2014 AMC 8 Problem 2
Attempt Problem 2 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).
2.
Paul owes Paula cents and has a pocket full of -cent coins, -cent coins, and -cent coins that he can use to pay her. What is the difference between the largest and the smallest number of coins he can use to pay her?
Answer: E
Small hint:
Use the smallest coins to maximize the number of coins.
Big hint:
Use a quarter and a dime to minimize the number of coins.
Solution:
To use the largest number of coins, Paul would use only -cent coins, which gives coins.
To use the smallest number of coins, Paul would use a -cent coin and a -cent coin, for a total of coins. The difference is .
Thus, E is the correct answer.
Problem 2 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
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