2022 AMC 8 Problem 13
Attempt Problem 13 of the 2022 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 2022 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
13.
How many positive integers can fill the blank in the sentence below?
“One positive integer is ___ more than twice another, and the sum of the two numbers is ”
Answer: D
Small hint:
Let the smaller of the two positive integers be
Big hint:
If the blank is , the two numbers can be and
Solution:
Let the smaller number be , and let the blank be . Then the other number is , where both and are positive integers.
The sum condition gives , so . For to be positive, , so .
Thus can be any integer from through , giving possible values of the blank.
Thus, the correct answer is D.
Problem 13 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
- 2001 AMC 8
- 2002 AMC 8
- 2003 AMC 8
- 2004 AMC 8
- 2005 AMC 8
- 2006 AMC 8
- 2007 AMC 8
- 2008 AMC 8
- 2009 AMC 8
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- 2011 AMC 8
- 2012 AMC 8
- 2013 AMC 8
- 2014 AMC 8
- 2015 AMC 8
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- 2019 AMC 8
- 2020 AMC 8
- 2023 AMC 8
- 2024 AMC 8
- 2025 AMC 8
- 2026 AMC 8