characteristics. So in this box, we’ll place red cars. In this box, we’ll place green cars. In this box, we’ll place red trucks and in this box, we will place green trucks. Now the question asks us to find the number of red cars, so let’s add this asterisk in this box to remind us of our goal.
Alright, it’s time to start adding information. First we are told that 35 of the vehicles are red. Now some of those red vehicles will be red cars, and some of those red vehicles will be red trucks. At the moment, we do not have enough information to place any of the 35 red vehicles in either of the two boxes. However, since 35 of the vehicles are red, we know that the sum of these two boxes will be 35.
So let’s add this here. We now know that the numbers in the 2 yellow boxes must add to 35. Now, if there are 80 vehicles all together and 35 of them are red, then we can conclude that the remaining 45 vehicles must be green. Now some of these green vehicles will be green cars and some will be green trucks, so we cannot place any number into either of these two boxes. However, we do know that the sum of these 2 boxes must be 45.
Next we are told that 60 of the vehicles are cars. Now some of these 60 cars are red cars and some are green cars. So we can’t place any of the cars in either of the two individual boxes. However, we do know that the sum of these two boxes must be 60, since we have 60 cars all together. Now if there are 80 vehicles in the parking lot and 60 of them are cars, then the remaining 20 vehicles must be trucks. So the sum of these 2 boxes must be 20.
At this point, we don’t have any information about the number of vehicles to be placed in each of our four individual boxes. We only know the sums of the boxes in each row and each column. To fill in each box, we need a seed and here it is. We are told that there are nine green trucks. Since this box is reserved for green trucks, we can add nine to this box.
Now that we know the value of one box, we can complete the rest of the table. For example, we already know that the sum of these 2 boxes must be 20. Since 1 box is 9, the other must be 11. We also know that the sum of these two boxes must be 45, so the top box must be 36. Finally, we know that the sum of these 2 boxes must be 60 and since 1 box is 36, the other box must be 24.
So of the 80 vehicles in the parking lot, there are 36 green cars, 9 green trucks, 11 red trucks and 24 red cars. The question asks us to find the total number of red cars, so it’s 24. As you can see, this method is great for effectively organizing information and this will come in handy when you tackle more advanced questions.