2021 AMC 12B Spring Problem 2
Attempt Problem 2 of the 2021 AMC 12B Spring 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 2021 AMC 12B Spring solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
2.
At a math contest, students are wearing blue shirts, and another students are wearing yellow shirts. The students are assigned into pairs. In exactly of these pairs, both students are wearing blue shirts. In how many pairs are both students wearing yellow shirts?
Answer: B
Small hint:
The all-blue pairs use blue students
Big hint:
Count the blue students left in mixed pairs, then remove that many yellow students
Solution:
The all-blue pairs account for blue students, leaving blue students.
Each of those blue students must be paired with a yellow student, so there are mixed pairs, using yellow students.
The remaining yellow students form all-yellow pairs.
Thus, the correct answer is B.
Problem 2 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
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- 2002 AMC 12A
- 2002 AMC 12B
- 2003 AMC 12A
- 2003 AMC 12B
- 2004 AMC 12A
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- 2005 AMC 12A
- 2005 AMC 12B
- 2006 AMC 12A
- 2006 AMC 12B
- 2007 AMC 12A
- 2007 AMC 12B
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- 2021 AMC 12A Spring
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