2006 AMC 8 Problem 11
Attempt Problem 11 of the 2006 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 2006 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
11.
How many two-digit numbers have digits whose sum is a perfect square?
Answer: C
Small hint:
The largest possible digit sum is .
Big hint:
Count the two-digit numbers whose digit sums are and .
Solution:
There is number whose digit sum is :
There are numbers whose digit sum is : and
There are numbers whose digit sum is : and
There are numbers whose digit sum is : and
Therefore, there are numbers that satisfy the problem statement.
Thus, C is the correct answer.
Problem 11 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
- 2007 AMC 8
- 2008 AMC 8
- 2009 AMC 8
- 2010 AMC 8
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- 2012 AMC 8
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- 2014 AMC 8
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