2019 AMC 12A Problem 1

Attempt Problem 1 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.

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1.

The area of a pizza with radius 44 inches is NN percent larger than the area of a pizza with radius 33 inches. What is the integer closest to N?N?

2525

3333

4444

6666

7878

Answer: E
Concepts:circle areapercentage
Difficulty rating: 770
Solution:

The areas are proportional to the squares of the radii, so the ratio of the larger area to the smaller is 169.\dfrac{16}{9}.

The percent increase is (1691)×100=700977.8. \left(\dfrac{16}{9} - 1\right) \times 100 = \dfrac{700}{9} \approx 77.8. The closest integer is 78.78.

Thus, the correct answer is E.

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