How Do You Solve Combination Problems for the GRE?

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In summary, the conversation discusses a problem involving an automotive manufacturer installing different parts into cars. The question asks for the total number of cars that contain either part A, part B, or both. The conversation also includes a request for advice on how to quickly solve this type of problem.
  • #1
greprep
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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? "
 
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  • #2
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?
 
  • #3
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?
 
  • #4
Can you construct a Venn diagram?
 

Related to How Do You Solve Combination Problems for the GRE?

1. What is the purpose of a combination question in scientific research?

A combination question is used to determine the effect of multiple variables on a single outcome in a scientific study. It allows researchers to understand the relationship between different factors and their impact on the results of an experiment or study.

2. How do scientists determine which variables to include in a combination question?

Scientists typically use prior research, theoretical frameworks, and statistical analyses to identify and select the most relevant variables to include in a combination question. They also consider the specific research question or hypothesis they are trying to test.

3. Can a combination question be used in all types of scientific studies?

Yes, a combination question can be used in various types of scientific studies, including experimental, observational, and correlational research. It is a useful tool for investigating relationships between different variables in any type of scientific study.

4. How do scientists analyze the results of a combination question?

Scientists typically use statistical analyses, such as regression or correlation, to analyze the results of a combination question. These analyses help determine the strength and direction of the relationships between variables and can provide insights into the underlying mechanisms at play.

5. Are there any limitations to using a combination question in scientific research?

While combination questions are a valuable tool in scientific research, they do have some limitations. For example, they may oversimplify complex relationships between variables, and the results may not be generalizable to all populations or contexts. Additionally, the validity of the results depends on the accuracy and reliability of the data collected.

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