2019 AMC 12A Problem 3
Attempt Problem 3 of the 2019 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 2019 AMC 12A solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
3.
A box contains red balls, green balls, yellow balls, blue balls, white balls, and black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least balls of a single color will be drawn?
Answer: B
Small hint:
Consider the worst case: draw as many as possible without ever reaching of one color
Big hint:
Take of each color that has at least and all balls of the smaller colors
Solution:
In the worst case, we draw each of red, green, and yellow, plus all of the blue white and black without reaching of any color.
That is balls.
The next ball must complete a set of so balls are needed.
Thus, the correct answer is B.
Problem 3 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
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- 1954 AMC 12
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