2021 AMC 12A Spring Problem 4
Attempt Problem 4 of the 2021 AMC 12A 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 12A Spring solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
4.
Tom has a collection of snakes, of which are purple and of which are happy. He observes that
• all of his happy snakes can add,
• none of his purple snakes can subtract, and
• all of his snakes that can’t subtract also can’t add.
Which of these conclusions can be drawn about Tom’s snakes?
Purple snakes can add.
Purple snakes are happy.
Snakes that can add are purple.
Happy snakes are not purple.
Happy snakes can’t subtract.
Answer: D
Small hint:
Chain the implications: purple can’t subtract can’t add
Big hint:
Happy snakes can add, but purple snakes cannot add; compare these two facts
Solution:
A purple snake cannot subtract, and any snake that cannot subtract also cannot add. So every purple snake cannot add.
Every happy snake can add. Since purple snakes cannot add, no happy snake can be purple; that is, happy snakes are not purple.
Thus, the correct answer is D.
Problem 4 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
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- 1998 AMC 12
- 1999 AMC 12
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- 2001 AMC 12
- 2002 AMC 12A
- 2002 AMC 12B
- 2003 AMC 12A
- 2003 AMC 12B
- 2004 AMC 12A
- 2004 AMC 12B
- 2005 AMC 12A
- 2005 AMC 12B
- 2006 AMC 12A
- 2006 AMC 12B
- 2007 AMC 12A
- 2007 AMC 12B
- 2008 AMC 12A
- 2008 AMC 12B
- 2009 AMC 12A
- 2009 AMC 12B
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- 2021 AMC 12B Spring
- 2021 AMC 12A Fall
- 2021 AMC 12B Fall
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