2013 AMC 8 Problem 19
Attempt Problem 19 of the 2013 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2013 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
Bridget, Cassie, and Hannah are discussing the results of their last math test. Hannah shows Bridget and Cassie her test, but Bridget and Cassie don’t show theirs to anyone. Cassie says, “I didn’t get the lowest score in our class,” and Bridget adds, “I didn’t get the highest score.” What is the ranking of the three girls from highest to lowest?
Hannah, Cassie, Bridget
Hannah, Bridget, Cassie
Cassie, Bridget, Hannah
Cassie, Hannah, Bridget
Bridget, Cassie, Hannah
Answer: D
Small hint:
Cassie can compare herself with Hannah because she sees Hannah’s test.
Big hint:
Cassie is above Hannah, while Bridget is below Hannah.
Video solution:
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Written solution:
Since Cassie deduced she didn’t get the lowest score, she must have got a higher score than Hannah. Similarly, Bridget’s statement reveals that she must have got a lower score than Hannah.
Therefore, the ranking from highest to lowest is Cassie, Hannah, and then Bridget.
Thus, D is the correct answer.
Problem 19 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
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