How Do You Solve Combination Problems for the GRE?

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SUMMARY

The discussion focuses on solving combination problems for the GRE, specifically a scenario involving an automotive manufacturer with parts A, B, and C installed in various cars. The user seeks to determine the total number of cars containing parts A or B, given specific conditions about overlaps. Key insights include the use of maximum and minimum calculations to find the total, with the maximum being the sum of cars with parts A and B (82 + 73) and the minimum calculated by considering overlaps (82 + 73 - 8). The suggestion to use a Venn diagram is also highlighted as a useful visual aid.

PREREQUISITES
  • Understanding of basic combinatorial principles
  • Familiarity with Venn diagrams for visualizing set relationships
  • Knowledge of GRE quantitative reasoning concepts
  • Ability to perform basic arithmetic operations and logical reasoning
NEXT STEPS
  • Study GRE quantitative reasoning practice problems focused on combinations
  • Learn how to effectively use Venn diagrams for solving set problems
  • Explore advanced combinatorial techniques and their applications
  • Review GRE test-taking strategies for time management on quantitative sections
USEFUL FOR

GRE test-takers, educators preparing students for standardized tests, and anyone looking to improve their problem-solving skills in combinatorial mathematics.

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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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?
 
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?
 
Can you construct a Venn diagram?
 

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