2019 AMC 12A Problem 2

Attempt Problem 2 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).

2.

Suppose aa is 150%150\% of b.b. What percent of aa is 3b?3b?
5050
662366\dfrac{2}{3}
150150
200200
450450
Answer: D
Concepts:percentageratio and proportion
Small hint:
Write a=1.5ba = 1.5b
Big hint:
Compute 3ba\dfrac{3b}{a} and convert to a percentage
Solution:
Since a=1.5b,a = 1.5b, we have 3ba=3b1.5b=2. \dfrac{3b}{a} = \dfrac{3b}{1.5b} = 2.
As a percentage, 3b3b is 200%200\% of a.a.
Thus, the correct answer is D.
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