2010 AMC 12A Problem 5
Attempt Problem 5 of the 2010 AMC 12A 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 2010 AMC 12A solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
5.
Halfway through a -shot archery tournament, Chelsea leads by points. For each shot a bullseye scores points, with other possible scores being and points. Chelsea always scores at least points on each shot. If Chelsea’s next shots are bullseyes she will be guaranteed victory. What is the minimum value for
Answer: C
Small hint:
Chelsea’s opponent can score at most points on each of the remaining shots
Big hint:
With bullseyes and at least points on the other shots, require
Solution:
The opponent can score at most on the last shots. Since Chelsea leads by she must score more than points on her remaining shots to guarantee victory.
Her bullseyes give points, and her other shots give at least points, so This simplifies to i.e.
Therefore Chelsea needs at least bullseyes.
Thus, C is the correct answer.
Problem 5 in other years
- 1950 AMC 12
- 1951 AMC 12
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