1987 AMC 8 Problem 17
Attempt Problem 17 of the 1987 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 1987 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
17.
Abby, Bret, Carl, and Dana are seated in a row of four seats numbered to Joe looks at them and says: “Bret is next to Carl.” “Abby is between Bret and Carl.” However, each one of Joe’s statements is false. Bret is actually sitting in seat Who is sitting in seat
Abby
Bret
Carl
Dana
There is not enough information to be sure
Answer: D
Small hint:
“Bret is next to Carl” is false, so Carl is not in seat or seat the only remaining seat for Carl is seat
Big hint:
Once Carl is in seat “Abby is between Bret and Carl” is false, so Abby cannot be in seat place Abby in the last open seat and see who is left
Solution:
Bret is in seat Since “Bret is next to Carl” is false, Carl is not in seat or seat so Carl must be in seat
The seat between Bret (seat ) and Carl (seat ) is seat Since “Abby is between Bret and Carl” is false, Abby is not in seat so Abby must be in seat
That leaves Dana in seat
Thus, the correct answer is D .
Problem 17 in other years
- 1985 AMC 8
- 1986 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
- 2010 AMC 8
- 2011 AMC 8
- 2012 AMC 8
- 2013 AMC 8
- 2014 AMC 8
- 2015 AMC 8
- 2016 AMC 8
- 2017 AMC 8
- 2018 AMC 8
- 2019 AMC 8
- 2020 AMC 8
- 2022 AMC 8
- 2023 AMC 8
- 2024 AMC 8
- 2025 AMC 8
- 2026 AMC 8