Math Help - Venn Diagrams

1. Venn Diagrams

A car dealer has 22 vehicles on his lot. If 8 of vehicles are vans and 6 of the vehicles are red, 10 vehicles are neither red nor vans. How many vans are red.

It tells me to make a Venn diagram. The answer to the question is 2. How did they get two? I do not think that I have enough information inorder to solve the problem or am I overthinking the problem? Any help would be great thanks.

2. Originally Posted by schinb64
A car dealer has 22 vehicles on his lot. If 8 of vehicles are vans and 6 of the vehicles are red, 10 vehicles are neither red nor vans. How many vans are red.

It tells me to make a Venn diagram. The answer to the question is 2. How did they get two? I do not think that I have enough information inorder to solve the problem or am I overthinking the problem? Any help would be great thanks.
If 10 vehicles are neither vans nor red, then there are 12 vehicles which are either a van, red, or both. So you have 8 vans and 6 red vehicles. If you add 8 and 6 you get 14. This would be the correct total of vehicles that are either a van, red, or both if there were no red vans. But since we know there are 12 vehicles in this category, that means in our previous count we must have counted two vehicles twice. Therefore, there are two red vans.

3. Hello, schinb64!

Did you sketch a Venn diagram?

A car dealer has 22 vehicles on his lot.
8 of vehicles are vans, and 6 of the vehicles are red,
10 vehicles are neither red nor vans.
How many vans are red. ?
Code:
      * - - - - - - - - - - - - - - - *
|                               |
|   * - - - - - - - *           |
|   | Vans          |           |
|   |       * - - - | - - - *   |
|   |       |       |       |   |
|   |       |       |       |   |
|   |       |       |       |   |
|   * - - - | - - - *       |   |
|           |           Red |   |
|  10       * - - - - - - - *   |
|                               |
* - - - - - - - - - - - - - - - *
We can reason it out . . .

There are 22 cars in the large rectangle.

There 10 which are neither red nor vans.
. . These are outside the two rings.
That leaves 12 cars to be inside the rings.

We are told that there are 8 cars in the Van ring and 6 cars in the Red ring.
. . But that would be a total of 14 cars inside the rings.

Hence, there must be an "overlap" of two cars.

Therefore, there are 2 cars which are both Vans and Red.