MHB How Do You Solve Combination Problems for the GRE?

[greprep]

Hi, All! Prepping for the GRE here and definitely notice a weakness in calculating potential combination questions. Any advice on how to solve the following type of problem quickly?

"An automotive manufacturer installed part A into 82 cars, part B into 73 cars, and part C into 25 cars. At least one of the cars contains both parts A and B, and exactly 8 cars contain both parts B and C. None of the cars contains both A, B, and C.

What are the total number of cars that contain part A, part B, or both? "

 

[Greg]

Hello greprep and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?

 

[greprep]

Of course, thanks for your help.

I'm thinking that I would look for the max and min. Meaning, the maximum number of cars that have A or B are if there is no overlap, meaning 82 + 73. And the minimum, is if there is full overlap (excluding the fact that 8 have B and C), and we know that we can't have A, B, and C. Meaning, the minimum would be 82 + 73 - 8?

 

[Greg]

Can you construct a Venn diagram?