2019 AMC 8 Problem 23
Attempt Problem 23 of the 2019 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 2019 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
23.
After Euclid High School’s last basketball game, it was determined that of the team’s points were scored by Alexa and were scored by Brittany. Chelsea scored points. None of the other team members scored more than points. What was the total number of points scored by the other team members?
Answer: B
Small hint:
The total score must be a multiple of
Big hint:
The other seven players together scored at most
Video solution:
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Written solution:
Let be the total number of points and be the desired answer.
Then from the problem statement we get that
Simplifying yields
We know that since none of the team members scored more than points.
We also know that must be a multiple of If then we get that which is not allowed.
If then we have that which works.
The next possible total is which would give Every larger multiple of makes still larger, so is the only possible value.
Thus, the correct answer is B.
Problem 23 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
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