2014 AMC 8 Problem 24
Attempt Problem 24 of the 2014 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 2014 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
24.
One day the Beverage Barn sold cans of soda to customers, and every customer bought at least one can of soda. What is the maximum possible median number of cans of soda bought per customer on that day?
Answer: C
Small hint:
The median is the average of the th and st ordered purchases.
Big hint:
Make the first purchases as small as possible.
Solution:
Order the purchases from least to greatest. The median is the average of the th and st entries. To maximize it, make the first entries as small as possible, so set them all equal to .
If the th entry were at least , then the total would be at least , too many cans. So the th entry is at most .
This maximum is attainable: use entries equal to , the th entry equal to , and the final entries equal to . The total is , and the median is .
Thus, C is the correct answer.
Problem 24 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
- 2010 AMC 8
- 2011 AMC 8
- 2012 AMC 8
- 2013 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