2007 AMC 8 Problem 13
Attempt Problem 13 of the 2007 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
13.
Sets and shown in the Venn diagram, have the same number of elements. Their union has elements and their intersection has elements. Find the number of elements in
Answer: C
Small hint:
Let each set have elements.
Big hint:
Use .
Solution:
Let be the number of elements in each and Also let be the number of elements in their intersection.
The conditions give us that and Plugging into the first equation yields
Thus, C is the correct answer.
Problem 13 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
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