2024 AMC 12B Problem 3
Attempt Problem 3 of the 2024 AMC 12B 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 2024 AMC 12B solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
3.
For how many integer values of is
Answer: E
Small hint:
Rewrite as and estimate as a decimal
Big hint:
Since count the integers from to
Solution:
The inequality is equivalent to The integers satisfying this run from to which is values.
Thus, the correct answer is E.
Problem 3 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
- 1958 AMC 12
- 1959 AMC 12
- 1960 AMC 12
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- 1963 AMC 12
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- 1971 AMC 12
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- 1996 AMC 12
- 1997 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
- 2010 AMC 12A
- 2010 AMC 12B
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- 2011 AMC 12B
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- 2012 AMC 12B
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- 2013 AMC 12B
- 2014 AMC 12A
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- 2015 AMC 12A
- 2015 AMC 12B
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- 2016 AMC 12B
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- 2017 AMC 12B
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- 2018 AMC 12B
- 2019 AMC 12A
- 2019 AMC 12B
- 2020 AMC 12A
- 2020 AMC 12B
- 2021 AMC 12A Spring
- 2021 AMC 12B Spring
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- 2021 AMC 12B Fall
- 2022 AMC 12A
- 2022 AMC 12B
- 2023 AMC 12A
- 2023 AMC 12B
- 2024 AMC 12A
- 2025 AMC 12A
- 2025 AMC 12B